contents=  Submitted to the Proceedings of the US Community Study on the
Future of Particle Physics (Snowmass 2021) ,
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# Snowmass2021 Cosmic Frontier White Paper:
Observational Facilities to Study Dark Matter

Sukanya Chakrabarti  School of Physics and Astronomy, Rochester Institute of
Technology, 84 Lomb Memorial Drive, Rochester, NY 14623  Alex Drlica-Wagner
Fermi National Accelerator Laboratory, P. O. Box 500, Batavia, IL 60510, USA
Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL
60637, USA  Department of Astronomy and Astrophysics, University of Chicago,
Chicago, IL 60637, USA  Ting S. Li  Department of Astronomy and Astrophysics,
University of Toronto, 50 St. George Street, Toronto ON, M5S 3H4, Canada
Neelima Sehgal  Physics and Astronomy Department, Stony Brook University,
Stony Brook, NY 11794, USA  Joshua D. Simon  Observatories of the Carnegie
Institution for Science, Pasadena, USA, 91101  Simon Birrer  Kavli Institute
for Particle Astrophysics and Cosmology and Department of Physics, Stanford
University, Stanford, CA 94305, USA  SLAC National Accelerator Laboratory,
Menlo Park, CA, 94025, USA  Duncan A. Brown  Department of Physics, Syracuse
University, Syracuse, NY 13244, USA  Rebecca Bernstein  Observatories of the
Carnegie Institution for Science, Pasadena, USA, 91101  Alberto D. Bolatto
Department of Astronomy, University of Maryland, College Park, MD 20742, USA
Philip Chang  Department of Physics, University of Wisconsin-Milwaukee, 3135
North Maryland Avenue, Milwaukee, WI 53211, USA  Kyle Dawson  Department of
Physics and Astronomy, University of Utah, Salt Lake City, UT 84112, USA  Paul
Demorest  National Radio Astronomy Observatory, P.O. Box O, Socorro, NM 87801,
USA  Daniel Grin  Department of Physics and Astronomy, Haverford College, 370
Lancaster Avenue, Haverford, Pennsylvania 19041, United States  David L.
Kaplan  Department of Physics, University of Wisconsin-Milwaukee, Milwaukee,
WI 53201, USA  Joseph Lazio  Jet Propulsion Laboratory, California Institute
of Technology, Pasadena, CA 91106, USA  Jennifer Marshall  George P. and
Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, and
Department of Physics and Astronomy, Texas A&M University, College Station, TX
77843, USA  Eric J. Murphy  National Radio Astronomy Observatory, 520 Edgemont
Road, Charlottesville, VA 22903, USA  Scott Ransom  National Radio Astronomy
Observatory, 520 Edgemont Road, Charlottesville, VA 22903, USA  Brant E.
Robertson  Department of Astronomy and Astrophysics, University of California,
Santa Cruz, Santa Cruz, CA, 95060, USA  Rajeev Singh  Institute of Nuclear
Physics Polish Academy of Sciences, PL-31-342 Kraków, Poland  Anže Slosar
Physics Department, Brookhaven National Laboratory, Upton NY 11973  Tommaso
Treu  Department of Physics and Astronomy, University of California, Los
Angeles, CA 90095, USA  Yu-Dai Tsai  Department of Physics and Astronomy,
University of California, Irvine, CA 92697-4575, USA  Benjamin F. Williams
Astronomy Department, University of Washington, Seattle, WA 98195, USA

###### Abstract

We present an overview of future observational facilities that will
significantly enhance our understanding of the fundamental nature of dark
matter. These facilities span a range of observational techniques including
optical/near-infrared imaging and spectroscopy, measurements of the cosmic
microwave background, pulsar timing, 21-cm observations of neutral hydrogen at
high redshift, and the measurement of gravitational waves. Such facilities are
a critical component of a multi-pronged experimental program to uncover the
nature of dark matter, while often providing complementary measurements of
dark energy, neutrino physics, and inflation.

###### Contents

  1. I Executive Summary
  2. II Introduction
  3. III Dark Matter Measurements with Future Facilities
  4. IV Current and Near-Future Facilities Relevant to Dark Matter
    1. IV.1 CMB-S4
    2. IV.2 Dark Energy Survey (DES)
    3. IV.3 Dark Energy Spectroscopic Instrument (DESI)
    4. IV.4 Rubin Observatory LSST
    5. IV.5 James Webb Space Telescope
    6. IV.6 Nancy Grace Roman Space Telescope
    7. IV.7 Advanced LIGO
  5. V Future CMB Facilities
    1. V.1 Key Measurement Opportunities
    2. V.2 CMB-HD
  6. VI Future Pulsar Timing Facilities
    1. VI.1 Key Measurement Opportunities
    2. VI.2 ngVLA & DSA-2000
  7. VII Future 21cm Facilities
    1. VII.1 Key Measurement Opportunities
    2. VII.2 LuSEE-Night
    3. VII.3 PUMA
  8. VIII Future Optical Facilities
    1. VIII.1 Key Measurement Opportunities
    2. VIII.2 Extremely Large Telescopes
    3. VIII.3 Wide-field Multi-Object Spectroscopy Facilities
      1. VIII.3.1 DESI-II
      2. VIII.3.2 MegaMapper
      3. VIII.3.3 Maunakea Spectroscopic Explorer
      4. VIII.3.4 SpecTel
      5. VIII.3.5 Comparison and Summary
  9. IX Future Gravitational Wave Facilities
    1. IX.1 Key Measurement Opportunities
    2. IX.2 Cosmic Explorer and Einstein Telescope
    3. IX.3 LIGO Voyager
  10. X Conclusion

##  I Executive Summary

The fundamental nature of dark matter represents one of the most compelling
open questions in physics. Since the last Snowmass, the experimental program
to determine the nature of dark matter has expanded dramatically
(Battaglieri:2017, ). The space of viable dark matter models spans nearly 90
orders of magnitude in particle mass, ranging from ultra-light dark matter
($m\sim 10^{-21}$ eV) to primordial black holes ($m\sim 10^{68}$ eV). To date,
all of the positive, empirical measurements of dark matter (including the
aforementioned upper and lower bounds on the dark matter mass) have come from
astronomical and cosmological observations. Furthermore, the microphysical
properties of dark matter (e.g., particle mass, interaction cross section(s),
etc.) can be extracted from the macroscopic distribution and clustering of
dark matter. Over the next decade, observational facilities spanning the
electromagnetic spectrum, as well as gravitational waves, offer the potential
to significantly expand our understanding of dark matter physics. In this
white paper, we discuss the scientific motivation and technological
opportunities for observational facilities focused on improving our
understanding of dark matter.

This white paper complements other white papers devoted to the description of
multi-messenger facilities (Multimessenger-Snowmass, ), gamma-ray and X-ray
experiments (CF1-GammaExp-Snowmass, ; CF7-GammaExp-Snowmass, ), and
gravitational wave facilities (GWFacilities-Snowmass, ).

Key Opportunities

  1. 1.

Astrophysical and cosmological observations currently provide the only
positive, empirical measurements of dark matter. In the coming decade,
observational facilities spanning the electromagnetic spectrum and
gravitational waves present an opportunity to significantly advance our
understanding of dark matter.

  2. 2.

Proposed millimeter-wavelength facilities, such as CMB-HD, will extend the
resolution and sensitivity of cosmic microwave background surveys by factors
of five or more. These facilities can determine the number of light thermal
species in the universe, constrain interactions between dark matter and
standard model particles, and measure the matter power spectrum on small
scales using gravitational lensing of the microwave background radiation.

  3. 3.

Proposed centimeter-wavelength radio observatories, including the ngVLA and
DSA-2000, can employ pulsar timing measurements to map the dark matter halo of
the Milky Way and the sub-structures it contains.

  4. 4.

Proposed low-frequency radio experiments, such as LuSEE Night and PUMA, can
use the 21-cm line of hydrogen from the Dark Ages through cosmic reionization
to probe dark matter physics via the thermal history of intergalactic gas and
the timing of the formation of the first stars and galaxies.

  5. 5.

Proposed optical/near-infrared telescopes, including TMT, GMT, MegaMapper,
MSE, and SpecTel, can determine the dark matter halo mass function down to
$10^{6}$ M⊙ and improve sensitivity to the dark matter particle mass and
interaction cross-sections through observations of gravitational lenses,
nearby dwarf galaxies, stars, and stellar streams.

  6. 6.

Proposed gravitational wave facilities, such as Cosmic Explorer and LIGO-
Voyager, can be used to probe dark matter, including axion-like particles in
binary neutron star mergers, ultralight bosons through their interactions with
black holes or directly as boson stars, dark matter spikes around black holes,
and primordial black holes.

  7. 7.

Contributions to the technical development and construction of observational
dark matter facilities will leverage the core technical and scientific
capabilities of the HEP community. Furthermore, the involvement of the HEP
community will maximize the scientific output of these facilities.

  8. 8.

Many proposed dark matter facilities will also offer complementary
capabilities to explore dark energy, neutrino properties, and inflationary
physics. The capability to probe dark matter physics should be considered in
the design phase of these facilities.

##  II Introduction

Over the past 50 years, observational facilities funded by the DOE, NSF, NASA,
and their international counterparts have produced all of the positive
empirical measurements of the fundamental properties of dark matter.
Observational discoveries during this period include the first convincing
evidence that dark matter exists, determination of the cosmological abundance
of dark matter, measurements of dark matter halos spanning seven orders of
magnitude in mass, and measurements of the local dark matter mass distribution
within our own Galaxy. These observations have directly constrained the
fundamental microscopic properties of dark matter, such as the minimum dark
matter particle mass, the maximum allowed coupling to the Standard Model, and
the maximum strength of a wide range of interactions in the dark sector.
Despite this tremendous progress, the landscape of dark matter models remains
wide open, and more powerful observational facilities will be needed to narrow
the allowed parameter space for dark matter, and — with luck — conclusively
identify the nature of dark matter.

In the last two decades, the high energy physics (HEP) community has been
critically important to advances in astronomical facilities and instruments
used to study our universe. Development of new instrumentation and technology
has been driven by the ambitious goal of extracting fundamental physics from
cosmology. HEP scientists played a crucial role in the construction and
operation of the Sloan Digital Sky Survey (SDSS) in the late 1990s and early
2000s (York:2000, ). The HEP interest in SDSS was driven by the desire to
constrain the matter–energy density of the universe, building on the growing
connection between quarks and the cosmos (Kolb:1986, ; Quarks2Cosmos:2003, ).
In the subsequent years, HEP observational interests have shifted toward
understanding the accelerating expansion of the universe (dark energy). This
interest has motivated unprecedented projects such as the Baryon Oscillation
Spectroscopic Survey boss2013 , the Dark Energy Survey DES:2005 , the Dark
Energy Spectroscopic Instrument desi2016 , and the Vera C. Rubin Observatory
(Ivezic:2019, ). In the coming decade, the Stage IV ground-based cosmic
microwave background experiment CMB-S4 will explore inflationary physics and
probe the abundance of light relics in the early universe Abazajian:2019eic .
Each of these facilities has made (or will make) crucial contributions to our
understanding of dark matter physics.

This white paper focuses on future observational facilities that can be
designed and built in the next decade to measure the fundamental properties of
dark matter. For these facilities, we strongly recommend that dark matter
physics be included as a fundamental mission goal that guides design decisions
and helps sets design requirements. Although we briefly describe the
contributions of current and near-future facilities, we leave a more detailed
discussion of those projects to white papers from the scientific
collaborations associated with specific facilities. Furthermore, this white
paper is intended to complement other white papers devoted to the description
of multi-messenger facilities (Multimessenger-Snowmass, ), gamma-ray and X-ray
experiments (CF1-GammaExp-Snowmass, ; CF7-GammaExp-Snowmass, ), and
gravitational wave facilities (GWFacilities-Snowmass, ).

##  III Dark Matter Measurements with Future Facilities

Astrophysical observations have indicated for decades that our Universe
contains large amounts of matter that is not made of ordinary baryons. What
this dark matter consists of is one of the biggest unsolved questions in
cosmology and particle physics. Theorists have developed many possible dark
matter models, some of which are discussed in ref. CF7_smallscales , that
could have different astrophysical signatures in regimes that new facilities
are aiming to probe. For example, new technology developments are enabling
next-generation facilities to probe structure on smaller scales than possible
before, and advances in detector technology are enabling unprecedented
sensitivities. Below we outline the key measurement opportunities enabled by
next-generation facilities that will probe the properties and nature of dark
matter, as depicted in Figure 1. The proposed facilities that can make these
measurements are listed in Table 1.

Figure 1: Shown are the connections between various dark matter models, the
ways that those models affect the observable universe, and the proposed future
facilities that will be discussed in this white paper. Acronyms are: CDM: cold
dark matter; WDM: warm dark matter; FDM: fuzzy dark matter; SIDM: self-
interacting dark matter; WFMOS: wide-field multi-object spectroscopic survey
facilities; ELT: extremely large telescope; ngVLA: next-generation Very Large
Array; PUMA: Packed Ultrawideband Mapping Array; LuSEE Night: Lunar Surface
Electromagnetics Experiment Night; CMB-HD: Cosmic Microwave Background-High
Definition; LIGO/Cosmic Explorer: Laser Interferometer Gravitational-Wave
Observatory-Voyager and Cosmic Explorer.

Future Astrophysical Facilities for Dark Matter Science  Facility Type
Reference Section Cosmic Microwave Background-High Definition (CMB-HD) CMB
(mm) Sehgal:2019ewc  § V.2 next-generation Very Large Array (ngVLA) radio (mm-
cm) Selina2018  § VI.2 Deep Synoptic Array-2000 (DSA-2000) radio (cm)
Hallinan2019  § VI.2 Lunar Surface Electromagnetics Experiment (LuSEE) Night
21 cm (m) Burns2021  § VII.2 Packed Ultrawideband Mapping Array (PUMA) 21 cm
(cm) Slosar2019  § VII.3 Thirty Meter Telescope (TMT) optical/near-IR
Sanders2013  § VIII.2 Giant Magellan Telescope (GMT) optical/near-IR Johns2012
§ VIII.2 Dark Energy Spectroscopic Instrument II (DESI-II) optical
Levi2019BAAS  § VIII.3.1 MegaMapper optical schlegel19  § VIII.3.2 Maunakea
Spectroscopic Explorer (MSE) optical/near-IR MSE_book2018  § VIII.3.3 SpecTel
optical/near-IR SpecTel:2017  § VIII.3.4 Cosmic Explorer gravitational wave
Evans:2021gyd  § IX.2 LIGO Voyager gravitational wave LIGO:2020xsf  § IX.3

Table 1: Future astrophysical facilities for dark matter science.

