# Accelerated Structure Formation: the Early Emergence of Massive Galaxies and
Clusters of Galaxies

Stacy S. McGaugh  Department of Astronomy, Case Western Reserve University,
Cleveland, OH 44106, USA  James M. Schombert  Institute for Fundamental
Science, University of Oregon, Eugene, OR 97403, USA  Federico Lelli  INAF –
Arcetri Astrophysical Observatory, Largo Enrico Fermi 5, I-50125, Firenze,
Italy  Jay Franck  1108 Sherman St., Longmont, CO 80501, USA

###### Abstract

Galaxies in the early universe appear to have grown too big too fast,
assembling into massive, monolithic objects more rapidly than anticipated in
the hierarchical $\Lambda$CDM structure formation paradigm. The available data
are consistent with there being a population of massive galaxies that form
early ($z\gtrsim 10$) and follow an approximately exponential star formation
history with a short ($\lesssim 1$ Gyr) e-folding timescale on the way to
becoming massive ($M_{*}\approx 10^{11}\;\mathrm{M}_{\sun}$) galaxies by
$z=0$, consistent with the traditional picture for the evolution of giant
elliptical galaxies. Observations of the kinematics of spiral galaxies as a
function of redshift similarly show that massive disks and their scaling
relations were in place at early times, indicating a genuine effect in mass
that cannot be explained as a quirk of luminosity evolution. That massive
galaxies could form by $z=10$ was explicitly predicted in advance by MOND. We
discuss some further predictions of MOND, such as the early emergence of
clusters of galaxies and the cosmic web.

Cold dark matter (265), Galaxy evolution (594), Galaxy formation (595), Galaxy
masses (607), High-redshift galaxies (734), MOND (1069), Protogalaxies (1298)

##  1 Introduction

The formation and evolution of galaxies has been a central concern of
cosmology since Hubble (1929) demonstrated that spiral nebulae are external
stellar systems of size comparable to the Milky Way. Ideas about the formation
of galaxies have ranged from the monolithic collapse of giant gas clouds
(Eggen et al., 1962) to assembly through the merger of numerous protogalactic
fragments (Searle & Zinn, 1978). With the launch of JWST, we now have the
opportunity to directly observing the assembly of galaxies at early epochs,
providing a direct test of these ideas.

In $\Lambda$CDM, galaxies form in dark matter halos that originate from
primordial density fluctuations that start small and grow gradually (Schramm,
1992; Peebles, 1993). Massive halos, and the galaxies that they contain,
assemble from the merger of smaller halos (Wechsler & Tinker, 2018). This
hierarchical formation of structure is often depicted as a merger tree
(Somerville & Kolatt, 1999). The objects that are giant galaxies today are the
products of the assembly of many protogalactic fragments.

There are two basic effects in play: (i) the assembly of mass and (ii) the
emergence of an observable, luminous galaxy through the accretion of gas and
its conversion into stars. The timeline of mass assembly (i) is well
quantified by N-body simulations (De Lucia et al., 2006; Srisawat et al.,
2013). The second step is highly uncertain, depending on many aspects of gas
physics and star formation. However, the luminosity of an individual galaxy
cannot outpace its assembly rate (Naab et al., 2009; van der Wel et al., 2009;
Nipoti et al., 2009). Observations of the luminosities of galaxies thus test
the predicted formation history.

We describe monolithic and hierarchical galaxy formation models to test with
the data in section 2. Constraints on the evolution of high redshift galaxies
predating the launch of JWST are discussed in section 3 and new insights from
JWST data are examined in section 4. Taken together, the data indicate that
structure formed in the early universe at an accelerated pace relative to the
predictions of $\Lambda$CDM. This result had been anticipated well in advance
of the observations (Sanders, 1998; McGaugh, 2015) as discussed in section 5.
Section 6 provides a succinct summary. We adopt a vanilla $\Lambda$CDM
universe with $\Omega_{m}=0.3$, $\Omega_{\Lambda}=0.7$, and
$H_{0}=70\;\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$ for cosmology-
dependent quantities.

##  2 Galaxy Formation Models

It is important to have at least two distinct hypotheses to compare and
contrast, so we consider both monolithic and hierarchical galaxy formation
models. The passive evolution of a monolithic galaxy that forms early is
motivated by traditional inferences about the evolutionary history of giant
ellipticals (Thomas et al., 2005; Renzini, 2006; Bregman et al., 2006;
Schombert & Rakos, 2009; Schombert, 2016). In contrast, hierarchical galaxy
formation is expected in $\Lambda$CDM (White & Frenk, 1991), with testable
predictions provided by both semi-analytic galaxy formation models (SAMs) and
hydrodynamical simulations. Though something of a straw-man on its own, the
monolithic case is useful as a proxy for the predictions (Sanders, 1998) of
MOND (Milgrom, 1983).