The challenge currently facing the community is that the landscape of viable
dark matter models is vast, with relatively weak guidance provided by theory
as to which types of dark matter should be judged as “best” or “most likely to
exist.” In this situation, astronomical facilities offer unique opportunities
for constraining many of the particle properties of dark matter:

  * •

Dark matter particle mass. The mass ranges for many varieties of dark matter
models will be examined by future astronomical facilities. Optical telescopes
can place lower limits on the mass of a warm dark matter particle by measuring
the mass function of dark matter halos on subgalactic scales via gravitational
lensing or direct acceleration measurements (§ VIII.2) or heating of stellar
streams (§ VIII.3). Millimeter-wave CMB observations can be sensitive to warm
dark matter and other dark matter models that suppress the matter power
spectrum on galactic or sub-galactic scales through gravitational lensing of
the CMB; they will also probe axion-like particles over several orders of
magnitude of particle mass via multiple mechanisms (§ V). Future pulsar timing
facilities, including ngVLA and DSA-2000, will also be able to probe dark
matter sub-structure (§ VI).

  * •

Dark matter self-interaction cross-section. Interactions between dark matter
particles, either self-interactions or interactions among multiple species of
dark matter, can only be probed with astronomical measurements. These
interactions are most detectable via their impact on the dark matter density
at the centers of halos and the internal density structure of halos. Future
spectroscopic survey facilities (§ VIII.3) and extreme-precision radial
velocity observations enabled by the ELTs (§ VIII.2) are likely to have the
largest impact in this area.

  * •

Dark matter coupling to standard model particles. Coupling between dark matter
particles and ordinary matter can produce standard model particles such as
photons. These interactions can be imprinted in the light from the early
Universe in both the primordial CMB signal and in tracers of reionization and
intergalactic medium heating. These signals can be directly probed by
millimeter-wave CMB observations (§ V) and global 21 cm measurements of the
dark ages (§ VII). In addition, gravitational probes can indirectly constrain
dark matter coupling with standard model particles via its impact on structure
formation; these tests can be carried out using deep optical observations of
the local dwarf galaxy population (§ VIII.2), measurements of the structure
distribution on small scales via CMB lensing, optical strong lensing, and
direct acceleration measurements (§ V, § VIII.2, §VI), and the clumping of
stellar streams (§ VIII.3).

  * •

Dark sector properties. Many dark-sector models contain new light particles
that were once in thermal equilibrium with standard model particles. These
light particles have a signature imprinted in the early Universe characterized
by the effective number of relativistic species, $N_{\rm{eff}}$. This can be
probed by millimeter-wave CMB observations (§ V).

##  IV Current and Near-Future Facilities Relevant to Dark Matter

This white paper focuses on future facilities that could begin construction
and operation in the next decade. Readers whose primary interest is in those
facilities may wish to skip this section. However, it is useful to set the
context by briefly discussing current and near-future facilities that probe
dark matter physics. In particular, we note that although the US HEP budget
has supported some fraction of the construction and operation for many of
these facilities, no funding has been provided for dark matter science effort.
Funding to carry out dark matter science with current facilities will be
critical for developing the technical and scientific expertise needed for the
future experiments that are the focus of this white paper.

###  IV.1 CMB-S4

CMB-S4 is a next-generation CMB experiment that received strong support from
the Astro2020 Decadal Survey and has achieved CD-0 within the DOE. The CMB-S4
science reach for constraining dark matter and light relics is discussed
extensively elsewhere (CMB-S4:2016, ), and we leave a further discussion in
the context of Snowmass to a white paper from the CMB-S4 Collaboration
(CMB-S4-Snowmass, ). CMB-S4 will develop critical technical and scientific
expertise for future CMB experiments with the potential to constrain dark
matter and inflation.

###  IV.2 Dark Energy Survey (DES)

The Dark Energy Survey (DES) is a DOE-funded Stage III dark energy experiment
using the 4-m Blanco Telescope in Chile. DES has delivered impactful
measurements of dark matter physics at low and high redshift (Bechtol:2015, ;
Koposov:2015, ; Drlica-Wagner:2015b, ; Drlica-Wagner:2015, ; Chen:2021, ). In
particular, Milky Way satellite galaxies discovered by DES have enabled strong
constraints on the allowed particle mass ranges for thermal relic dark matter
and fuzzy dark matter, as well as the dark matter-proton scattering cross
section (Nadler:2021, ). However, funding for DES from the US HEP community
has focused solely on the dark energy mission objectives. DES is now in the
final analysis stages, and thus is not a topic for the current Snowmass
process, but we note that it has been critical for developing scientific
expertise for dark matter physics with the upcoming Rubin Observatory.

###  IV.3 Dark Energy Spectroscopic Instrument (DESI)

The Dark Energy Spectroscopic Instrument (DESI) is a Stage IV dark energy
instrument located on the 4-meter Mayall Telescope at Kitt Peak National
Observatory. Full survey operations began in 2021 and are supported by the DOE
Office of Science. The primary goal of DESI is to constrain the properties of
dark energy using baryon acoustic oscillations observed in the three-
dimensional clustering of galaxies, quasars, and the Ly-$\alpha$ forest.
Although DESI was designed specifically as a dark energy experiment, it
presents many avenues for studying dark matter through spectroscopic
observations of the nearby and distant Universe. For more information, we
direct the interested reader to the white paper contributed by the DESI
Collaboration (DESI-Snowmass, ). We note that dark matter science with DESI is
currently unfunded by the US HEP program, but that developing expertise in
DESI is extremely relevant to the future dark matter facilities discussed in
this paper (see § VIII.3).

###  IV.4 Rubin Observatory LSST

Originally conceived as the “Dark Matter Telescope” (Tyson:2001, ), the Vera
C. Rubin Observatory Legacy Survey of Space and Time (LSST) provides extensive
opportunities as a dark matter facility through observations of gravitational
lenses, stars, stellar streams, dwarf galaxies, and large-scale structure
(Drlica-Wagner:2019, ). Telescopes such as the Rubin Observatory will also
discover a factor of five more Solar System minor objects, which can help
constrain the dark matter abundance and ultralight dark matter effects through
measurements of their precessions 2020arXiv200907653V ; Pitjev:2013 ;
Poddar:2020exe ; Tsai:2021irw . Since the Rubin Observatory is already under
construction, we do not to discuss it extensively in this white paper.
However, we do emphasize that dark matter science with the Rubin Observatory
is currently not funded by the US HEP program. Funding for dark matter science
with Rubin will be critical for developing the scientific expertise to
maximize the impact of future dark matter facilities. We leave further
discussion of this issue to a white paper from the Dark Matter Working Group
within the LSST Dark Energy Science Collaboration (DESC-Snowmass, ).

It is worth mentioning that LSST is funded as a 10-year survey program, which
is currently scheduled to end in 2034. The Rubin Observatory as a facility
will certainly retain great utility for dark matter science even with 10 years
of data in hand. As of now, no specific plans have been made for the use of
the Rubin facility beyond that time horizon. However, given the capabilities
of the telescope, either as constructed or with possible additional upgrades,
we encourage the community to develop concepts for future probes of dark
matter with the Rubin Observatory. In particular, we note that operation of
the Rubin Observatory beyond its first 10 years offers the potential for
increased synergy with ELTs, which may not be completed before the end of the
LSST survey. The future of the Rubin Observatory is discussed in more detail
in another white paper Rubin-II-Snowmass .

###  IV.5 James Webb Space Telescope

The James Webb Space Telescope (JWST) affords several key measurement
opportunities to constrain dark matter properties. High-redshift observations
by JWST could provide constraints on the nature of dark matter based on the
abundance of the smallest galaxies (Schultz2014, ; Dayal2015, ; Khimey2021, ).
Much of this work has focused on articulating differences in early structure
formation between warm dark matter and cold dark matter cosmologies. The
dependence on baryonic processes has also been investigated, though there are
still significant uncertainties in modeling baryonic processes in galaxies
(Khimey2021, ; Rudakovskyi2021, ). JWST can also contribute significantly to
measurements of flux ratio anomalies in gravitationally lensed quasars (see §
VIII.2), which are sensitive to the dark matter halo mass function, because of
its high angular resolution and sensitivity at mid-infrared wavelengths. A
complementary route to constrain the nature of dark matter with JWST can also
be realized by measuring the accelerations of stars within the Milky Way. The
Kepler mission observed eclipsing binaries (Southworth2015, ; Windemuth2019, )
so precisely that the shift in the eclipse mid-point time induced by the
Galactic potential in the intervening decade is in principle measurable today
with JWST (ChakrabartiET, ). Although the shift in the eclipse mid-point
induced by the Galactic potential is very small, $\sim$ 0.1 seconds, space-
based missions that afford exquisite photometric and timing precision for
eclipsing binary stars can detect it with sources for which other dynamical
effects are sub-dominant to the Galactic signal. For the sample of $\sim 200$
eclipsing binaries for which Kepler established a very precise baseline a
decade earlier, JWST can in principle now provide a new route for direct
acceleration measurements and constraints on dark matter sub-structure
ChakrabartiET .

###  IV.6 Nancy Grace Roman Space Telescope

The _Nancy Grace Roman Space Telescope_ (RST) is a 2.4 m space telescope
scheduled to be launched in the mid-2020s by NASA (spergel2015a, ;
akeson2019a, ). RST will have spatial resolution comparable to the _Hubble
Space Telescope_ , but a $>$100$\times$ larger field of view and higher
sensitivity in the near infrared, providing a large increase in survey
capabilities. RST will undertake an ambitious set of mission surveys including
a large-area cosmology survey ($\sim 2000~{}\mathrm{deg}^{2}$) with multiband
imaging ($H\sim 26.7$ AB magnitude limit) and slitless grism spectroscopy
($\sim 10^{-16}~{}\mathrm{erg}~{}\mathrm{s}^{-1}~{}\mathrm{cm}^{-2}$ line
sensitivity at $\lambda\sim 1.5$ $\mu$m).

The cosmology mission surveys are designed to constrain structure formation
and the expansion history of the Universe through weak lensing and baryon
acoustic oscillations. However, RST will also make significant contributions
to measuring the dark matter halo mass function through strong gravitational
lensing. RST and the Rubin Observatory will be the best sources of lensed
quasars; Ref. oguri2010a  predicted that the RST cosmology survey would
increase the sample of quadruply-imaged lenses by more than a factor of twenty
to $\sim 1000$ objects. As described in § VIII.2, diffraction-limited imaging
and spectroscopy of large samples of lenses with ELTs will provide one of the
best avenues for pushing mass function measurements to unprecedentedly low
masses.

In addition, RST will be able to map the resolved stellar halos for hundreds
of galaxies within $\sim$10 Mpc, improving current sample sizes by two orders
of magnitude. These maps of the debris that remains after $\sim 13$ Gyr of
galaxy accretion and disruption will reveal significant samples of tidal
streams (hendel2019, ; pearson2019, ) that can be used to constrain the
existence of low mass dark matter halos (banik2019, ). Within the Milky Way,
RST can enable even more precise measurements of accelerations by measuring
the shift in the eclipse mid-point time (ChakrabartiET, ) since the Kepler
mission to provide unprecedented constraints on dark matter sub-structure.
While these measurements are possible today with HST and JWST, like all
acceleration measurements their precision improves significantly with time,
and in this case quadratically with time. Thus, RST observations a decade in
the future will significantly improve the constraints on dark matter sub-
structure that are possible today with very precise observations of
exquisitely timed eclipsing binary stars.

###  IV.7 Advanced LIGO

The gravitational-wave discoveries made by NSF-funded Advanced LIGO detectors
and the French-Italian Advanced Virgo detector have revolutionized our view of
the universe LIGOScientific:2016aoc ; LIGOScientific:2017vwq . The LIGO and
Virgo observatories have continued to increase their reach and discovery rate,
revealing populations of astrophysical events and routinely issuing alerts to
the broader astronomical community. At its 2020 sensitivity, this network was
reporting observations of tens of black hole mergers and of order one merger
involving a neutron star per year LIGOScientific:2021djp ;
LIGOScientific:2021psn . In the next few years, the Advanced LIGO and Virgo
detectors will continue to observe together, and will be joined by the
Japanese KAGRA observatory and by a LIGO detector located in India
KAGRA:2013rdx . An upgrade to the Advanced LIGO detectors, known as A$+$, is
currently under development and is expected improve the detector’s sensitivity
by 50% Shoemaker:2019bqt ; Miller:2014kma . These gravitational-wave
observatories are exploring the nature of dark matter both directly
LIGOScientific:2021odm ; LIGOScientific:2021job ; Nitz:2022ltl , by the
imprint of dark matter on the gravitational-wave signal from merging black
holes and neutron stars Zhang:2021mks , and by the effect of dark matter on
the masses and spins of observed black holes Ng:2020ruv ; Ziegler:2020klg .

##  V Future CMB Facilities

###  V.1 Key Measurement Opportunities

To date, some of the most compelling evidence for the existence of non-
baryonic dark matter comes from measurements of the Cosmic Microwave
Background (CMB) temperature and polarization power spectra, which map the
gravitational interplay between dark and baryonic matter in the early
Universe. Mature CMB facilities have allowed us to obtain tight constraints on
models of dark matter through the CMB power spectra Madhavacheril:2013cna ;
Planck:2018vyg , birefringence Namikawa:2020:ACT-biref ; Bianchini:2020:SPT-
biref , polarization oscillation Fedderke:2019ajk ; BICEPKeck:2020hhe ;
BICEPKeck:2021sbt , and lensing measurements Hlozek:2016lzm ; Hlozek:2017zzf ;
Li:2018zdm . Continuing this tremendous progress, future CMB measurements have
vast potential to constrain or detect dark matter particle properties by
exploiting the novel regime that a lower-noise, higher-resolution CMB facility
will open. Some of the key measurements anticipated from such a new facility
include:

  1. 1.

CMB Lensing on Small Scales. Increasing the resolution and lowering the noise
of CMB surveys by at least a factor of five compared to precursor surveys
would enable the measurement of the small-scale matter power spectrum on
scales of $k\sim 10~{}h$Mpc-1 from weak gravitational lensing using the CMB as
a backlight. A measurement that would distinguish between the matter power
spectrum predicted by cold dark matter (CDM) and that predicted by models that
can explain observational puzzles of small-scale structure, with at least
$5\sigma$ significance, requires instrument noise levels in temperature of 0.5
$\mu$K-arcmin over half the sky and a resolution of $\sim 15$ arcseconds
Han:2021vtm ; Sehgal:2019nmk ; Sehgal:2019ewc  (see left panel of Figure 2).
Such a measurement would result in a high-resolution map of the projected dark
matter distribution over half the sky. The CMB-S4 under construction and
precursor CMB experiements can only reach $k\sim 1\,h$ Mpc-1 given their
sensitivity and noise levels. Using gravitational lensing to measure the
matter power spectrum on these scales removes the uncertainty inherent in
relying on baryonic tracers of the matter distribution. The advantages of
using the CMB as a backlight to measure gravitational lensing is that 1) it is
at a well-defined redshift, 2) it has well-known intrinsic properties, and 3)
it is behind all collapsed dark matter structure. This measurement of small-
scale CMB lensing would constrain ultra-light axions (with $m_{a}\simeq
10^{-22}~{}{\rm eV})$, warm dark matter (with $m_{\nu}\simeq 2~{}{\rm keV}$),
self-interacting dark matter, and any other dark matter model that alters the
matter power spectrum on scales of $k\sim 10\,h$ Mpc-1 Markovic:2013iza ;
Hlozek:2016lzm ; Hlozek:2017zzf ; Nguyen:2017zqu ; Li:2018zdm ; Sehgal:2019nmk
; Sehgal:2019ewc . If the dark sector has multiple components, these
measurements could also determine the energy density in a hypothetical sub-
dominant component that affects CMB weak lensing, such as structure
suppression from ultra-light axions with $10^{-27}~{}{\rm eV}\lesssim
m_{a}\lesssim 10^{-23}~{}{\rm eV}$. A challenge facing the interpretation of
the small-scale dark matter distribution is the degeneracy between suppression
of structure due to baryonic effects and suppression due to alternative models
of dark matter. An advantage of measuring the full shape of the CMB lensing
power spectrum is that the shape information can potentially be used to
distinguish between baryonic effects and dark matter models since each impacts
the shape in significantly different ways Nguyen:2017zqu .