###  2.1 Monolithic Models

An important touchstone in galaxy evolution is the case of the passive
evolution of a monolithic island universe (Eggen et al., 1962). The assumption
implicit in this hypothesis is that practically all of the mass currently in a
galaxy has always been part of it; it evolves as a closed box since a
formation redshift $z_{f}$. This provides a convenient picture, but is an
unrealistic oversimplification. Galaxy-mass balls of gas do not magically
appear in the early universe; mass must assemble from the initial condition of
a nearly homogeneous early universe (Planck Collaboration et al., 2020). This
picture nevertheless provides a useful null hypothesis, and a starting point
for more realistic models that assemble mass rapidly if not instantaneously.

####  2.1.1 Exponential Star Formation History

The growth of the stellar mass of a monolithic galaxy is determined by its
star formation history. A common prescription for the passive evolution of a
predominantly old stellar population like that of a typical elliptical galaxy
(Bregman et al., 2006; Rakos et al., 2008; Schombert & Rakos, 2009; Schombert,
2016) is an exponential star formation history,

$\psi(t)=\psi_{0}e^{-u}.$ (1)

Here, $\psi_{0}$ is a star formation rate that sets the scale that leads to a
final mass $M_{f}$, and

$u=\frac{t-t_{i}}{\tau}$ (2)

where $t_{i}$ is the time after the Big Bang when star formation begins that
we equate to the redshift of galaxy formation $z_{f}$, and $\tau$ is the
timescale over which star formation activity fades. A population can be said
to be passively evolving if this timescale is much shorter than a Hubble time
so that most of the stars form in the early universe and evolve passively
thereafter. The stellar mass increases as

$M_{*}(t)=M_{f}(1-e^{-u}).$ (3)

With this prescription for the build-up of stellar mass $M_{*}(t)$ and the
time-redshift relation of vanilla $\Lambda$CDM, the luminosity evolution
$L(z)$ can be calculated using the methods of stellar population synthesis
(Renzini, 2006).

Franck & McGaugh (2017) constructed an exponential model with $\tau=1$ Gyr and
a formation redshift $z_{f}=10$ corresponding to $t_{i}=464$ Myr for vanilla
$\Lambda$CDM. This was done to provide a baseline against which to compare
more realistic models. It was intended as an unrealistic example of a
passively evolving galaxy that formed at absurdly high redshift, which
$z_{f}=10$ was considered to be at the time. Surprisingly, this particular
model proved to be the most successful of the many considered by Franck &
McGaugh (2017); we refer the reader to this work for other possibilities.

Here, we wish to characterize the evolution of a typical galaxy. To this end,
we utilize Schechter (1976) function fits to the luminosity functions of
clusters and protocluster candidates (Mancone et al., 2010; Wylezalek et al.,
2014; Franck & McGaugh, 2017) over a large range of redshifts. We take the
characteristic Schechter luminosity $L^{*}$ to be representative of these
populations of galaxies. This enables us to examine the redshift evolution of
the corresponding apparent magnitude $m^{*}$ and stellar mass $M^{*}_{*}$. The
virtue of this approach is that it provides a representation of the typical
galaxy in an entire galaxy population, not just an individual galaxy, and does
so for each cluster at every redshift.

The relation of a model galaxy’s luminosity to its stellar mass depends on the
adopted initial mass function (IMF) and the details of the population
modeling. These are uncertain at the factor of two level, if not more. Here we
adopt an empirical calibration by equating the final mass $M_{f}$ to the
characteristic stellar mass $M^{*}_{*}=9\times 10^{10}\;\mathrm{M}_{\sun}$ of
the Schechter fit to local early type galaxies (Driver et al., 2022) and by
matching the corresponding luminosity $L^{*}$ to the characteristic apparent
magnitude $m^{*}$ of cluster galaxies at $z\approx 1$ (Mancone et al., 2010).
This data-informed choice of the mass-to-light ratio is within the range
expected for the stellar population models built by Franck & McGaugh (2017):
evolutionary theory and data agree at the expected level.

####  2.1.2 Generalized Star Formation with Quenching

Implicit in the exponential model is the notion that the total baryonic mass
of a galaxy assembles promptly and star formation commences at a high rate
instantaneously upon assembly. All of the mass that will become stars by $z=0$
is present as gas at $z_{f}$ but forms no stars until $t_{i}$ when the star
formation rate is at its maximum. This is simple conceptually, but obviously
naive: stars may form in small clumps (e.g., globular clusters) while the
larger quasi-monolithic entity is still in the process of assembling, and gas
may continue to accrete and fuel star formation after the bulk of the quasi-
monolithic baryonic mass is in place. To improve on this without adding much
complexity, we also consider a generalization that allows for a finite ramp-up
of star formation before it quenches.

Kelson et al. (2016) show that stochastic star formation leads to an average
linear ramp up in the star formation rate $\psi\sim t$ as galaxies accrete
gas. This will quickly build up stellar mass as $M_{*}\sim t^{2}$. This
process is more monolithic than hierarchical, as it envisions in situ star
formation from gas accretion onto a single object. Indeed, star formation must
quench rapidly in order not to overproduce stellar mass. Regardless of the
precise mechanism by which quenching occurs (Peng et al., 2015), an obvious
choice to model it is an exponential attenuation with a short e-folding time.
Combining this with an initially linear ramp-up gives

$\psi(u)=\psi_{0}ue^{-u}$ (4)

This is only a slight modification to the traditional exponential star
formation history described above, providing it with a more realistic initial
condition. In principle, we could consider separate timescales for the ramp up
of star formation and for its quenching, and could also insert a time delay
for the commencement of quenching. We eschew these details for now as
unnecessary complications, as we seek only to quantify the approximate time
scales relevant to explaining observations of massive galaxies at high
redshift. We thus restrict ourselves to the two timescales $t_{i}$ and $\tau$
that are built into the definition of $u$ (eq. 2).