  2. 2.

Number of Light Particle Species. A CMB survey with lower noise levels would
also enable measurements of the number of light particle species,
$N_{\rm{eff}}$, that were in thermal equilibrium with the known standard-model
particles at any time in the early Universe, with a $1\sigma$ uncertainty of
$\sigma({N_{\rm{eff}}})=0.014$. This accuracy would cross the critical
threshold of 0.027, which is the amount that any new thermal particle species
changes $N_{\rm{eff}}$ away from its Standard Model value of 3.04. In
contrast, the expected target of CMB-S4 is $\sigma({N_{\rm{eff}}})=0.03$
Abazajian:2019eic . Achieving $\sigma({N_{\rm{eff}}})=0.014$ would rule out or
find evidence for new light thermal particles with at least $95\%$ confidence,
and is possible with instrument noise levels of 0.5 $\mu$K-arcmin over half
the sky if the measurements are made at high enough angular resolution ($\sim
15$ arcseconds) to remove contaminating foregrounds Sehgal:2019nmk ;
Sehgal:2019ewc  (see right panel of Figure 2). Such a measurement is
important, since many dark-sector models predict additional new light thermal
particle species Baumann:2015rya ; Boehm:2013jpa .

  3. 3.

CMB Photon Conversion to Axion-like Particles. CMB surveys can also constrain
or discover axion-like particles by observing the resonant conversion of CMB
photons into axion-like particles in the magnetic fields of galaxy clusters.
Nearly massless pseudoscalar bosons, often generically called axion-like
particles, appear in many extensions of the standard model PhysRevLett.38.1440
; Weinberg:1977ma ; PhysRevLett.40.279 ; Svrcek:2006yi ; Arvanitaki:2009fg ;
Acharya:2010zx . A detection of such particles would have major implications
both for particle physics and for cosmology, not least because axion-like
particles are also a well-motivated dark matter candidate. A CMB experiment
with 0.5 $\mu$K-arcmin over half the sky and $\sim 15$ arcsecond resolution
would provide a world-leading probe of the electromagnetic interaction between
axion-like particles and photons using the resonant conversion of CMB photons
and axion-like particles Raffelt:1996wa ; Mukherjee:2018oeb  in the magnetic
field of galaxy clusters Mukherjee:2019dsu . It would explore the mass range
of $10^{-13}$ eV $<m_{a}\lesssim 2\times 10^{-12}$ eV and improve the
constraint on the axion coupling constant by over two orders of magnitude over
current particle physics constraints to $g_{a\gamma}<0.1\times 10^{-12}$
GeV-1. These ranges are unexplored to date and are complementary with other
cosmological searches for the imprints of axion-like particles on the cosmic
density field.

  4. 4.

Time-dependent CMB Polarization Rotation. Another feature of CMB surveys is
that they can constrain or discover axion-like dark matter by measuring time-
dependent CMB polarization rotation. Ultralight axion-like dark-matter fields
that couple to photons via $g_{a\gamma}$ cause a time-dependent photon
birefringence effect which manifests as a temporal oscillation of the local
CMB polarization angle (i.e., a local $Q\leftrightarrow U$ oscillation in
time) Fedderke:2019ajk . This rotation effect is in-phase across the entire
sky, and the oscillation period is fixed by the axion-like particle mass to be
at observable timescales of $\sim$months to $\sim$hours for masses in the
range $10^{-21}\,\textrm{eV}\lesssim m_{a}\lesssim 10^{-18}\,\textrm{eV}$.
Searches for this effect are not limited by cosmic variance since it is a
time-dependent oscillation of the _observed_ CMB polarization pattern.
Improvements in the polarization map-depth and sky coverage achieved by
reaching noise levels of 0.7 $\mu$K-arcmin in polarization over half the sky
promise improvements for this search by a couple of orders of magnitude in the
coupling $g_{a\gamma}$ as compared to existing BICEP/Keck analyses
BICEPKeck:2020hhe ; BICEPKeck:2021sbt , and exceed the CMB-S4 projected reach
by a factor of $\mathcal{O}(2)$.

  5. 5.

Cosmic Birefringence. The novel low-noise regime of future CMB surveys can
enable world-leading constraints on beyond standard model physics. In
particular, such surveys enable measurements of isotropic birefringence and
the scale-invariant birefringence power spectrum to test for new physics by
searching for a rotation of linear polarization as the CMB photons propagate
to us from the surface of last scattering. This polarization rotation, called
cosmic birefringence, can be used to constrain very light axion-like particles
of $m_{a}\lesssim 10^{-28}$ eV Harari:1992:axion ; Carroll:1998 ; Li:2008 ;
Pospelov:2009 ; Capparelli:2019:CB , the axion string network
Agrawal:2019:biref , axion dark matter Liu:2016dcg , general Lorentz-violating
physics in the context of Standard Model extensions Leon:2017 , and primordial
magnetic fields through Faraday rotation Kosowsky:1996 ; Harari:1997 ;
Kosowsky:2004:FR . Achieving 0.7 $\mu$K-arcmin in polarization over half the
sky will result in $1\sigma$ uncertainties of 0.035 arcmin and $1.4\times
10^{-6}$ deg2, for isotropic birefringence and the scale-invariant
birefringence power spectrum, respectively. This will improve statistical
uncertainties on birefringence measurements by several orders of magnitude
over the existing constraints Planck:2016soo ; Choi:2020ccd ;
Minami:2020:biref ; Namikawa:2020:ACT-biref ; Bianchini:2020:SPT-biref ;
Mandal:2022tqu .

###  V.2 CMB-HD

Figure 2: Left: CMB-HD would generate via gravitational lensing a high-
resolution map, out to $k\sim 10~{}h$Mpc-1, of the projected dark matter
distribution over half the sky. Shown is the CMB lensing power spectrum for an
$m\sim 10^{-22}$ eV FDM model and a CDM model. Error bars correspond to CMB-HD
expectations of 0.5 $\mu$K-arcmin noise in temperature and 15 arcsecond
resolution over $50\%$ of the sky. Right: CMB-HD can achieve
$\sigma({N_{\rm{eff}}})=0.014$, which would cross the critical threshold of
0.027, ruling out or finding evidence for new light thermal particles, at any
time in the early Universe, with at least $95\%$ confidence. Original figure
from Green:2019glg ; Wallisch:2018rzj ; modified with addition of CMB-HD
forecast.

CMB-HD is an ambitious leap beyond previous (e.g., SPT-3G, ACT) and upcoming
(e.g., Simons Observatory, South Pole Observatory, CMB-S4) ground-based
millimeter-wave experiments. CMB-HD consists of two new 30-meter-class off-
axis crossed Dragone telescopes to be located at Cerro Toco in the Atacama
Desert. Each telescope would host 800,000 detectors (200,000 pixels), for a
total of 1.6 million detectors. The CMB-HD survey would cover half the sky
($\sim$20,000 deg2) over 7.5 years. These observations would result in an
ultra-deep, high-resolution millimeter-wave map with 0.5 $\mu$K-arcmin
instrument noise in temperature (0.7 $\mu$K-arcmin in polarization) in
combined 90 and 150 GHz channels and 15-arcsecond resolution at 150 GHz. For
comparison, this survey would have three times lower noise and six times
higher resolution than the CMB-S4 experiment Abazajian:2019eic , opening a
qualitatively new regime of millimeter-wave science. CMB-HD would also observe
at seven different frequencies between 30 and 350 GHz to mitigate foreground
contamination.

Recently, the Astro2020 Decadal Survey report expressed strong support for CMB
science in general, and indicated that it had a long future horizon of science
to offer. CMB-HD would cross important thresholds and provide definitive
answers to many fundamental physics questions, including the nature of dark
matter, the light particle content of the Universe, the existence and
mechanism of inflation, and whether there is new physics in the early Universe
beyond the Standard Model, as suggested by recent H0 measurements
Riess:2021jrx . A summary of the key science goals motivating the CMB-HD
survey and the flowdown to measurement and instrument requirements are given
in the Astro2020 Science White Paper Sehgal:2019nmk , Astro2020 CMB-HD APC
Sehgal:2019ewc , Astro2020 CMB-HD RFI Sehgal:2020yja , and the Snowmass2021
CMB-HD White Paper CMB-HD-Snowmass . In addition, further information can be
found at https://cmb-hd.org.

##  VI Future Pulsar Timing Facilities

###  VI.1 Key Measurement Opportunities

The accelerations of stars provide the most direct window into the mass
distributions of galaxies. The motions of stars trace the distribution of
gravitating matter and can be used to measure both the smooth and clumpy
distribution of dark matter. For more than a century, these accelerations have
been _estimated_ by measuring the positions and velocities of stars (Oort1932,
; Kuijken_Gilmore1989, ; Bovy_Tremaine2012, ; McKee2015, ; Schutz2018, ). Such
analyses assume equilibrium in order to relate the phase-space distribution of
stars to the potential. The large-scale potential is then described by
parameters like the average mid-plane density (also known as the Oort limit),
the local dark matter density (essential for interpreting direct detection
experiments), the shape of the Galactic potential, and the slope of the
rotation curve. However, observations of the gas and the stellar disk show
that our Galaxy has had a highly dynamic history (LevineBlitzHeiles2006, ;
Xu2015, ; antoja2018, ; Helmi2018, ; Belokurov2018, ). In such a time-
dependent potential, direct measurement of accelerations can capture the
complexity of the time-dependent Galactic mass distribution, including both
the dark matter and stellar contributions, without making any of the
assumptions of equilibrium or symmetry that are inherent in kinematic
analyses. Simulations of interacting galaxies find differences in the _true_
density in the simulation relative to what is _estimated_ from the Jeans
analysis by up to a factor of $\sim 2$ in the solar neighborhood (Haines2019,
), which shows that the assumption of equilibrium for a time-dependent
potential like that of the Milky Way does not produce accurate results in
characterizing the mass density of the Galaxy, or other fundamental Galactic
parameters. Using the Poisson equation,
$\nabla^{2}\Phi=-\nabla\cdot\vec{a}=4\pi G\rho$, acceleration measurements can
be straightforwardly related to the Galactic potential, $\Phi$, and the mass
density, $\rho$, without assumptions.

Stellar accelerations in the Milky Way are small (of order $\sim 10$ cm s-1
over a decade, or about $\sim 3\times 10^{-8}~{}\rm cm~{}s^{-2}$, for stars
within $\sim$ a few kpc of the Sun), but these measurements have recently
become possible with analyses of compiled pulsar timing observations
(Chakrabarti2021, ). Ref. Chakrabarti2021  used the observed time-rate of
change of the binary period, $\dot{P}_{b}$, of fourteen binary millisecond
pulsars to derive the Galactic acceleration. The best-timed pulsars have an
extent of $\sim 1$ kpc in radius and vertical height relative to the Sun, and
therefore provide a more significant constraint in the smaller dimension,
i.e., the vertical dimension. Given the pulsar accelerations, the Oort limit
was measured to 3$\sigma$ significance. The local dark matter density
determined from pulsar timing currently has large errors, but should improve
significantly with future pulsar timing facilities. The shape of the Galactic
potential traced by the pulsars was also tightly constrained, and resembles a
disk rather than a spherical halo (Chakrabarti2021, ). These observations thus
far come from current radio facilities, including the North American Nanohertz
Observatory for Gravitational Waves (NANOGrav) Nano2018 , the European Pulsar
Timing Array (EPTA) (EPTA2016, ), and the Parkes Pulsar Timing Array (PPTA)
PPTA .

Future radio telescopes like ngVLA and DSA-2000 will enable more sensitive
pulsar timing observations that have the potential to carry out precise
measurements out to larger distances in the Galaxy. In addition, these data
will constrain dark matter sub-structure down to $\sim 10^{6}$ M⊙, and could
thereby eliminate competing dark matter models. These facilities will benefit
from both improvements in increased sensitivity and longer time baseline
observations. Very roughly (i.e., for a homogeneous dataset), the improvement
in precision for $\dot{P}_{b}\propto t^{-5/2}SNR^{-1}$ (LorimerKramer2012, ).
The primary limiting factor for acceleration measurements presently (and
derived properties such as the local dark matter density) is the precision of
the observed $\dot{P}_{b}$ and parallaxes as determined from pulsar timing.
These measurements will improve significantly as noted above for a homogeneous
dataset, although in practice how well different components of the
acceleration are recovered will depend on the distribution of sources. The
point-source sensitivity for ngVLA is expected to be about ten times better
than that of VLA or GBT (Selina2018, ). Observations enabled by ngVLA are
expected to reach sufficient precision for the best-timed pulsars to produce
acceleration measurements out to the Magellanic Clouds, and possibly beyond
(Nanograv, ). Fluctuations in the gravitational potential along the line of
sight to radio pulsars, such as might arise from clumps of dark matter or
primordial black holes, can be discerned by correlating or comparing different
lines of sight. ngVLA would deliver higher precision pulsar timing by virtue
of its higher sensitivity than existing telescopes, particularly at higher
frequencies ($\sim$ 3 GHz), which are used to mitigate systematic effects due
to the propagation through the Galaxy’s interstellar medium.

Techniques to characterize dark matter using pulsar timing observations are
reviewed in Ref. (BurkeSpolaor2019, ), and include the possible detection of
very small-scale dark matter clumps from the Doppler delay due to the
acceleration of a pulsar (or the Earth) from an intervening compact dark
matter clump. The Square Kilometer Array (SKA) is expected to provide
sensitivities to $\sim 10^{-9}$ M⊙ compact sub-halos, assuming concentrations
of $c\sim 10^{8}$ and extremely close passages, of order $\sim 10^{-3}~{}\rm
pc$ (Dror2019, ). This work was later generalized to a passing ensemble of
sub-halos (Ramani2020, ). One potential caveat in determining accelerations
from spin periods arises from the well-known degeneracy between the observed
spin-down of a pulsar and magnetic braking (LorimerKramer2012, ). An
especially interesting constraint on the nature of dark matter that can
realized by next-generation pulsar timing facilities is the detection of
periodic variations in the pulse arrival times, as would be produced by
ultralight scalar field dark matter which leads to an oscillating
gravitational potential at nanohertz frequencies. The Parkes Pulsar Timing
Array searched for this signal but did not find a statistically significant
detection (Porayko2018, ); future facilities should improve these searches in
the regime of astrophysically allowed masses ($\gtrsim 10^{-22}~{}\rm eV$).