Figure 1: Merger trees for two model galaxies from the TNG50-1 simulation
(Pillepich et al., 2019; Nelson et al., 2019) selected to have $M_{*}\approx
9\times 10^{10}\;\mathrm{M}_{\sun}$ at $z=0$; i.e., the stellar mass of a
local $L^{*}$ early type galaxy (Driver et al., 2022). Mass assembles
hierarchically, starting from small halos at high redshift (bottom edge) with
the largest progenitor traced along the left of edge each merger tree. The
size of the symbol is proportional to the total halo mass and the color bar
illustrates the specific star formation rate. A galaxy that quenched long ago
is shown at left (labelled ETG); one in which star formation continues to the
present epoch is shown at right (LTG).

Integrating equation 4, the stellar mass grows as

$M_{*}(u)=M_{f}[1-(1+u)e^{-u}]$ (5)

where $M_{f}$ is the final stellar mass. While no individual galaxy will have
exactly this star formation history, eq. 5 provides a simple way to describe
the formation and quenching timescales that characterize of a population of
galaxies as represented by a typical $L^{*}$ galaxy.

We shall see that to explain bright galaxies at high redshift (Melia, 2023)
requires that both the formation time and the e-folding time of quenching be
rather short: $\tau\approx t_{i}\lesssim 0.5$ Gyr, corresponding to formation
redshifts $z_{f}>9$. These are obvious candidates to be the progenitors of
massive, local galaxies with $M_{f}\approx M^{*}_{*}$ at $z=0$. That some
galaxies have short quenching timescales and evolve into red and dead early
type galaxies is not surprising. That such galaxies can form as individual
objects that become massive already within the first billion years after the
big bang is surprising.

###  2.2 Hierarchical Models

In contrast to a monolithic model, the hierarchical formation of structure in
$\Lambda$CDM is a complex combination of in situ growth and growth via
merging. The largest galaxies are predicted to form latest, as they take the
longest to assemble. That large galaxies are observed to contain the oldest
stars (Bregman et al., 2006; Schombert, 2016) may thus seem like a
contradiction, but it may simply mean that many of the stars formed in
protogalaxies at early times prior to them merging into the final giant galaxy
(De Lucia et al., 2006; Cattaneo et al., 2008; van der Wel et al., 2009;
Nipoti et al., 2009). We thus expect to see many small precursor galaxies at
high redshift for every modern giant (Newman et al., 2012; Conselice et al.,
2022).

There are many papers in the literature discussing the evolution of galaxies,
including theoretical works that attempt to predict how observable galaxies
are associated with their parent dark matter halos. While important details
vary from model to model (Knebe et al., 2015), the basic prediction of the
hierarchical build up of mass is common to all as it is fundamental to the
$\Lambda$CDM structure formation paradigm. This is well documented by many
simulations, for example the IllustrisTNG suite of magnetohydrodynamical
simulations (Springel et al., 2018; Pillepich et al., 2018; Marinacci et al.,
2018; Naiman et al., 2018; Nelson et al., 2018). Fig. 1 illustrates
hierarchical galaxy formation as realized in the high resolution TNG50
simulation (Pillepich et al., 2019; Nelson et al., 2019).

An important aspect of hierarchical galaxy formation is that a massive galaxy
at $z=0$ is the sum of many parts. As we look to high redshift, we do not
expect to see an early version of the modern galaxy, but rather its many
precursor components. In contrast to a monolithic galaxy, there is no single
entity whose evolution we can trace. The closest thing to that is the largest
progenitor, which is necessarily smaller at every epoch than the equivalent
monolith. For example, a monolith that forms at $z_{f}=10$ and evolves with an
exponential star formation history with an e-folding time $\tau=1$ Gyr will
form half of its stellar mass by $z=5$. In contrast, hierarchically assembled
galaxies in the Illustris simulation (Rodriguez-Gomez et al., 2016) do not
reach this benchmark until $z\approx 0.7$, taking about half a Hubble time to
form half their stars.

The observable light depends on many factors, including the star formation
efficiency, the stellar IMF, the mode of gas accretion, and the effects of
stellar feedback. These factors provide considerable flexibility to adjust
models to account for data, so, as with any theory, the important predictions
are those that were made in advance of observation (Mo et al., 1998; Sanders,
1998, 2008; McGaugh, 2015; Henriques et al., 2015; Rodriguez-Gomez et al.,
2016; Anglés-Alcázar et al., 2017; Behroozi & Silk, 2018; McGaugh, 2022).
Whenever possible, it is better to trace the underlying dark mass, the
assembly of which is well predicted.

Fig. 1 makes viscerally clear why it is surprising to observe massive galaxies
at high redshift. Each present-day $L^{*}$ galaxy is predicted to be split
into a multitude of small progenitors. At $z>6$, all progenitors are tiny,
including the most massive one. This only becomes more severe at $z>10$. Since
it takes a long time to hierarchically assemble the mass necessarily to make
an $L^{*}$ galaxy, it should be possible to distinguish this prediction from
the null hypothesis of a monolith in spite of the uncertainties in the details
of star formation. Many small objects at $z=10$ does not look like one big
galaxy.

##  3 High Redshift Galaxies Before JWST

As we look to high redshift, the first objects we see are always the brightest
beacons that have been lit at that time. We must therefore take care to
consider how typical these objects are. To do so, we utilize Schechter (1976)
function fits to quantify the characteristic stellar mass $M^{*}_{*}$ of large
number of galaxies at each redshift. Locally, giant ellipticals galaxies have
$M^{*}_{*}=9\times 10^{10}\,h_{70}^{-2}\;\mathrm{M}_{\sun}$ (Driver et al.,
2022). We wish to know the evolution of the typical galaxy, $M^{*}_{*}(z)$. Of
course, we cannot see the evolution of a single galaxy over cosmic time, and
must attempt to infer $M^{*}_{*}(z)$ from snapshots at different redshifts.
This is famously problematic, as we can never relate a particular galaxy to
its progenitor at higher redshift (Bell et al., 2004). Nevertheless, we can
compare the data to evolutionary tracks from models to see which might work
and which do not.

Figure 2: The redshift dependence of the Spitzer [4.5] apparent magnitude
$m^{*}$ of Schechter function fits to populations of galaxies in clusters and
candidate protoclusters. Data from Mancone et al. (2010, black circles),
Wylezalek et al. (2014, dark blue circles), and Franck & McGaugh (2017, blue
circles) all have spectroscopic redshifts. The orange line is the prediction
of the Munich galaxy formation model (Henriques et al., 2015) based on the
Millennium simulations (Springel et al., 2005; Boylan-Kolchin et al., 2009).
Open squares are mock observations of this model using the same algorithm that
was applied to the data (Franck & McGaugh, 2016a). The predicted
characteristic magnitude is fainter than observed, diverging systematically
for $z>2$. The purple line is a model of a galaxy formed at $z_{f}=10$ with an
expanential star formation history (eq. 1) with $\tau=1$ Gyr (Franck &
McGaugh, 2017) normalized at $z\approx 1$. Galaxies like this apparently exist
in the high redshift universe, before they were predicted to have assembled,
and are common enough to dominate the Schechter fit for $m^{*}$.

The first data from JWST has brought the formation epoch of galaxies and
evolution of $M^{*}_{*}(z)$ into sharp focus. While this is a story in
progress, it is possible to place these data in the context of precursor work
with deep fields observed by HST and Spitzer. Critically, we are not limited
to photometric redshifts; there exist many spectroscopic redshifts for many
sources (see, e.g., the compilations of Franck & McGaugh, 2016a, b).

###  3.1 Galaxies with Spectroscopic Redshifts

Giant elliptical galaxies are routinely found in dense regions like clusters
of galaxies (Dressler et al., 1997) that typically have well-defined red
sequences (Bell et al., 2004). This makes clusters and protoclusters
convenient environments in which to find a sufficient number of galaxies at
the same redshift to construct luminosity functions. This has been done to
progressively higher redshifts by Mancone et al. (2010), Wylezalek et al.
(2014), and Franck & McGaugh (2017). These studies are all informed by
galaxies with spectroscopically observed redshifts, so there is no ambiguity
about their cosmic distance as can happen with photometric redshifts. The
structures identified as [proto]clusters are redshift spikes in the $N(z)$
diagrams of redshift surveys (Franck & McGaugh, 2016a, b), so they represent a
population of galaxies at the same point in the history of the universe
regardless of whether they are indeed a bound structure.

Fig. 2 shows the dependence of the AB Spitzer [4.5] apparent magnitude $m^{*}$
(Franck & McGaugh, 2017) corresponding to the characteristic luminosity
$L^{*}$ obtained from Schechter function fits to many dozens, and sometimes
hundreds of galaxies in clusters and protocluster candidates. This is a
characteristic quantity of the galaxy population, not just a few anecdotal
examples. Franck & McGaugh (2017) found no significant difference between the
characteristic luminosity of cluster luminosity functions and that of galaxies
in the surrounding fields at $z>2$, so there does not appear to be a strong
environment bias at high redshift.

Galaxies become fainter with increasing redshift, as expected (Fig. 2).
However, observed galaxies are brighter than anticipated by contemporaneous
models, e.g., the Munich galaxy formation model (Henriques et al., 2015). The
model behaves as expected: earlier galaxies are small protogalaxies, so their
characteristic luminosity becomes progressively fainter with increasing
redshift. This generic expectation of $\Lambda$CDM diverges progressively from
the data at $z>2$ (Fig. 2).