###  VI.2 ngVLA & DSA-2000

The next-generation Very Large Array (ngVLA) is an interferometric array that
will provide an order-of-magnitude improvement in sensitivity relative to the
Jansky VLA and ALMA operating at the same wavelengths, as well as factor of 30
increase in baselines, yielding milliarcsecond resolution (Selina2018, ). The
ngVLA operates at frequencies of 1.2 GHz (25 cm) to 116 GHz (2.6 mm), building
on the legacy of the Jansky VLA, ALMA and the VLBA as the next major national
facility in ground-based radio astronomy (Selina2018, ). This proposed radio
interferometer is optimized to bridge the gap between ALMA at wavelengths of 2
mm and shorter, and the future Square Kilometer Array (SKA) at decimeter to
meter wavelengths. The ngVLA opens a new window on the Universe through ultra-
sensitive imaging of thermal line and continuum emission down to
milliarcsecond resolution, while also delivering unprecedented broadband
continuum imaging and polarimetry of non-thermal emission.

The ngVLA will comprise an array of 214 antennas, each 18 m in diameter,
supplemented with a short baseline array of 19 smaller 6 m-diameter antennas,
to deliver the shortest baselines (largest structures on the sky). Each fixed
antenna is outfitted with receivers spanning the frequency range 1.2–50.5 GHz
(25 cm–5.9 mm) and 70–-116 GHz (4.3 mm–2.6 mm). The array achieves high
surface brightness sensitivity and high-fidelity imaging on angular scales
down to 1 mas, by distributing a large fraction of the total collecting area
in a core array area with extensions out to $\sim$1000 km. An additional 30 18
m antennas are placed in stations to provide even longer baselines (up to
8,860 km) reaching across North America and Hawai’i. These antennas can be
used separately or together with the main array, and will deliver 0.1 mas
resolution and enable microarcsecond precision interferometric astrometry. The
ngVLA was highly ranked by the Astro2020 Decadal Survey, it is currently
beginning the construction and testing of a prototype antenna, and can
potentially start full construction by mid-decade. The ngVLA can operate both
in interferometric and phased-array modes, and can be broken in up into
subarrays. One of the ngVLA Key Science Goals is the study of pulsars in the
Galactic Center, and its signal chain is designed from the start to provide up
to 10 phased-array beams within the $48^{\prime}\,(1.2\,{\rm GHz}/\nu)$
antenna field of view, appropriate for pulsar timing and/or searches. Each of
these phased-array beams will have a robustly-weighted angular resolution near
20 mas in Band 3 (12–20 GHz) to 160 mas in Band 1 (1.2–3.5 GHz).

The Deep Synoptic Array-2000 (DSA-2000) is a proposed radio survey telescope
that will consist of 2000 $\times$ 5 m dishes, having an equivalent point
source sensitivity to SKA-mid (Hallinan2019, ), spanning an area of 19 km
$\times$ 15 km in Nevada. The DSA-2000 will instantaneously cover the
frequency range from 0.7–-2 GHz (42–15 cm). It is designed to serve as an all-
sky survey instrument, and is therefore very complementary to ngVLA, and is
the radio counterpart to the Rubin Observatory (Hallinan2019, ). It will have
near complete sampling of the uv-plane, thereby replacing a traditional
correlator digital backend with a “radio camera.” In a five-year prime phase,
the DSA-2000 will image the entire viewable sky ($\sim$30,000 deg2) repeatedly
over sixteen epochs, detecting $>$1 billion radio sources in a combined full-
Stokes sky map with 500 nJy beam-1 rms noise. One of the primary objectives of
DSA-2000 is to serve as a pulsar timing array (25% of the time), and it will
be the main instrument comprising NANOGrav in the future. It is expected to
produce timing precision better than $\sim 1$ ms for 2000–10,000 millisecond
pulsars (Hallinan2019, ).

Given measurements of accelerations enabled by future pulsar timing
facilities, one can expect to characterize the Galactic potential and
fundamental parameters that describe the Galaxy out to tens of kpc.
Constraints on these parameters have been obtained from a variety of analyses
of current and prior surveys from kinematic modeling. Key large-scale
descriptors of the Galactic potential include the density profile, the
rotation curve, and the shape of the Galactic potential. Given the improved
sensitivity of ng-VLA and DSA-2000, it should be possible to derive these
fundamental Galactic parameters from direct acceleration measurements out to
large distances. Relative to earlier determinations of the local dark matter
density from pulsar timing (Chakrabarti2021, ), one can expect improvements in
precision that should be formally competitive with kinematic estimates.
Perhaps, the most exciting aspect for dark matter studies is the ability to
constrain not only the smooth component of the mass distribution, but also
directly measure dark matter sub-structure, potentially down to the $\sim
10^{6}$ M⊙ scale.

##  VII Future 21cm Facilities

###  VII.1 Key Measurement Opportunities

The baryonic content of the universe is dominated by hydrogen, which
constitutes approximately three quarters of all baryons. Hydrogen
recombination produces the CMB and hydrogen is the fuel of star formation.
During the different ages and places in the universe, hydrogen can be found in
many forms: fully ionized, atomic and molecular. Atomic hydrogen shines in the
21 cm transition. This is a forbidden very low energy transition between the
atomic hydrogen with proton and electron spins being aligned and anti-aligned.
It corresponds to a line at frequency of approximately 1420 MHz, or
equivalently, a wavelength of 21 cm.

During the evolution of the universe, the dominant emission mechanism through
which 21 cm photons are produced varies between cosmic epochs. These different
regimes therefore present different opportunities for constraining dark matter
through observations of the 21 cm signal. They are sensitive to different
physics, but the techniques share many technicalities in common and therefore
from the instrumentation and data analysis point of view, the problems are
variations on a few fundamental issues. The primary challenge at all
frequencies relevant for 21 cm observations is foreground emission, emitted
largely as synchrotron radiation from the MW and other galaxies. This
foreground emission is spectrally smooth, but to successfully filter it out
requires instrumental dynamic range spanning 4–8 orders of magnitude. This
requires an exquisite instrumental calibration that has never been fully
achieved in practice. We emphasize that these are purely technical challenges
that are currently being solved by the radio astronomy community. DOE HEP can
strongly contribute to his effort through funding the appropriate
instrumentation development required to enable these measurements as a part of
generic detector development, as well as pursuing full scale system
simulations that will inform the next generation of system design and data
reduction algorithms. An extended discussion of this technique in the context
of DOE HEP, can be found in the dedicated Snowmass2021 White Paper CF5_21cm .

  1. 1.

Dark Ages Cosmology. After recombination, the universe was filled with neutral
hydrogen and CMB photons. The physics of this universe remains perfectly
describable by linearized general relativity, thermodynamics and atomic
physics. This remains true until the first stars turn on, after which the
complex and highly non-linear physics of star formation prevents us from
making first-principle calculations. The so-called Dark Ages, between
redshifts $z\sim 1100$ and $z\sim 30$, thus offer a unique cosmological
window. The physics is as accurately predictable as that of the CMB, but the
field itself is three-dimensional, having 10 orders of magnitude more linear
fluctuation modes accessible to study through their 21 cm emission. This
signal has the potential to enable the ultimate sensitivity to cosmological
parameters, including those from early-universe inflation and primordial
gravitational waves. Although this experimental end-game will take decades to
develop, the first steps toward this eventual goal can be taken now. We note
that the Astro2020 Decadal Survey identified Dark Ages Cosmology as the sole
Discovery Area from the Panel on Cosmology.

Although the signal from density fluctuations in the Dark Ages is a ways away,
detecting the overall monopole signal — the Dark Ages equivalent of the
discovery of the CMB (PenziasWilson1965, ) — is within reach this decade. The
monopole in this case corresponds to a net absorption of CMB photons,
appearing as a broad spectral dip centered at $\sim 20$ MHz. The shape of this
dip is very sensitive to any non-standard physics or dark matter interactions
at that epoch and in particular any energy injection (or sink) from the baryon
fluid at that epoch. For this reason, the Dark Ages monopole has also been
dubbed the _Cosmic Calorimeter_. Because these predictions are naturally
robust, deviation would be a smoking gun for new physics. In fact, a large
number of theoretical proposals exist that can cause deviations, including
dark matter-baryon scattering 1509.00029 ; 1408.2571 ; 1803.06698 ; 1803.09734
, millicharged dark matter 1802.10094 ; 1803.03091 , dark-matter annihilation
1211.0283 ; 1604.02457 , primordial black holes 1803.09390 , axions 1804.10378
, neutrino decay, charge sequestration 1803.10096 , quark nuggets, dark
photons 1809.01139 , interacting dark energy 1803.07555  and even a drift in
the value of the fundamental constants astro-ph/0701752 . More details can be
found in an Astro2020 Decadal Survey submission 1903.06212 .

Unfortunately, Dark Ages cosmology is not feasible from the Earth because of
ubiquitous sources of radio interference, both human-made and meteorological,
as well as ionospheric effects that become very difficult to control with
precision below 50 MHz.

  2. 2.

Cosmic Dawn and the Epoch of Reionization. The formation of the first luminous
objects marks the end of the Dark Ages, ushering in the subsequent era of
Cosmic Dawn (when Population III stars began to form) and Epoch of
Reionization (EoR; when first-generation galaxies formed). This has several
important consequences on the behavior of the 21cm line. First, Ly$\alpha$
photons from the first stars induce the Wouthuysen-Field effect, which causes
the 21cm brightness temperature to be coupled to the Ly$\alpha$ background.
Thus, 21cm emission ceases to simply trace the matter distribution but is
instead sensitive to Ly$\alpha$ fluctuations. Eventually, the Ly$\alpha$
background becomes sufficiently strong that it serves as a uniform background
since its effects saturate everywhere. Following this, X-ray heating (e.g.,
from X-ray binaries forming inside the first galaxies) causes temperature
variations in the IGM, resulting in spin temperature fluctuations that imprint
themselves on the 21cm line. Eventually, these heating effects also saturate,
with their effect again becoming that of a uniform background. This cycle
repeats itself a final time with reionization, where UV photons from the first
galaxies ionize the IGM around them. This has the effect of imprinting strong
spatial fluctuations in the form of ionized bubbles, until the entire IGM
ionizes.

Observations of the 21 cm line during Cosmic Dawn and the EoR will be powerful
probes of the astrophysics of the era. However, indirect probes of cosmology
and fundamental physics still hold considerable promise. For example, a deep
(and empirically confirmed) understanding of reionization removes a key
nuisance for CMB experiments seeking to constrain fundamental parameters such
as neutrino masses Liu:2016 ; Billings:2021 ; Fialkov:2016 . Relative velocity
effects between dark matter and baryons Tseliakhovich:2010  also imprint
themselves on the Cosmic Dawn power spectrum, resulting in the fairly model-
independent signature of velocity-induced acoustic oscillations (VAOs)
Munoz2019 . These VAOs can be used, for instance, as standard rulers that
enable high-redshift determinations of the Hubble parameter Munoz2019ruler .
Finally, recent studies have suggested that the 21 cm brightness temperature
may be perturbative for at least part of the EoR McQuinn:2018 ; Hoffmann:2019
. Thus, there remains the possibility that the astrophysics of the EoR can be
brought under control by the marginalization of a small handful of effective
parameters, leaving just constraints on the matter field.

  3. 3.

Galaxy Surveys in 21 cm. Below redshift of around $z\sim 6$, the intergalactic
medium becomes essentially fully ionized. Galaxies produce a sufficient number
of ionizing photons that any hydrogen atoms whose density is below that
required for self-shielding are maintained in an ionized state. The main
exceptions are pockets of dense neutral hydrogen inside individual galaxies.
Therefore, it is in principle possible to perform a galaxy survey in 21 cm.
However, this emission is weak and therefore looking at individual galaxies is
inefficient. Instead, relying on the fact that there is no important
interloper for the 21 cm line, we can rely on the intensity mapping technique.
In this approach, rather than imaging individual galaxies, a low-resolution
instrument measures the fluctuations in the mean intensity of 21 cm emission
in space and time. This emission tracks the 21 cm weighted number density of
galaxies and contains all the necessary information required to model the
growth of large scale structure. Such surveys are complementary to optical
galaxy surveys in many respects. First, the signal is dominated by galaxies
residing in considerably less massive dark matter halos than those typically
targeted with optical galaxy surveys, with the majority of the signal coming
from dark matter halos of mass $\sim 10^{10}M_{\odot}$. The main advantage of
such a survey is that it is almost invariably limited by the thermal noise of
the receiver rather than Poisson noise of the underlying sources. By probing a
large number of linear modes, this epoch enables exceptionally tight
constraints on a range of postulated dark matter candidates Gluscevic19 . Some
of these constraints follow indirectly from measuring the radiation content of
the universe, i.e. the $N_{\rm eff}$ parameter Green17 ; Green21 , but other
models provide a more direct route to large changes in observable
correlations. Examples of non-standard models probed by high-precision power
spectrum measurements include those with dark matter-baryon scattering
Dvorkin14 , dark matter interactions Leagourgues16 ; Pan18 ; Archidiacono19
or ultra-light axions Hlozek15 . Moreover, a very broad class of DM models
that can be described with the effective theory of structure formation (ETHOS)
framework ETHOS .

###  VII.2 LuSEE-Night

LuSEE (Lunar Surface Electromagnetics Experiment) Night is a proposed
collaboration between DOE and NASA to install a test-bed radio receiver on the
far side of the Moon. It will be launched on the Commercial Lunar Payload
Services flight CS-3 in early 2025. It will consist of 4 monopole antennas
that actuate in altitude and azimuth. The lander and all the other experiments
will become electrically inactive during the first lunar dawn and LuSEE Night
will employ strong mitigation techniques to prevent self-contamination with
radio frequency interference. The current plans include a far-field calibrator
on the satellite that will deliver a coded signal from orbit and enable
precise characterization of instrumental response, including that of the lunar
regolith. LuSEE Night is expected to acquire data for at least 12 lunar
nights. At the end of the mission it will provide the most exquisite
measurements of the low-frequency radio sky below 50 MHz to date and
demonstrate the feasibility of Dark Ages cosmology from the far side of the
Moon.

###  VII.3 PUMA

The Packed Ultra-wideband Mapping Array (PUMA) is a proposed wideband radio
instrument to map half the sky in the 200–1100 MHz frequency range,
corresponding to the redshift range $z\sim 0.3-6$ when used as a 21 cm
intensity mapper. PUMA is a very large transit radio array proposed in two
configurations. A 5000- dish configuration (PUMA-5K) can act as a pathfinder
while still completing important science goals, including very high precision
measurements of the expansion history of the universe, while the full-sized
array will approach sample-variance-limited observations. As discussed above,
PUMA will provide strong constraints on dark matter properties in particular
through high precision measurement of the 2-point and 3-point correlation
function at high redshift. Its sample-variance-limited measurement at lower
redshift could open up new avenues for dark matter studies, but the details
remain open for further theoretical investigation.