As a check that the same quantity was being measured in both data and model,
Franck (2018) made mock observations of lightcones from the Munich model
(Henriques et al., 2015). The same algorithm was applied to the mock data that
was used to identify protocluster candidates in the real data (Franck &
McGaugh, 2016a, b). The mock observations recover basically the same answer
that is known directly from the model (squares in Fig. 2). If the real
universe looked like the prediction of the Munich model, we could easily tell.
While it is tempting to blame the details of star formation in this particular
model, the primary problem is more fundamental. Model galaxies are faint
because hierarchical assembly is incomplete at $z>3$ (compare Figs. 1 and 2).

In contrast, the data fall around the line representing a monolithic giant
that formed at $z_{f}=10$ and followed an exponential star formation history
(eq. 1). If massive galaxies form early and evolve passively, it would look
like the characteristic magnitudes that are observed. In addition to capturing
the general trend of the data at high redshift, the data are very well fit at
low redshift ($z<1.5$). This represents passive stellar evolution over most of
cosmic time ($\sim 9$ Gyr) after essentially all the stellar mass has been
formed and early stochastic variations have had time to subside. These data
look very much like the evolution of a massive monolith that was assembled
into a single object already at high redshift, and not like $\Lambda$CDM
models in which the largest progenitor should have been much smaller and
fainter at $z>2$ (Figs. 1 and 2).

As noted in section 2.1.1, no single model line will fit all the data in Fig.
2. The scatter at high redshift presumably reflects stochastic variations in
star formation rates at early times (Kelson et al., 2016; Pallottini &
Ferrara, 2023) before the red sequence was established (Bell et al., 2004;
Rakos et al., 2008; Schombert & Rakos, 2009; Franck et al., 2015).
Nevertheless, the evolutionary trend predicted by the monolithic model
captures the essence of the data in a way that the nominal prediction of
$\Lambda$CDM does not.

###  3.2 Galaxies at $z>6$ Before JWST

The bulk of the data discussed above are for $z<4$ with a couple of candidate
protoclusters extending to $z\approx 6$ (Franck & McGaugh, 2016b) There have
been many studies of galaxies to still higher redshift that predate JWST
(e.g., Finkelstein, 2016; Grazian et al., 2015; Song et al., 2016; Stefanon et
al., 2021). These works provide $M^{*}_{*}$ for field galaxies with stellar
mass functions measured independently of any of the data described above,
albeit at the cost of relying more, if not entirely, on photometric redshifts.

Figure 3: The characteristic stellar mass of the Schechter mass function
$M^{*}_{*}$ as a function of time with the corresponding redshift noted at
top. The data from Fig. 2 (Mancone et al., 2010; Wylezalek et al., 2014;
Franck & McGaugh, 2017) are augmented with higher redshift data (Stefanon et
al., 2021, light blue points). The purple line is the passively evolving model
from Fig. 2 normalized to $M^{*}_{*}=9\times 10^{10}\;\mathrm{M}_{\sun}$ for
local elliptical galaxies (Driver et al., 2022, grey point). The dotted orange
line shows the build-up of the most massive progenitor of a galaxy that
reaches this mass by $z=0$ in the Munich SAM (Henriques et al., 2015). This is
indistinguishable from the result of Illustris (Rodriguez-Gomez et al., 2016,
red dashed line). Stellar mass in the FIRE simulation (Anglés-Alcázar et al.,
2017, green dot-dash line) grows faster, but only a little.

Fig. 3 shows the characteristic stellar mass $M^{*}_{*}$ as a function of
redshift. The data from Fig. 2 are shown assuming an exponential star
formation history to provide a mapping from magnitude to mass that preserves
the distribution of the data. This compares well to the data at higher
redshift for which the stellar mass estimates are entirely independent
(Finkelstein, 2016; Grazian et al., 2015; Song et al., 2016).

We include in Fig. 3 the data of Stefanon et al. (2021) together with those
from Fig. 2. This is the most conservative choice in the sense that the
stellar mass estimates of Stefanon et al. (2021) are the lowest available at
these redsfhits. This happens in large part because Stefanon et al. (2021)
make larger corrections for line emission from non-stellar sources. The data
are all consistent; they simply attribute less of the observed luminosity to
stars.

The data are consistent with a population of massive galaxies that formed
early and evolved passively. Despite its naive simplicity, the exponential
star formation history (eq. 3 with $\tau=1$ Gyr) provides a remarkably
reasonable depiction of the build up of the characteristic stellar mass seen
in Fig. 3. This is highly non-trivial, as the mass build-up happens early
while the luminosity evolution is most pronounced at late times (Fig. 2).

More complex star formation histories are admissible. Indeed, stochastic star
formation may well drive the scatter seen in the data around $z\approx 3$ when
the universe was only $\sim 2$ Gyr old and stellar populations were
necessarily still young. Regardless of the details of the early star formation
history, it appears that there exists a population of massive galaxies that
formed early and in which most of the stars were made long ago in a single
object rather than the multiplicity of progenitors envisioned in hierarchical
galaxy formation.