##  VIII Future Optical Facilities

###  VIII.1 Key Measurement Opportunities

Many observations that focus on detecting the effects of dark matter via its
gravitational interactions with baryons have been made at optical wavelengths
due to the combination of telescope sensitivity and the fact that the energy
output from stars peaks at these wavelengths. Dark matter is studied with
optical telescopes in two primary ways: using the observed velocities and
accelerations of stars, gas, and galaxies to infer the gravitational potential
that is causing their motions, and using gravitational lensing to calculate
the mass surface density along the line of sight to the lensed object. Despite
the relative maturity of this observational domain, future instruments and
facilities are poised to make significant technological advances in image
resolution, sensitivity, and the number and precision of spectroscopic
velocity measurements. These advances will greatly increase the observational
sensitivity to fundamental dark matter properties. Some of the key
measurements that will be enabled by new facilities include:

  1. 1.

The mass function of dark matter halos from $10^{6}-10^{8}$ M⊙. The upper end
of this range will be probed directly by ELT measurements of the masses of
dwarf galaxies that will be discovered by the Vera Rubin Observatory (e.g.,
Nadler2020, ). Dark matter halos below $10^{7}$ M⊙ are unlikely to contain any
baryons, and therefore cannot be seen directly. These halos can be detected in
the Milky Way from the perturbations they impart to dynamically cold stellar
streams (e.g., Ngan2014, ; Erkal2015, ; Bonaca2019, ; Drlica-Wagner:2019, )
and the Galactic acceleration field (Chakrabarti2020, ), and at cosmological
distances from the changes in image brightnesses and positions they cause in
gravitational lens systems (e.g., Vegetti2012, ; Hezaveh2016, ; Gilman2020, ).
The former can be measured by wide-field spectroscopic facilities (e.g.,
MegaMapper, MSE, and SpecTel) and extreme-precision radial velocity
spectrographs, and the latter by integral field spectrographs on ELTs. The
halo mass function is closely tied to the primordial matter power spectrum and
fundamental dark matter properties such as particle mass. The mass function
also constrains interactions between dark matter and standard model species
(e.g., Nadler19, ; Maamari21, ; Nguyen21, ).

  2. 2.

The central densities of the smallest luminous dark matter halos
($10^{8}-10^{9}$ M⊙). In small dwarf galaxies, the measured stellar velocity
dispersion translates directly to the mean density of dark matter in the
innermost $\sim 100$ pc of the galaxy (e.g., Read19, ; Guerra2021, ). For the
closest Milky Way satellites, these stellar kinematics can be obtained with
existing instruments, but for more distant systems that have not been altered
by interactions with a massive host galaxy, ELTs will be needed. The maximum
density dark matter can reach on these scales is affected by the dark matter
particle mass and its self-interaction cross-section at low velocities.

  3. 3.

The internal mass distribution of dark matter halos in dwarf galaxies. The
standard $\Lambda$CDM model makes clear predictions for halo density profiles
(NFW1996, ), which largely do not match those determined observationally
(e.g., Oh2011, ; Adams2014, ; Relatores2019, ). A cold, collisionless particle
should result in a cuspy ($\rho(r)\propto r^{-1}$) inner profile, with a
steeper decline at large radii, although the degree to which baryons should
alter the pure dark matter expectation as a function of halo mass remains
controversial (e.g., Orkney2014, ; Wheeler2019, ; Lazar2020, ). Robust
measurements of the density profiles in the most dark matter-dominated dwarf
galaxies are a highly-anticipated goal of next-generation facilities. Two
observational approaches are possible: radial velocities for $\sim 10^{4}$
stars per dwarf galaxy from wide-field spectroscopic facilities, or proper
motions for $\sim 10^{3}$ stars per dwarf from ELTs (Guerra2021, ).

  4. 4.

The mass and density profile of the Milky Way. The total mass of our Galaxy is
a crucial variable for understanding the results of both astrophysical dark
matter measurements and direct detection experiments. Currently uncertain at
the factor of $\sim 2$ level (e.g., Deason2021, ; Craig2021, ; Necib2022, ),
the Milky Way mass can be determined with percent-level accuracy with future
measurements of velocities in stellar streams by wide-field spectroscopic
facilities (Bonaca2018, ). The velocities of stars in the outer reaches of the
Milky Way’s dark matter halo, obtained with the same instruments, may also
contribute to this measurement. The Milky Way mass determines the expected
abundance of satellite dark matter halos (see above) as well as the velocity
distribution of dark matter particles near the Earth. Galactic acceleration
measurements from extremely precise time-series radial velocities and eclipse
timing (§ IV.5) can also improve constraints on the overall mass distribution
within the Milky Way, providing dark matter limits as described in point 3
above.

  5. 5.

The density of dark matter in the solar neighborhood can be determined in less
than a decade with current-generation high-precision spectrographs (with RV
precision $\sim 10$ cm s-1) from direct acceleration measurements
(Chakrabarti2020, ), and compared to earlier determinations from pulsar
timing. This quantity is critical for the interpretation of dark matter direct
detection experiments.

Figure 3:  Conceptual designs of the Thirty Meter Telescope (left; courtesy
TMT International Observatory) and the Giant Magellan Telescope (right; Giant
Magellan Telescope – GMTO Corporation). Both projects are at an advanced stage
of development and have commenced construction of their primary optics.

###  VIII.2 Extremely Large Telescopes

Two US-led partnerships are in the process of building giant ground-based
telescopes with apertures of $25-30$ m, offering an order of magnitude
increase in collecting area and a factor of three improvement in the
diffraction limit compared to the largest current optical telescopes. The
Giant Magellan Telescope (GMT) is a 24.5 m telescope under construction at Las
Campanas Observatory in Chile, and the Thirty Meter Telescope (TMT) is a 30 m
segmented mirror telescope planned to be located in either Hawaii or the
Canary Islands. The highest priority recommendation from the Astro2020 decadal
survey for ground-based facilities is that the federal government join both
projects as the dominant partner to provide access to extremely large
telescopes (ELTs) for the entire US astrophysics community.

ELTs are expected to make significant contributions to dark matter science
through observations of gravitational lenses, dwarf galaxies, and direct
acceleration measurements of objects in the halo of the Milky Way. Such
observations will be sensitive to a small-scale cutoff in the halo mass
function between $10^{6}$ and $10^{8}$ M⊙, the density structure within
(nearly) pure dark matter halos, and interactions between dark matter
particles and either other dark matter particles or Standard Model species.

High resolution imaging of strong lenses. Constraining dark matter using
strong lens systems requires high-sensitivity and high-angular resolution
imaging and spectroscopy. For the gravitational imaging technique, comparisons
of HST vs. adaptive optics (AO) imaging data from the 10 m Keck telescope have
confirmed that sensitivity scales with image resolution. The current AO system
on Keck produces a typical angular resolution of 60–90 mas and a Strehl ratio
of $\sim$ 10%–30% for off-axis targets. With a bigger mirror, a better AO
system, and a larger population of potential tip-tilt stars, ELT performance
will be significantly better. The AO systems on next-generation telescopes are
designed to reach Strehl ratios as high as 90% in K band. Furthermore, they
will include built-in PSF reconstruction software that provides a model of the
PSF for data analysis. The combination of improvements in resolution,
sensitivity, and PSF quality and knowledge will make the ELTs much more
capable than current systems. Specifically, only the brightest handful of
lenses in the sky can currently be targeted with 8–10 m class telescopes. The
US ELTs, on the other hand, will provide virtually full sky access, allowing
us to target large samples of rare quadruply-imaged objects, selecting the
ones with the best (i.e., the ones containing the most structure) extended
images for the gravitational imaging technique. Moreover, Fisher analyses of
simulated data have shown that lens modeling of spectroscopically resolved
images can mitigate the source-subhalo degeneracies, dramatically increasing
the sensitivity of the observations to low-mass subhalos (Hezaveh:2013, ).

For the flux-ratio anomaly technique, a very promising route forward is AO-
assisted IFU spectroscopy. Integral field spectroscopy allows the measurement
of flux ratios from the narrow-line region of the lensed active galactic
nucleus (AGN), which should be immune to microlensing (see Nierenberg:2014, ;
Nierenberg:2017, ; Nierenberg:2020, ). Unfortunately, the technique is
currently restricted to only a handful of quad lenses, given the limitations
of tip-tilt stars and the need to have the narrow AGN emission lines fall in
transparent windows of the Earth’s atmosphere. As in the case of gravitational
imaging, a two-hemisphere US ELT system will enable the application of the
technique to the much larger samples required to provide definitive
conclusions on the nature of dark matter by virtue of their sensitivity
(exploiting the $D^{4}$ advantage of large telescopes for observing point
sources in diffraction-limited mode), resolution (for astrometry of the
images), and full-sky access.

In order to measure the dark matter halo mass function in the range
$10^{7}-10^{10}$ M⊙, forward-modeling simulations indicate that samples of
$\sim$ 50 extended arcs and $\leq$ 50 quadruply-imaged quasars would be
needed. The former provide sufficient statistics of the rarer $10^{9}-10^{10}$
M⊙ substructures, while the latter are needed for direct and statistical
constraints on the mass function in the range $10^{7}-10^{9}$ M⊙. For the
gravitational imaging technique, the brighter the source galaxy, the more
clumpy its structure, and the better the separation between the lens galaxy
and the background lensed object, the better the substructure constraints will
be. The sample of lenses should contain low and high redshift lenses (and
sources) to statistically break the degeneracy between structure along the
line of sight and subhalos bound to the main deflector and characterize
possible evolutionary trends. Gravitational imaging will also be able to
provide constraints on the inner density slope of the massive subhalos ($\sim
10^{10}$ M⊙), while the flux ratios of lensed quasars are sensitive to the
dark matter self-interaction cross-section in addition to the mass function
(Gilman2021, ). Observations of each lens system are expected to require
integration times of a few hours on an ELT.

Figure 4: Illustration of the effect of angular resolution on sensitivity of a
gravitationally lensed arc to dark matter substructure. The top row shows
images of a galaxy lensed into a near-Einstein ring simulated with the
lenstronomy package (lenstronomy, ), and the bottom row displays the per-pixel
residuals between simulations where the lens includes substructure or does
not. In the left column, the resolution is that provided by the Hubble Space
Telescope (HST). In the middle left column, the resolution is twice that of
HST, corresponding to the use of adaptive optics on a current telescope. In
the middle right column, the resolution is increased by another factor of 10,
comparable to what is expected for diffraction-limited ELT imaging. Only at
this resolution is the substructure signal detectable in the bottom row. The
far right column shows the full mass function of substructures expected in
$\Lambda$CDM in the top panel, where the single mass bin included in the
simulation is highlighted, and the spatial distribution of the substructures
in the bottom panel.

Astrometry and spectroscopy of Milky Way satellite galaxies. Complementing
measurements of the mass function of dark matter subhalos around distant
galaxies from lensing, the dwarf galaxies orbiting the Milky Way provide the
best probe of the subhalo mass function above $\sim 10^{8}$ M⊙ in the local
universe. The mass contained within the half-light radius of a dwarf can be
accurately determined from the velocity dispersion of the stars in the galaxy
(Wolf2010, ). Although the mass contained within this central region is only a
small fraction of the total halo mass, the mass function can be recovered from
a well-defined sample of high-quality kinematic measurements (e.g.,
Nadler2020, ). However, given the large number of new dwarfs expected to be
identified by the Rubin Observatory, and the typical distances and
luminosities of those systems, it will not be possible to obtain a complete
sample of mass measurements with existing spectroscopic resources (Simon2019,
). The increased sensitivity provided by ELTs, especially if combined with
relatively wide-field spectroscopic instruments, will be required to observe
all of the Rubin dwarf galaxies.

ELTs will also enable the first unambiguous measurements of the dark matter
density profiles of the lowest-mass dwarf galaxies. There is an extensive
literature of density profile measurements for larger dwarf galaxies
stretching back more than two decades (e.g., Flores1994, ; deBlok2001, ;
Oh2011, ; Relatores2019, ), but the dark matter distribution at those mass
scales is thought to be altered by feedback processes (e.g., Governato2012, ).
In much lower-mass galaxies such as the Milky Way satellites, stellar feedback
should not be strong enough to grossly affect the density profile.
Unfortunately, the most recent modeling indicates that clearly distinguishing
central dark matter cusps from cores in Milky Way satellites cannot be
achieved with radial velocity measurements alone (Guerra2021, ). As originally
suggested by Strigari2007 , though, combining proper motion measurements of
dwarf galaxy stars with radial velocities will break the degeneracies that
have plagued previous studies. The $\sim 20$ $\mu$as astrometric precision of
ELTs will make it possible to detect the motions of dwarf galaxy stars as they
orbit within their host galaxies over a time baseline of five years
(Simon2019b, ). ELTs will also provide the sensitivity needed to achieve this
precision at faint enough magnitudes to provide large stellar samples. In
concert with existing or new radial velocity data sets, ELT astrometry will
clearly distinguish cuspy and cored density profiles, offering a crucial test
of dark matter models.

Time-series extreme precision radial velocity observations (“optical timing”).
Traditionally, kinematic modeling has been used to estimate Galactic
accelerations, and thereby the mass distribution of the Milky Way. In a time-
dependent potential like that of our Galaxy, kinematic modeling can lead to an
inaccurate inference of the Galactic mass distribution (Haines2019, ).
Measurements of the accelerations of stars that live within the gravitational
potential of the Galaxy have recently become feasible due to advances in
technology, and in principle provide the most precise characterization of the
dark matter distribution in the Galaxy. Because this approach requires
extreme-precision time-series measurements, we denote it “optical timing” in
analogy with pulsar timing. Over decade baselines, the expected Galactic
acceleration, i.e., the change in the line-of-sight velocity, $\Delta RV$,
experienced by stars at $\sim$ few kpc distances from the Sun is $\sim$ 10 cm
s-1 decade-1 (SilverwoodEasther2019, ; Ravi2019, ; Chakrabarti2020, ). The
current generation of stabilized spectrographs such as NEID (Schwab2016, ) and
ESPRESSO (Pepe2021, ) are approaching this level of RV precision (e.g.,
Netto2021, ), but because they are on 3.5 m and 8 m telescopes respectively,
they only allow for measurements of accelerations of relatively bright stars
within a few kpc of the Sun.