Fig. 3 also shows the a priori predictions of several $\Lambda$CDM models.
These include the Munich SAM (Henriques et al., 2015, as in Fig. 2) and the
hydrodynamical simulations Illustris (Rodriguez-Gomez et al., 2016) and FIRE
(Anglés-Alcázar et al., 2017). These all show basically the same thing.
Galaxies are predicted to assemble gradually, with their most massive
progenitor not reaching half the final stellar mass until half a Hubble time
has passed ($z<1$). To give a specific example, the Munich SAM reaches half
the final stellar mass at $z=0.68$ when the universe is 7.3 Gyr old. The star
formation prescription of FIRE makes more stars earlier, but it is only a
small shift of the same basic result: mass assembles too slowly in
$\Lambda$CDM models. Making star formation more efficient makes more stars
earlier, but it does not assemble them into the massive individual galaxies
that are observed.

The shortfall of stellar mass in individual galaxies is especially severe at
high redshift. At $z\approx 3$, the largest progenitor of an $L^{*}$ galaxy is
only a tenth of its eventual $z=0$ mass in FIRE. It is even less in Illustris,
about 3%. At $z\approx 5$, individual progenitor galaxies are not expected to
have grown massive enough to even appear on Fig. 3, let alone to do so at
$z\approx 10$. Yet at these redshifts the data show that many galaxies with
masses that already approach $M^{*}_{*}(z=0)$ — enough galaxies to define
$L^{*}$ in a Schechter fit for every point in Fig. 3. This is the normal
galaxy population, not just a few extreme individuals. Moreover, spectroscopic
redshifts are required to be a part of the samples (Franck & McGaugh, 2016a,
b) that inform the Schechter function fits of Franck & McGaugh (2017), so
there is no uncertainty due to photometric redshifts.

###  3.3 Galaxy Kinematics at Intermediate Redshifts

Kinematic observations provide an independent line of evidence that mature
galaxies appeared early in the history of the Universe. Disk galaxies at
intermediate redshift ($1<z<3$) are observed to have large rotation speeds
(Neeleman et al., 2020), to be dynamically cold (Di Teodoro et al., 2016;
Lelli et al., 2018, 2023; Rizzo et al., 2023), and to follow scaling relations
like Tully-Fisher (Miller et al., 2012; Pelliccia et al., 2017). The Tully-
Fisher relation persists up to at least $z\approx 2.5$ when the universe was
$\sim 2.5$ Gyr old (Nestor Shachar et al., 2023). Individual galaxies with
high circular speeds and relatively high rotation-to-velocity dispersion
ratios are found up to $z\approx 5$ (Rizzo et al., 2020, 2021; Lelli et al.,
2021; Roman-Oliveira et al., 2023), barely one billion years after the Big
Bang. The early appearance of massive, dynamically cold disks in the first few
billion years after the Big Bang is contradictory to both early $\Lambda$CDM
predictions (Mo et al., 1998, “present-day discs were assembled recently (at
$z\leq 1$)”) and the expected hierarchical assembly (Fig. 1) in which early
disks are expected to be small and dynamically hot (Dekel & Burkert, 2014;
Zolotov et al., 2015; Krumholz et al., 2018; Pillepich et al., 2019).

Figure 4: The baryonic Tully-Fisher (left) and dark matter fraction–surface
brightness (right) relations. Local galaxy data (circles) are from Lelli et
al. (2019) for the Tully-Fisher relation and for spiral disks (Hubble stage
$T<9$) from SPARC Lelli et al. (2016) for the dark matter fraction–surface
brightness relation. Higher redshift data (squares) are from Nestor Shachar et
al. (2023) in bins with equal numbers of galaxies color coded by redshift:
$0.6<z<1.22$ (blue), $1.22<z<2.14$ (green), and $2.14<z<2.53$ (red). Open
squares with error bars illustrate the typical uncertainties. The relations
known at low redshift also appear at higher redshift with no clear indication
of evolution over a lookback time up to 11 Gyr.

The high rotation speeds observed in early disk galaxies are remarkable. These
sometimes exceed 250 (Neeleman et al., 2020) or even 300
$\mathrm{km}\,\mathrm{s}^{-1}$ (Nestor Shachar et al., 2023), comparable to
the most massive local spirals (Noordermeer et al., 2007; Di Teodoro et al.,
2021, 2023). This is important, because the kinematics indicate large
dynamical masses for these early galaxies. The problem is not limited to
luminosity and the corresponding stellar mass; the underlying dynamical mass
is also larger than expected.

The study of kinematics at still higher redshift is a nascent field, but there
are already important individual cases. For example, the kinematics of ALESS
073.1 at $z\approx 5$ indicate the presence of a massive stellar bulge as well
as a rapidly rotating disk (Lelli et al., 2021). A similar case has been
observed at $z\approx 6$ (Tripodi et al., 2023). These kinematic observations
indicate the presence of mature, massive disk galaxies well before they were
expected to be in place (Pillepich et al., 2019; Wardlow, 2021). This is
consistent with the ubiquity of disk galaxies in JWST images up to $z\sim 6$
(Ferreira et al., 2022, 2023; Kuhn et al., 2023).

Fig. 4 shows two scaling relations at both low and high redshift: the baryonic
mass–circular speed relation (Tully & Fisher, 1977; McGaugh et al., 2000) and
the dark matter fraction–surface brightness relation (de Blok & McGaugh, 1997;
Starkman et al., 2018). Both relations are clearly present in the data of
Nestor Shachar et al. (2023). Indeed, there is no clear sign of evolution in
either relation up to $z\approx 2.5$. The good agreement between low and high
redshift samples is remarkable given that we have made no attempt to reconcile
the precise definition of baryonic mass, which is sensitive to the stellar
population model (Schombert et al., 2019), or circular velocity measurement
(Lelli et al., 2019). Any systematic differences are apparently within the
scatter induced by measurement uncertainties.