Future instruments, such as G-CLEF (Szent2017, ) on the GMT and MODHIS on the
TMT (Mawet2019, ), are expected to allow much greater dynamic range and enable
direct acceleration measurements across the Galaxy. Like pulsar timing, these
observations will yield a direct measurement of Galactic accelerations, which
provides the mass distribution (both the smooth component and dark matter
substructure) without the assumptions of equilibrium or symmetry inherent in
traditional kinematic analyses. It should be possible to characterize the
upper mass range of the dark matter halo mass function ($10^{9}-10^{10}$ M⊙)
with a sample of tens of “quiet” stars (i.e., stars with low enough RV jitter
such that those intrinsic stellar velocity fluctuations do not contaminate the
Galactic signal (WrightRobertson2017, )). Moreover, one has to ensure that
such sources trace the Galactic signal and are not contaminated by binaries,
planets, or intrinsic stellar variability (“stellar jitter”) (Chakrabarti2020,
). Perhaps the most serious contaminating factor to directly measure Galactic
accelerations down to the $\sim$ 10 cm s-1 decade-1 level with EPRV
observations is stellar jitter. Recent analyses suggest that machine learning
techniques may be able to mitigate this to some extent (Debeurs2020, ).
Analysis of publicly available detailed RV observations of the Sun may also
provide a means of better understanding stellar jitter (Lin2021, ).
Observations in the near-infrared should also help to mitigate intrinsic RV
variability (Mawet2019, ). The current generation of spectrographs have
demonstrated significant gains in precision, and enough so to make a
compelling argument to measure Galactic accelerations. The main technical
challenge that now needs to be overcome is the demonstration of stability over
decade timescales that can allow for such a measurement. Relative to current
extreme-precision radial velocity (EPRV) surveys that can be conducted by
ESPRESSO and existing spectrographs, the ELTs will allow for not only greater
coverage in volume, but also should allow for a denser sampling of sources
(hundreds) and thereby constraints on lower-mass dark matter subhalos, perhaps
extending as far as $\sim 10^{6}$ M⊙. A key point here is that EPRV is equally
well a tool for dark matter science as it is for detecting and characterizing
exoplanets.

###  VIII.3 Wide-field Multi-Object Spectroscopy Facilities

Figure 5:  Conceptual designs of MegaMapper (left; (schlegel19, )) and the
Maunakea Spectroscopic Explorer (right; (MSE_book2018, )). These are two of
the proposed wide-field multi-object spectroscopic facilities.

A critical missing link in the international portfolio of astronomical
observatories for the next decade is a dedicated wide-field multi-object
spectroscopy (WFMOS) facility on an 8-meter class telescope. As described in
more detail in Section VIII.1, highly-multiplexed spectroscopy on a large
telescope offers significant potential for constraining the dark matter
particle mass and interaction cross-section, as well as the properties of the
Milky Way’s dark matter halo. Several WFMOS facilities on 2.5- to 4-meter
telescopes are either already operating or expected to begin in the near
future, including but not limited to:

  * •

The SDSS-V survey on two 2.5-meter telescopes (Kollmeier2017, )

  * •

The DESI survey on the 4-meter Mayall telescope (desi2016, )

  * •

The 4MOST survey on the 4-meter VISTA telescope (deJong2011, )

  * •

The WEAVE survey on the 4-meter William Herschel Telescope (Dalton2016, ).

However, due to their aperture size, these facilities have limited capacity to
observe the faint objects that will be the highest-priority targets identified
by the Rubin Observatory. In contrast, the Prime Focus Spectrograph (PFS) on
the 8.2-meter Subaru Telescope will provide similar multiplexing and a larger
aperture (Takada2014, ), but it does not offer access to most of the US
community, it will share time on the telscope with other Subaru instruments,
and it has limited sky overlap with the Rubin survey area given its location
in Hawaii. Thus, although the need for such a capability has been broadly
agreed upon by the international community (see below), there is currently no
dedicated next-generation WFMOS facility that has been funded or approved for
construction.

In particular, a US community study supported by NSF and the Kavli Foundation
included as one of its top recommendations that the US “[d]evelop or obtain
access to a highly multiplexed, wide-field optical multi-object spectroscopic
capability on an 8m-class telescope” (Najita2016, ). The following year, a
working group from the European Southern Observatory came to a similar
conclusion: “We consider the scientific case for a large aperture (10-12m
class) optical spectroscopic survey telescope with a field of view comparable
to that of LSST. We find that such a facility could enable transformational
progress in several broad areas of astrophysics, and may constitute an
unmatched ESO capability for decades” (Ellis2017, ). Most recently, the
Astro2020 Decadal Survey identified highly multiplexed spectroscopy as a
strategic priority. It emphasized the need for new capabilities in highly
multiplexed spectroscopy to complement the Rubin Observatory and to advance
the scientific priorities of the survey. Astro2020 recommended that a major
(MSRI-2 scale) investment could be made in a large, dedicated facility late in
the coming decade. However, because the NSF MSRI-2 cost cap is $\sim\$100$
million, partnerships with other organizations or agencies are likely to be
required to complete such an ambitious project.

Here we describe several proposed (but not funded) next-generation WFMOS
facilities that could make the key measurements listed in Section VIII.1.

####  VIII.3.1 DESI-II

DESI (§ IV.3) is an ambitious multi-fiber optical spectrograph using 5000
robotically-positioned fibers in an 8 deg2 focal plane on the Kitt Peak
National Observatory Mayall 4-meter telescope. Fibers feed a bank of 10
triple-arm spectrographs that measure the full bandpass from 360 nm to 980 nm
at a spectral resolution of $R\sim 2000$ in the UV and over $R\sim 4000$ in
the red and near-infrared. The DESI five-year survey will probe dark energy
and cosmic structure by obtaining redshifts for more than 35 million galaxies
and quasars at $z<3.5$ over 14,000 deg2 of the sky (desi2016, ). In addition
to the galaxy and quasar survey, DESI will observe roughly ten million stars
in the Milky Way. Because these observations will be conducted during brighter
conditions, the stellar targets are selected over the magnitude range
$16<r<19$, ensuring a sufficient signal-to-noise ratio for measurements of
radial velocities and stellar parameters.

Beyond the end of its planned survey, DESI will remain a state-of-the-art
facility for wide-field surveys. Given the field of view, multiplex,
throughput, and resolution, a second phase of DESI (DESI-II) offers the
potential for exciting scientific opportunities for studying dark matter in
the 2026-2031 time frame. For example, DESI-II could dedicate a significant
amount of dark time to spectroscopic targets for dark matter science. The
observation of fainter stars (e.g., pushing from $\sim 19$ mag in DESI to
$\sim 21$ mag in DESI-II) in the Milky Way will probe the dark matter halo
distribution in our Milky Way at both small and large scales (Dey2019BAAS, ).
Increasing the sample size of the faintest, low redshift galaxies will improve
the constraints of the satellite luminosity function (saga2, ).

Although DESI will still be a premier spectroscopic facility in its current
configuration, there may also be opportunities for augmentation. For example,
the spectrographs could be upgraded to include Ge CCDs for near-infrared
wavelength coverage up to 1.3 $\mu$m, or with ultra-low noise Skipper CCDs to
improve performance at blue wavelengths (Drlica-Wagner:2020, ). Not including
any major upgrades, the cost to operate a second-generation DESI survey is
likely to be $\sim$$10–15 million per year (Levi2019BAAS, ).

####  VIII.3.2 MegaMapper

MegaMapper is a very wide-field 6.5-m telescope in the initial phases of
facility design. With the exception of modifications to the primary mirror to
greatly increase the field of view, the telescope will be a copy of the two
Magellan telescopes. This shared design takes advantage of Magellan’s
successful engineering heritage and two decades of operational experience. The
current optical design for the system offers a field of view of $\sim 7$ deg2.
The envisioned instrument to be paired with the telescope consists of a bank
of medium-resolution spectrographs fed by 20,000 optical fibers, although a
wide variety of other spectroscopic configurations are also possible. The
initial projection for the construction cost is approximately $\$160$ million.
The telescope construction may be funded by NSF through the MSRI program, as
suggested by the Astro2020 decadal survey report, while the spectrographs,
detectors, fiber positioners, and front-end electronics present attractive
opportunities for potential DOE contributions, building on the success and
technical capabilities pioneered by DESI.

With its combination of substantially larger aperture, wider field of view,
and significant increase in spectroscopic multiplexing, MegaMapper offers a
survey speed exceeding any other existing facility by an order of magnitude
(schlegel19, ). As described in several Snowmass Letters of Interest, as well
as documentation provided to Astro2020, MegaMapper will conduct a galaxy
redshift survey of $\sim 10^{8}$ galaxies. These measurements will provide the
tightest available constraints on non-Gaussianity and measure the fraction of
dark energy at the $<1\%$ level to $z=4.5$.

Through either simultaneous observations or a separate dedicated program,
MegaMapper could also enable important new constraints on dark matter models.
Specifically, precise kinematic measurements for enormous samples of stars in
nearby dwarf galaxies and stellar streams will probe the mass function of dark
matter halos below $10^{8}$ M⊙, set new limits on the mass of warm dark matter
and fuzzy dark matter particles, and constrain the interaction cross-section
of dark matter particles with one another and with Standard Model species (see
halo WP). In addition, velocities of stars in streams and the halo of the
Milky Way will significantly improve mass measurements of the Milky Way, which
are critical to a broad set of direct and indirect detection experiments, as
well as cosmic probes of dark matter.

####  VIII.3.3 Maunakea Spectroscopic Explorer

The Maunakea Spectroscopic Explorer (MSE) will transform the CFHT 3.6m optical
telescope into an 11.25 meter aperture telescope to feed 4,332 fibers over a
wide 1.52 deg2 field of view, based on its 2018 Conceptual Design (Figure 5;
(MSE_book2018, )). In its current design, among the 4332 fibers, 2166 of them
will be fed to 3 low resolution spectrographs with a wavelength coverage of
0.36–1.00 $\mu$m and a spectral resolution of $R\sim 5000-6000$, 1083 fibers
will be fed to 2 infrared spectrographs with a wavelength coverage of 1.00 -
1.80 and a spectral resolution of $R\sim 5000-7000$, and the remaining 1083
fibers will be fed to 2 high-resolution spectrographs with a spectral
resolution of $R\sim 30000$ at smaller wavelength coverage. Furthermore, trade
studies are currently underway to investigate significantly increasing the
number of fibers (by a factor of $\sim 5$) in the focal plane by implementing
a quad-mirror, Rubin Observatory-style telescope design, with a 14-meter
aperture primary mirror. MSE has completed its Conceptual Design; since that
time it has been advancing the instrument design and is currently preparing to
begin a two-year Preliminary Design Phase in late 2022, with science
operations expected to begin in 2032.

MSE has assembled a Detailed Science Case document mse_dsc , of which one
chapter focuses on the concrete ways that astrophysical probes can elucidate
the particle nature of dark matter with MSE (mse_dm, ). The dark matter-
related science cases range from determining the line-of-sight velocities of a
large number of faint stars in the Milky Way’s stellar streams and nearby
dwarf spheroidal galaxies, obtaining the redshifts of low-mass galaxies in the
local Universe ($z<0.05$), to searching for strongly lensed galaxies at higher
redshift. N-body and hydrodynamical simulations of cold, warm, fuzzy and self-
interacting dark matter show that non-trivial dynamics in the dark sector will
leave an imprint on structure formation. Sensitivity to these imprints will
require extensive and unprecedented kinematic datasets for stars down to
$r\sim 23$ mag and redshifts for galaxies down to $r\sim 24$ mag. A 10m class
wide-field, high-multiplex spectroscopic survey facility like MSE is required
in the next decade to provide a definitive search for deviations from the cold
collisionless dark matter model.

MSE is expected to build on the existing Canada-France-Hawaii collaboration
with more international partners including Australia, China, India, South
Korea, and the US and UK astronomical communities. The total construction cost
of MSE is about $450 million and the expected funding model involves cost
sharing between partners, $\sim 30\%$ of which is expected from the US.

####  VIII.3.4 SpecTel

SpecTel is a spectroscopic facility proposed for construction in Chile,
largely motivated by the ESO working group response to community needs as
described in the beginning of Section VIII.3. The conceptual design of the
telescope includes an 11.4-meter aperture with a 4.91 square degree field of
view and a focal plane at the Cassegrain focus well-suited for fiber-fed
spectroscopy. The focal plane has a 1.43 meter diameter, enabling
instrumentation of 15,000 robotically-controlled fibers using the 10.4 mm
pitch design from DESI (SpecTel:2017, ; SpecTel:2019, ).

New fiber positioner technologies such as the 6.5 mm pitch positioners
proposed for the MegaMapper facility would allow a significant increase in
multiplex number. The Cosmic Visions panel suggested a goal of a 5-mm pitch
for a new fiber positioner technology cosmicvisions2018 . Reaching that
spacing would allow simultaneous spectroscopy from 60,000 fibers, enough for a
program that covers 10% of the galaxies in the LSST Gold Sample. Research and
Development effort for new positioners has begun at DOE labs and could be a
major contribution from the US community toward instrumenting SpecTel or any
other spectroscopic facility. The conceptual design for SpecTel provides an
optical quality that would allows spectral wavelength coverage over a range of
$360<\lambda<1330$ nm. Ge CCD development for the IR portion of this range and
expertise in spectrograph design and construction could also be be significant
US contributions to such a facility. Finally, the expertise from DESI in
spectroscopic pipeline development and data management could be directed
toward a future spectroscopic program as a US contribution.

The science cases for SpecTel identified by the ESO working group are very
similar to those in MSE. The consistency in observational programs, including
those that would provide new insights into dark matter, further highlight the
need for a wide-field, highly multiplexed spectroscopic facility. The primary
design difference between SpecTel and MSE lies in the optical path. The
Cassegrain focal plane in the preliminary SpecTel design includes only a
three-lens transmissive element that serves as both field flattener and
atmospheric differential corrector. The most recent MSE design relies on only
reflective surfaces to minimize achromatic effects and increase the potential
wavelength coverage.

The ESO community is pursuing a conceptual design study for SpecTel which
would be required to establish the cost and the construction schedule.
Preliminary cost estimates (FY2019) for the telescope and enclosure were
$200M. Additional costs for the instrument would depend on the scope of the
spectroscopic system, where both medium resolution and high resolution options
are being considered.

####  VIII.3.5 Comparison and Summary

Wide-field MOS Facilities/Surveys |  DESI-II |  MegaMapper |  MSE |  SpecTel
---|---|---|---|---
Telescope aperture diameter (m) |  4 |  6.5 |  11.25–14 |  11.4
Field-of-view (deg2) |  8.94 |  7.06 |  1.52 |  4.91
Number of fibers |  5000 |  20000 |  4332–21000 |  15000–60000
Spectral resolution $\lambda/\delta\lambda$ |  3000 |  4000 |  5000/20000 |  4000/40000
Wavelength range ($\mu$m) |  0.36-1 |  0.36-1 |  0.36-1.8 |  0.36-1.3
Timescale/first light |  2026 |  2030 |  2032 |  $>$2035
Total project cost |  low |  medium |  high |  high
Expected US contribution (in $ million) |  $<50$ |  160 |  135 |  ???
Site location |  US/Arizona |  Chile |  US/Hawai’i |  Chile
Table 2: Summary and Comparison of the Key Parameters of Four WFMOS Facilities
Discussed in this White Paper.

The scientific need for a next-generation massively-multiplexed spectroscopic
facility on a large telescope is clear. Such a project will not only make a
major impact on dark matter physics, but the same facility would also enable
tremendous progress on studies of dark energy, inflation, neutrino masses, and
a broad set of astrophysics. Above we have described four candidate facilities
that could achieve these goals in different forms, but this list is not
intended to be exclusive; for example, the FOBOS spectrograph for Keck
(Bundy2020, ) is a smaller scale instrument that could contribute to some of
the same science. In addition, an ELT spectrograph offering higher
multiplexing than their currently-planned instruments could be competitive for
some of the WFMOS science goals because of the large collecting area of these
telescopes.

In Table 2, we summarize the key parameters of the WFMOS facilities discussed
in this section, and below we elaborate on this comparison.

The scientific capabilities of these facilities are a function of four main
parameters: the telescope collecting area, its field of view, the number of
fibers, and the spectrograph characteristics. According to the currently
available designs, the greatest sensitivity is offered by MSE and SpecTel
thanks to their larger primary mirrors, while DESI-II and MegaMapper provide
the widest fields of view. However, all of the projects are in early stages of
design so that significant design changes are still possible. For example, a
range of options is presented for fiber number for MSE and SpecTel, and MSE
may consider a larger telescope diameter as well. We note that the importance
of field of view relative to multiplexing depends on the surface density of
the targets of interest. Choices about the number of fibers for each facility
were generally driven by science goals unrelated to dark matter, and the
multiplexing of these facilities should not be the limiting factor for any of
the measurement opportunities discussed in Section VIII.1.

Any one of the three new telescope projects can accomplish the dark matter
science goals described above. There are differences in detail among their
capabilities, which will enable certain measurements to be made more
efficiently, or dark matter limits to be extended further, with some
facilities. For example, the higher spectral resolution offered by MSE will
enable more accurate stellar velocity measurements, potentially constraining
the dark matter subhalo mass function down to $10^{5}$ M⊙, compared to the
$10^{6}$–$10^{7}$ M⊙ limits obtainable at lower spectral resolution (mse_dsc,
). For similar reasons, a high resolution option is being considered for
SpecTel. The larger field of view of MegaMapper would facilitate mapping of
stellar streams more quickly, while the larger apertures of MSE and SpecTel
can provide larger samples of faint stars in both streams and dwarfs. However,
quantitative estimates for the impact of depth and field of view on dark
matter constraints are not yet available.

The locations of the various WFMOS facilities will also play a role in their
ability to constrain dark matter parameters. MegaMapper and SpecTel will have
complete overlap with the Rubin Observatory LSST footprint, so that they are
able to follow up all dwarf galaxies and streams identified in the LSST data.
On the other hand, MSE will only be able to observe $\sim 50$% of the Rubin
survey area, but can see a larger fraction of the sky, including northern
targets that are inaccessible from Chile.

Finally, there are large differences between projects in cost, and perhaps
time scale. At one extreme, DESI is already operating, and therefore only
continuing operation funds are needed for DESI-II. DESI-II is expected to
start operating in 2026 after the conclusion of the current 5-yr DESI survey
(2021-2026). By relying on established hardware and technology as much as
possible, MegaMapper aims to minimize the project cost and technical risk, and
will be the least expensive of the three proposed facilities. MSE and SpecTel
are projected to be factors of $\sim 3$–5 more expensive, although because
they are based on international partnerships that are still being developed,
the US contribution remains uncertain.

The bottom line is that construction of one of the massively multiplexed
spectroscopic facilities will be important for the next generations of cosmic
constraints on dark matter. From the perspective of dark matter science alone,
the choice of which facility the US should pursue is less critical. Cost,
schedule, risk, and the needs of other scientific areas in the Cosmic Frontier
may reasonably drive that decision.

##  IX Future Gravitational Wave Facilities

###  IX.1 Key Measurement Opportunities

The interaction of dark matter with astrophysical compact objects (black holes
and neutron stars) allows gravitational wave observatories to constrain a wide
variety of dark matter candidates including axion-like particles, ultralight
bosons, and primordial black holes. Cosmic Explorer, a next-generation
gravitational-wave observatory that is planned construction in the United
States, will yield a factor of ten improvement over the sensitivity of
Advanced LIGO Reitze2019 ; Evans:2021gyd . A possible upgrade to the LIGO
facilities, known as LIGO Voyager LIGO:2020xsf , is also under considerations.
Figure 6 shows the sensitivity of Cosmic Explorer and Voyager compared to the
current Advanced LIGO detectors (at their O3 sensitivity), the funded LIGO A+
upgrade, and the Einstein Telescope, a planned European next-generation
detector ET . Some of the key measurements that next-generation detectors
could provide include:

  1. 1.

Searches for axionlike particles. Light axions inside neutron stars can modify
the inspiral waveform yielding a dark matter signature detectable in the
gravitational waveform. Constraints can be placed on axions with masses below
$10^{-11}$eV and decay constants ranging from $10^{16}$ GeV to $10^{18}$ GeV,
with next-generation facilities improving current constraints by a factor of
$\sim 3$ Zhang:2021mks .

  2. 2.

Superradiant instabilities of rotating black holes. Spinning black holes can
superradiantly amplify excitations in a surrounding field, generation long-
lived “bosonic clouds” that slowly dissipate energy through the emission of
gravitational waves Arvanitaki:2014wva ; Arvanitaki:2016qwi . A large number
of unresolved sources can contribute to the stochastic gravitational wave
background, allowing Cosmic Explorer to constrain bosons in the mass range
$\sim[7\times 10^{-14},2\times 10^{-11}]$ eV Yuan:2021ebu . In addition to
direct detection, the boson cloud spins down the black hole to a
characteristic spin determined by the boson mass and the black hole mass. With
the large number of high signal-to-noise ratio events that will be seen by
Cosmic Explorer, the existance of noninteracting bosons in the mass range
$10^{-13}$ to $10^{-12}$ eV could be confirmed through their imprint on the
black hole spin distribution Ng:2019jsx .

  3. 3.

Boson Stars. Next-generation detectors could distinguish between binaries
containing boson stars from binary neutron stars and binary black holes by
measuring the compactness parameter of the stars, which typically lies between
that of black holes and neutron stars Sennett:2017etc ; Toubiana:2020lzd .

  4. 4.

Primordial Black Holes. Primordial black holes (PBHs) have been of
longstanding candidate for some fraction of dark matter. Binaries containing
containing sub-solar mass black holes or black hole binaries observed at very
large red shifts would indicate the presence of PBHs as a dark matter
component Nakamura_1997 ; Bird:2016dcv . Primordial black holes could be
surrounded by spikes of particle dark matter which could influence the
dynamics of a binary merger allowing Cosmic Explorer to probe dark matter
candidates with masses heavier than approximately $m_{a}\sim 10^{-6}$ eV
Bertone:2019irm .

Figure 6: Amplitude spectral densities of detector noise for Cosmic Explorer,
the current (O3) and upgraded (A+) sensitivities of Advanced LIGO, LIGO
Voyager, the proposed Australian NEMO detector, and the three paired detectors
of the triangular Einstein Telescope. At each frequency the noise is referred
to the strain produced by a source with optimal orientation and polarization.

###  IX.2 Cosmic Explorer and Einstein Telescope

In the United States, the next-generation Cosmic Explorer facility will have
ten times the sensitivity of Advanced LIGO and will push the reach of
gravitational-wave astronomy toward the edge of the observable universe
($z\sim 100$) Reitze2019 ; Evans:2021gyd . A complementary observatory, known
as Einstein Telescope, is under development in Europe. Cosmic Explorer’s
order-of-magnitude sensitivity improvement will be realized using a dual-
recycled Fabry–Pérot Michelson interferometer, as in Advanced LIGO. Cosmic
Explorer’s increased sensitivity comes primarily from scaling up the
detector’s length from 4 to 40 km. The longer arms increase the amplitude of
the observed signals with effectively no increase in the detector noise. The
Cosmic Explorer Horizon Study has considered a reference concept of a 40 km
detector and a 20 km detector, both located in the United States. The
sensitivity of Cosmic Explorer provides access to significantly more sources,
spread out over cosmic time, as well as high-fidelity measurements of strong,
nearby sources. These precision measurements will enable the exploration of
dark matter candidates through their interaction with compact objects and
gravity. The Einstein Telescope is proposed as a 10 km triangular
interferometer with $60^{\circ}$ angles, to be build underground to minimize
low-frequency noise. Both Cosmic the target is data taking in the mid 2030s.

###  IX.3 LIGO Voyager

Beyond the A+ upgrade, LIGO is exploring an future upgrade that uses cryogenic
silicon optics and suspensions and reduces quantum and Newtonian (gravity
gradient) noise; this upgrade is known as Voyager LIGO:2020xsf . LIGO-Voyager
represents the best path to maximizing the sensitivity of the existing LIGO
facilities, although it does not reach the sensitivity possible in a new
facility like Cosmic Explorer or Einstein Telescope. The Voyager technologies
are complementary to those being explored for next-generation detectors.
Options for lasers, photodiodes, electro-optics for Voyager’s planned 2 $\mu$m
operating wavelength, and cryogenic engineering solutions to cool the
suspended optics will be tested in the Caltech 40-m prototype interferometer
and by the European Einstein Telescope pathfinder prototype.

##  X Conclusion

The design and requirements of observational facilities for studying dark
matter overlap heavily with facilities that measure dark energy and inflation.
Furthermore, these facilities leverage the core capabilities and expertise of
the HEP community. For example, the HEP community has demonstrated extensive
capability in massively multiplexed spectroscopy through SDSS, BOSS, eBOSS,
and DESI. Furthermore, DOE has been extensive involved in detector development
and packaging for DES, DESI, and Rubin, as well as R&D on future ultra-low
noise Skipper CCDs for future spectroscopic surveys. Current efforts in
detector fabrication and readout systems that are being developed for CMB-S4
will translate directly to future CMB experiments. Additional efforts are
already underway to develop radio capabilities. The development of next-
generation gravitational-wave observatories will open new windows on dark
matter both directly and through their interactions with astrophysical compact
objects. The HEP national laboratories provide extensive expertise in
cryogenics, mechanical engineering, readout electronics, precision metrology,
vacuum technology, project management, and large-scale computing.

Observational facilities are a necessary avenue to explore the fundamental
nature of dark matter. For some dark matter models, they will provide
important measurements to complement terrestrial experiments, while other dark
matter models can only be accessed by observational facilities. The technical
and scientific capabilities of the HEP community provide an essential resource
for constructing, operating, and analyzing these experiments in the coming
decade.

###### Acknowledgements.

We thank Katelin Schutz for providing helpful feedback on a draft of this
manuscript. We are grateful to the CF3 conveners, Alex Drlica-Wagner, Chanda
Prescod-Weinstein, and Hai-Bo Yu, for their guidance and management of the
Snowmass process. This research has made use of NASA’s Astrophysics Data
System Bibliographic Services.