The dark matter fraction $f_{DM}=1-(V_{b}/V_{c})^{2}$, where $V_{c}$ is the
observed circular velocity and $V_{b}$ is that due to the baryons at the same
radius. The latter quantity is maximized at 2.2 scale lengths for an
exponential disk (Freeman, 1970). Many high surface brightness galaxies are
maximal disks in which $V_{b}\rightarrow V_{c}$ so $f_{DM}\rightarrow 0$
(Starkman et al., 2018) and becomes very sensitive to the stellar population
model, which determines the amplitude of $V_{b}$. This is less critical for
low surface brightness galaxies, which have long been known to be dark matter
dominated (de Blok & McGaugh, 1997). Fig. 4 shows that the relation between
the dark matter fraction and surface brightness was already in place at
intermediate redshift (Nestor Shachar et al., 2023) and has not evolved
noticeably over cosmic time (Sharma et al., 2023).

Figure 5: The UV luminosity function (left) observed by Donnan et al. (2024,
points) compared to that predicted for $\Lambda$CDM by (Yung et al., 2023,
lines) as a function of redshift. Lines and points are color coded by
redshift, with dark blue, light blue, green, orange, and red corresponding to
$z=9$, 10, 11, 12, and 14, respectively. There is a clear excess in the number
density of galaxies that becomes more pronounced with redshift, ranging from a
factor of $\sim 2$ at $z=9$ to an order of magnitude at $z\geq 11$ (right).

Kinematic observations to date show that dynamically cold, massive disks are
already present in the universe at early times. These disk galaxies appear to
follow the same kinematic scaling relations that are known locally. The
presence of dynamically massive galaxies in settled kinematic scaling
relations corroborates the ample photometric and spectroscopic data predating
JWST (Rocca-Volmerange et al., 2004; Steinhardt et al., 2016; Franck &
McGaugh, 2017; Merlin et al., 2019) that indicate that galaxies grew too big
too fast.

##  4 High Redshift Galaxies with JWST

JWST has made the observation of galaxies at $z>10$ seem mundane, so it is
worth recalling that this is a recent development. Franck & McGaugh (2017)
built the model with $z_{f}=10$ shown in Figures 2 and 3 as an extreme upper
limit in the context of the widespread presumption at the time that there was
no possibility for massive galaxies to have formed that early. Consequently,
early JWST results came as a surprise. However, they merely extend the trends
already seen in earlier data, corroborating previous indications that galaxies
grew too big too fast (e.g., Finkelstein et al., 2022a; Merlin et al., 2022;
Melia, 2023; Ferrara et al., 2023). While it is early days for JWST, the
simple observation is that the high redshift universe contains a bounty of
bright, morphologically mature galaxies (Ferreira et al., 2022, 2023) that are
more luminous than had been anticipated by $\Lambda$CDM models (e.g., Yung et
al., 2019a, 2022; Behroozi et al., 2020).

###  4.1 The UV Luminosity Function

There is a clear excess in the number density of $\sim
10^{10}\;\mathrm{M}_{\sun}$ galaxies (Stefanon et al., 2021) over the
predictions of contemporaneous $\Lambda$CDM models (Yung et al., 2019a, b) at
$z\approx 8$ (McGaugh, 2024). This becomes more challenging to assess at
$z>10$ where much of the observed luminosity is in the ultraviolet where the
short-lived nature of high mass stars makes it is difficult to assess the
corresponding stellar mass. Bearing this caveat in mind, we can nevertheless
compare observations (Donnan et al., 2024) and predictions (Yung et al., 2023)
(Fig. 5). Again we see a clear excess that is apparent at all luminosities.
Similar results follow from comparison to other predictions (e.g., Behroozi et
al., 2020) and other analyses of the observations (Robertson et al., 2023).
$\Lambda$CDM models did not anticipate the large number of relatively bright
galaxies that are observed.

The excess in the number density of UV-bright galaxies is not subtle, being an
order of magnitude at $z\geq 11$. This is true despite an upward adjustment of
the density in the models by 0.3 to 0.4 dex from Yung et al. (2019a) to Yung
et al. (2023). One can imagine a number of ways to further enhance the UV
luminosity per unit mass (Finkelstein et al., 2023), but the salient
observational fact is that the UV luminosity function barely evolves over the
redshift range that the dark matter halo mass function is evolving rapidly.
Consequently, any appeal to the efficiency of UV light production must
necessarily be fine-tuned to balance the barely-evolving UV luminosity
function with the rapidly evolving dark matter halo mass function over a
rather small window of cosmic time, there being only $\sim 10^{8}$ years
between $z=14$ and 11.

Irrespective of the ultimate interpretation, Fig. 5 clearly illustrates the
excess in the number of bright high redshift galaxies over that predicted a
priori.