## References

  * (1) M. Battaglieri et al., _US Cosmic Visions: New Ideas in Dark Matter 2017: Community Report_ , in _U.S. Cosmic Visions: New Ideas in Dark Matter_ , 7, 2017 [1707.04591].
  * (2) K. Engel et al., _Advancing the Landscape of Multimessenger Science in the Next Decade_ , _Contribution to Snowmass 2021_ (2022) .
  * (3) T. Aramaki et al., _Snowmass2021 Cosmic Frontier: The landscape ofcosmic-ray and high-energy photon probes ofparticle dark matter_ , _Contribution to Snowmass 2021_ (2022) .
  * (4) K. Engel et al., _The Future of Gamma-Ray Experiments in theMeV–EeV Range_ , _Contribution to Snowmass 2021_ (2022) .
  * (5) R. Adhikari et al., _Gravitational Wave Facilites_ , _Contribution to Snowmass 2021_ (2022) .
  * (6) D.G. York, J. Adelman, J. Anderson, John E., S.F. Anderson, J. Annis, N.A. Bahcall et al., _The Sloan Digital Sky Survey: Technical Summary_ , _AJ_ 120 (2000) 1579 [astro-ph/0006396].
  * (7) E.W. Kolb, M.S. Turner, D. Lindley, K. Olive and D. Seckel, _Inner space/outer space : the interface between cosmology and particle physics_ (1986).
  * (8) National Research Council, _Connecting quarks with the cosmos : eleven science questions for the new century_ , The National Academies Press, Washington, DC (2003), 10.17226/10079.
  * (9) K.S. Dawson, D.J. Schlegel, C.P. Ahn, S.F. Anderson, É. Aubourg, S. Bailey et al., _The Baryon Oscillation Spectroscopic Survey of SDSS-III_ , _AJ_ 145 (2013) 10 [1208.0022].
  * (10) The Dark Energy Survey Collaboration, _The Dark Energy Survey_ , _arXiv e-prints_ (2005) astro [astro-ph/0510346].
  * (11) DESI Collaboration, A. Aghamousa, J. Aguilar, S. Ahlen, S. Alam, L.E. Allen et al., _The DESI Experiment Part I: Science,Targeting, and Survey Design_ , _arXiv e-prints_ (2016) arXiv:1611.00036 [1611.00036].
  * (12) Ž. Ivezić, S.M. Kahn, J.A. Tyson, B. Abel, E. Acosta, R. Allsman et al., _LSST: From Science Drivers to Reference Design and Anticipated Data Products_ , _ApJ_ 873 (2019) 111 [0805.2366].
  * (13) K. Abazajian, G. Addison, P. Adshead, Z. Ahmed, S.W. Allen, D. Alonso et al., _CMB-S4 Science Case, Reference Design, and Project Plan_ , _arXiv e-prints_ (2019) arXiv:1907.04473 [1907.04473].
  * (14) R. Brito et al., _Snowmass2021 Cosmic Frontier White Paper: Probing dark matter with small-scale astrophysical observations_ , _Contribution to Snowmass 2021_ (2022) .
  * (15) N. Sehgal, S. Aiola, Y. Akrami, K. Basu, M. Boylan-Kolchin, S. Bryan et al., _CMB-HD: An Ultra-Deep, High-Resolution Millimeter-Wave Survey Over Half the Sky_ , in _Bulletin of the American Astronomical Society_ , vol. 51, p. 6, September, 2019 [1906.10134].
  * (16) R.J. Selina, E.J. Murphy, M. McKinnon, A. Beasley, B. Butler, C. Carilli et al., _The ngVLA Reference Design_ , in _Science with a Next Generation Very Large Array_ , E. Murphy, ed., vol. 517 of _Astronomical Society of the Pacific Conference Series_ , p. 15, Dec., 2018 [1810.08197].
  * (17) G. Hallinan, V. Ravi, S. Weinreb, J. Kocz, Y. Huang, D.P. Woody et al., _The DSA-2000 — A Radio Survey Camera_ , in _Bulletin of the American Astronomical Society_ , vol. 51, p. 255, Sept., 2019 [1907.07648].
  * (18) J.O. Burns, R. MacDowall, S. Bale, G. Hallinan, N. Bassett and A. Hegedus, _Low Radio Frequency Observations from the Moon Enabled by NASA Landed Payload Missions_ , _Planet. Sci. J._ 2 (2021) 44 [2102.02331].
  * (19) A. Slosar, Z. Ahmed, D. Alonso, M.A. Amin, E.J. Arena, K. Bandura et al., _Packed Ultra-wideband Mapping Array (PUMA): A Radio Telescope for Cosmology and Transients_ , in _Bulletin of the American Astronomical Society_ , vol. 51, p. 53, Sept., 2019 [1907.12559].
  * (20) G.H. Sanders, _The Thirty Meter Telescope (TMT): An International Observatory_ , _Journal of Astrophysics and Astronomy_ 34 (2013) 81.
  * (21) M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira et al., _Giant Magellan Telescope: overview_ , in _Ground-based and Airborne Telescopes IV_ , L.M. Stepp, R. Gilmozzi and H.J. Hall, eds., vol. 8444 of _Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series_ , p. 84441H, Sept., 2012, DOI.
  * (22) M. Levi, L.E. Allen, A. Raichoor, C. Baltay, S. BenZvi, F. Beutler et al., _The Dark Energy Spectroscopic Instrument (DESI)_ , in _Bulletin of the American Astronomical Society_ , vol. 51, p. 57, Sept., 2019 [1907.10688].
  * (23) D. Schlegel, J.A. Kollmeier and S. Ferraro, _The MegaMapper: a z¿2 spectroscopic instrument for the study of Inflation and Dark Energy_ , in _Bulletin of the American Astronomical Society_ , vol. 51, p. 229, September, 2019 [1907.11171].
  * (24) A. Hill, N. Flagey, A. McConnachie, K. Szeto, A. Anthony, J. Ariño et al., _The Maunakea Spectroscopic Explorer Book 2018_ , _arXiv e-prints_ (2018) arXiv:1810.08695 [1810.08695].
  * (25) R.S. Ellis, J. Bland-Hawthorn, M. Bremer, J. Brinchmann, L. Guzzo, J. Richard et al., _The Future of Multi-Object Spectroscopy: a ESO Working Group Report_ , _arXiv e-prints_ (2017) arXiv:1701.01976 [1701.01976].
  * (26) M. Evans et al., _A Horizon Study for Cosmic Explorer: Science, Observatories, and Community_ , 2109.09882.
  * (27) LIGO collaboration, _A cryogenic silicon interferometer for gravitational-wave detection_ , _Class. Quant. Grav._ 37 (2020) 165003 [2001.11173].
  * (28) K.N. Abazajian, P. Adshead, Z. Ahmed, S.W. Allen, D. Alonso, K.S. Arnold et al., _CMB-S4 Science Book, First Edition_ , _arXiv e-prints_ (2016) arXiv:1610.02743 [1610.02743].
  * (29) C. Dvorkin, R. Hlozek, R. An et al., _Snowmass2021 Cosmic Frontier White Paper: Dark Matter Physics from the CMB-S4 Experiment_ , _Contribution to Snowmass 2021_ (2022) .
  * (30) K. Bechtol, A. Drlica-Wagner, E. Balbinot, A. Pieres, J.D. Simon, B. Yanny et al., _Eight New Milky Way Companions Discovered in First-year Dark Energy Survey Data_ , _ApJ_ 807 (2015) 50 [1503.02584].
  * (31) S.E. Koposov, V. Belokurov, G. Torrealba and N.W. Evans, _Beasts of the Southern Wild: Discovery of Nine Ultra Faint Satellites in the Vicinity of the Magellanic Clouds._ , _ApJ_ 805 (2015) 130 [1503.02079].
  * (32) A. Drlica-Wagner, A. Albert, K. Bechtol, M. Wood, L. Strigari, M. Sánchez-Conde et al., _Search for Gamma-Ray Emission from DES Dwarf Spheroidal Galaxy Candidates with Fermi-LAT Data_ , _ApJ_ 809 (2015) L4 [1503.02632].
  * (33) A. Drlica-Wagner, K. Bechtol, E.S. Rykoff, E. Luque, A. Queiroz, Y.Y. Mao et al., _Eight Ultra-faint Galaxy Candidates Discovered in Year Two of the Dark Energy Survey_ , _ApJ_ 813 (2015) 109 [1508.03622].
  * (34) A. Chen, D. Huterer, S. Lee, A. Ferté, N. Weaverdyck, O. Alves et al., _Constraints on dark matter to dark radiation conversion in the late universe with DES-Y1 and external data_ , _Phys. Rev. D_ 103 (2021) 123528 [2011.04606].
  * (35) E.O. Nadler, A. Drlica-Wagner, K. Bechtol, S. Mau, R.H. Wechsler, V. Gluscevic et al., _Constraints on Dark Matter Properties from Observations of Milky Way Satellite Galaxies_ , _Phys. Rev. Lett._ 126 (2021) 091101 [2008.00022].
  * (36) M. Valluri, S. Chabanier, V. Iršič et al., _Snowmass2021 Cosmic Frontier White Paper: Dark Matter Constraints from DESI_ , _Contribution to Snowmass 2021_ (2022) .
  * (37) J.A. Tyson, D.M. Wittman and J.R.P. Angel, _The Dark Matter Telescope_ , in _Gravitational Lensing: Recent Progress and Future Go_ , T.G. Brainerd and C.S. Kochanek, eds., vol. 237 of _Astronomical Society of the Pacific Conference Series_ , p. 417, Jan., 2001 [astro-ph/0005381].
  * (38) A. Drlica-Wagner, Y.-Y. Mao, S. Adhikari, R. Armstrong, A. Banerjee, N. Banik et al., _Probing the Fundamental Nature of Dark Matter with the Large Synoptic Survey Telescope_ , _arXiv e-prints_ (2019) arXiv:1902.01055 [1902.01055].
  * (39) Vera C. Rubin Observatory LSST Solar System Science Collaboration, R.L. Jones, M.T. Bannister, B.T. Bolin, C.O. Chandler, S.R. Chesley et al., _The Scientific Impact of the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST) for Solar System Science_ , _Bulletin of the AAS_ 53 (2020) arXiv:2009.07653 [2009.07653].
  * (40) N.P. Pitjev and E.V. Pitjeva, _Constraints on dark matter in the solar system_ , _Astronomy Letters_ 39 (2013) 141–149.
  * (41) T. Kumar Poddar, S. Mohanty and S. Jana, _Constraints on long range force from perihelion precession of planets in a gauged $L_{e}-L_{\mu,\tau}$ scenario_, 2002.02935.
  * (42) Y.-D. Tsai, Y. Wu, S. Vagnozzi and L. Visinelli, _Asteroid astrometry as a fifth-force and ultralight dark sector probe_ , 2107.04038.
  * (43) A. Peter, Y.-Y. Mao et al., _Snowmass2021 Cosmic Frontier White Paper: A Flagship Dark Matter Experiment with the Vera C. Rubin Observatory_ , _Contribution to Snowmass 2021_ (2022) .
  * (44) K. Heitmann et al., _Snowmass2021 Cosmic Frontier White Paper: Rubin The Next-Generation_ , _Contribution to Snowmass 2021_ (2022) .
  * (45) C. Schultz, J. Oñorbe, K.N. Abazajian and J.S. Bullock, _The high-z universe confronts warm dark matter: Galaxy counts, reionization and the nature of dark matter_ , _MNRAS_ 442 (2014) 1597 [1401.3769].
  * (46) P. Dayal, A. Mesinger and F. Pacucci, _Early Galaxy Formation in Warm Dark Matter Cosmologies_ , _ApJ_ 806 (2015) 67 [1408.1102].
  * (47) D. Khimey, S. Bose and S. Tacchella, _Degeneracies between baryons and dark matter: the challenge of constraining the nature of dark matter with JWST_ , _MNRAS_ 506 (2021) 4139 [2010.10520].
  * (48) A. Rudakovskyi, A. Mesinger, D. Savchenko and N. Gillet, _Constraints on warm dark matter from UV luminosity functions of high-z galaxies with Bayesian model comparison_ , _MNRAS_ 507 (2021) 3046 [2104.04481].
  * (49) J. Southworth, _DEBCat: A Catalog of Detached Eclipsing Binary Stars_ , in _Living Together: Planets, Host Stars and Binaries_ , S.M. Rucinski, G. Torres and M. Zejda, eds., vol. 496 of _Astronomical Society of the Pacific Conference Series_ , p. 164, July, 2015 [1411.1219].
  * (50) D. Windemuth, E. Agol, A. Ali and F. Kiefer, _Modelling Kepler eclipsing binaries: homogeneous inference of orbital and stellar properties_ , _MNRAS_ 489 (2019) 1644 [1908.00139].
  * (51) S. Chakrabarti, D.J. Stevens, J. Wright, R.R. Rafikov, P. Chang, T. Beatty et al., _Eclipse timing the Milky Way’s gravitational potential_ , _arXiv e-prints_ (2021) arXiv:2112.08231 [2112.08231].
  * (52) D. Spergel, N. Gehrels, C. Baltay, D. Bennett, J. Breckinridge, M. Donahue et al., _Wide-Field InfrarRed Survey Telescope-Astrophysics Focused Telescope Assets WFIRST-AFTA 2015 Report_ , _arXiv e-prints_ (2015) arXiv:1503.03757 [1503.03757].
  * (53) R. Akeson, L. Armus, E. Bachelet, V. Bailey, L. Bartusek, A. Bellini et al., _The Wide Field Infrared Survey Telescope: 100 Hubbles for the 2020s_ , _arXiv e-prints_ (2019) arXiv:1902.05569 [1902.05569].
  * (54) M. Oguri and P.J. Marshall, _Gravitationally lensed quasars and supernovae in future wide-field optical imaging surveys_ , _MNRAS_ 405 (2010) 2579 [arXiv:1001.2037].
  * (55) D. Hendel, K.V. Johnston, R.K. Patra and B. Sen, _A machine-vision method for automatic classification of stellar halo substructure_ , _MNRAS_ 486 (2019) 3604 [1811.10613].
  * (56) S. Pearson, T.K. Starkenburg, K.V. Johnston, B.F. Williams, R.A. Ibata and R. Khan, _Detecting Thin Stellar Streams in External Galaxies: Resolved Stars and Integrated Light_ , _ApJ_ 883 (2019) 87 [1906.03264].
  * (57) N. Banik and J. Bovy, _Effects of baryonic and dark matter substructure on the Pal 5 stream_ , _MNRAS_ 484 (2019) 2009 [1809.09640].
  * (58) LIGO Scientific, Virgo collaboration, _Observation of Gravitational Waves from a Binary Black Hole Merger_ , _Phys. Rev. Lett._ 116 (2016) 061102 [1602.03837].
  * (59) LIGO Scientific, Virgo collaboration, _GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral_ , _Phys. Rev. Lett._ 119 (2017) 161101 [1710.05832].
  * (60) LIGO Scientific, VIRGO, KAGRA collaboration, _GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run_ , 2111.03606.
  * (61) LIGO Scientific, VIRGO, KAGRA collaboration, _The population of merging compact binaries inferred using gravitational waves through GWTC-3_ , 2111.03634.
  * (62) KAGRA, LIGO Scientific, Virgo, VIRGO collaboration, _Prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo and KAGRA_ , _Living Rev. Rel._ 21 (2018) 3 [1304.0670].
  * (63) LIGO Scientific collaboration, _Gravitational wave astronomy with LIGO and similar detectors in the next decade_ , 1904.03187.
  * (64) J. Miller, L. Barsotti, S. Vitale, P. Fritschel, M. Evans and D. Sigg, _Prospects for doubling the range of Advanced LIGO_ , _Phys. Rev. D_ 91 (2015) 062005 [1410.5882].
  * (65) LIGO Scientific, Virgo, KAGRA collaboration, _Constraints on dark photon dark matter using data from LIGO’s and Virgo’s third observing run_ , 2105.13085.
  * (66) LIGO Scientific, VIRGO, KAGRA collaboration, _Search for subsolar-mass binaries in the first half of Advanced LIGO and Virgo’s third observing run_ , 2109.12197.
  * (67) A.H. Nitz and Y.-F. Wang, _Broad search for gravitational waves from subsolar-mass binaries through LIGO and Virgo’s third observing run_ , 2202.11024.
  * (68) J. Zhang, Z. Lyu, J. Huang, M.C. Johnson, L. Sagunski, M. Sakellariadou et al., _First Constraints on Nuclear Coupling of Axionlike Particles from the Binary Neutron Star Gravitational Wave Event GW170817_ , _Phys. Rev. Lett._ 127 (2021) 161101 [2105.13963].
  * (69) K.K.Y. Ng, S. Vitale, O.A. Hannuksela and T.G.F. Li, _Constraints on Ultralight Scalar Bosons within Black Hole Spin Measurements from the LIGO-Virgo GWTC-2_ , _Phys. Rev. Lett._ 126 (2021) 151102 [2011.06010].
  * (70) J. Ziegler and K. Freese, _Filling the black hole mass gap: Avoiding pair instability in massive stars through addition of nonnuclear energy_ , _Phys. Rev. D_ 104 (2021) 043015 [2010.00254].
  * (71) M.S. Madhavacheril, N. Sehgal and T.R. Slatyer, _Current dark matter annihilation constraints from CMB and low-redshift data_ , _Phys. Rev. D_ 89 (2014) 103508 [1310.3815].
  * (72) Planck Collaboration, N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi et al., _Planck 2018 results. VI. Cosmological parameters_ , _A &A_ 641 (2020) A6 [1807.06209].
  * (73) T. Namikawa, Y. Guan, O. Darwish, B.D. Sherwin, S. Aiola, N. Battaglia et al., _Atacama Cosmology Telescope: Constraints on cosmic birefringence_ , _Phys. Rev. D_ 101 (2020) 083527 [2001.10465].
  * (74) F. Bianchini, W.L.K. Wu, P.A.R. Ade, A.J. Anderson, J.E. Austermann, J.S. Avva et al., _Searching for anisotropic cosmic birefringence with polarization data from SPTpol_ , _Phys. Rev. D_ 102 (2020) 083504 [2006.08061].
  * (75) M.A. Fedderke, P.W. Graham and S. Rajendran, _Axion dark matter detection with CMB polarization_ , _Phys. Rev. D_ 100 (2019) 015040 [1903.02666].
  * (76) BICEP/Keck, P.A.R. Ade, Z. Ahmed, M. Amiri, D. Barkats, R. Basu Thakur et al., _BICEP/Keck XII: Constraints on axionlike polarization oscillations in the cosmic microwave background_ , _Phys. Rev. D_ 103 (2021) 042002 [2011.03483].
  * (77) BICEP/Keck Collaboration, :, P.A.R. Ade, Z. Ahmed, M. Amiri, D. Barkats et al., _BICEP / Keck XIV: Improved constraints on axion-like polarization oscillations in the cosmic microwave background_ , _arXiv e-prints_ (2021) arXiv:2108.03316 [2108.03316].
  * (78) R. Hložek, D.J.E. Marsh, D. Grin, R. Allison, J. Dunkley and E. Calabrese, _Future CMB tests of dark matter: Ultralight axions and massive neutrinos_ , _Phys. Rev. D_ 95 (2017) 123511 [1607.08208].
  * (79) R. Hložek, D.J.E. Marsh and D. Grin, _Using the full power of the cosmic microwave background to probe axion dark matter_ , _MNRAS_ 476 (2018) 3063 [1708.05681].
  * (80) Z. Li, V. Gluscevic, K.K. Boddy and M.S. Madhavacheril, _Disentangling dark physics with cosmic microwave background experiments_ , _Phys. Rev. D_ 98 (2018) 123524 [1806.10165].
  * (81) D. Han and N. Sehgal, _Mitigating Foreground Bias to the CMB Lensing Power Spectrum for a CMB-HD Survey_ , _arXiv e-prints_ (2021) arXiv:2112.02109 [2112.02109].