###  4.2 The Mass and Evolution of Individual Galaxies

Despite the clear excess in bright galaxies seen in Fig. 5, it is not yet
possible to define a robust population-wide estimate of the corresponding
stellar mass $M^{*}_{*}$ as seen in Fig. 3. Nevertheless, there are many
individual galaxies (Fig. 6) that have a reasonably persuasive claim to being
high mass at high redshift (Adams et al., 2023; Atek et al., 2023; Labbé et
al., 2023; Naidu et al., 2022; Harikane et al., 2023; Finkelstein et al.,
2022b; Donnan et al., 2023; Robertson et al., 2023). Most of these are based
on photometric redshifts, of which we may reasonably be skeptical. However, it
seems unlikely that they are all grossly incorrect given the many independent
estimates. Moreover, the essential outstanding feature that they share is how
relatively bright they are: galaxies simply do not appear to be as faint as
anticipated by $\Lambda$CDM models (Fig. 2). Indeed, a change in the
photometric redshift (as sometimes happens: Adams et al., 2023) does not
necessarily reduce the stellar mass, as a reduction in distance is accompanied
by a shift of the flux to bands where the stellar mass-to-light ratio is
larger than in the UV. The data discussed by Labbé et al. (2023) are a case in
point: all of the initial redshifts and masses were revised downwards after
accounting for the on-sky calibration of JWST, but all of them remain
problematic in terms of their mass for their redshift. The observational
situation will continue to improve as spectroscopic redshifts become available
(Wang et al., 2023; Carniani et al., 2024).

Figure 6: Mass estimates for high redshift galaxies based on JWST data from
Adams et al. (2023, dark blue triangles), Atek et al. (2023, green circles),
Labbé et al. (2023, squares), Naidu et al. (2022, stars), Harikane et al.
(2023, yellow diamonds), Finkelstein et al. (2022b, pink down-pointing
triangle), Casey et al. (2023, light blue left-pointing triangles), Donnan et
al. (2023, open cross), Robertson et al. (2023, right-pointing triangles),
Wang et al. (2023, orange squares) and Carniani et al. (2024, orange circles).
The latter two have spectroscopic redshifts. The upper limit for the most
massive galaxy in TNG100 (Springel et al., 2018) as assessed by Keller et al.
(2023) is shown by the light blue line. This is consistent with the maximum
stellar mass expected from the stellar mass–halo mass relation of Behroozi et
al. (2020, solid blue line). These merge smoothly into the trend predicted by
Yung et al. (2019b) for galaxies with a space density of
$10^{-5}\;\mathrm{dex}^{-1}\;\mathrm{Mpc}^{-3}$ (dashed blue line), though
Yung et al. (2023) have revised this upwards by $\sim 0.4$ dex (dotted blue
line). This closely follows the most massive objects in TNG300 (Pillepich et
al., 2018, red line). The light grey region represents the parameter space in
which galaxies were not expected in $\Lambda$CDM. The dark grey area is
excluded by the limit on the available baryon mass (Behroozi & Silk, 2018;
Boylan-Kolchin, 2023).

Figure 6 shows the stellar masses and redshifts of high redshift galaxies
identified in early JWST data (Adams et al., 2023; Atek et al., 2023; Labbé et
al., 2023; Naidu et al., 2022; Harikane et al., 2023; Finkelstein et al.,
2022b; Donnan et al., 2023; Robertson et al., 2023; Casey et al., 2023; Wang
et al., 2023). Unlike Fig. 3, the objects in Fig. 6 are individual galaxies
rather than the results of Schechter fits to many. Consequently, they are more
plausibly subject to the concern of being rare instances of extreme outliers.
However, the masses of these galaxies are very much consistent with a
continuation in the trend already seen at intermediate redshift, so the most
obvious empirical interpretation is that they are indeed typical galaxies.
This should become more clear as the sky coverage of deep JWST surveys
increases.

A priori $\Lambda$CDM predictions for what JWST should see (e.g., Yung et al.,
2019b; Behroozi et al., 2020) do not fare well (e.g., Boylan-Kolchin, 2023;
Keller et al., 2023). The galaxy stellar mass function predicted at high
redshift falls precipitously with increasing masses, so Yung et al. (2019b)
and Behroozi et al. (2020) anticipate similar limits to the most massive
galaxy that should have be seen (Fig. 6). These predictions are corroborated
by the analysis of hydrodynamical simulations by Keller et al. (2023), who
finds that the locus along which the most massive galaxies should appear.
According to Illustris TNG100 (Springel et al., 2018), this locus is
essentially the same as that anticipated by Yung et al. (2019b) and Behroozi
et al. (2020). Galaxies should be exceedingly rare to the right of this line,
yet appear to be commonplace as assessed by many different observers (Adams et
al., 2023; Atek et al., 2023; Labbé et al., 2023; Naidu et al., 2022; Harikane
et al., 2023; Finkelstein et al., 2022b; Donnan et al., 2023).

Yung et al. (2023) reassessed their predictions in the light of higher
resolution simulations. This results in an upward shift by a factor of $\sim
2$ (dotted line in Fig. 6). This helps, but only a bit. There remain galaxies
of larger mass at higher redshift than should be possible, including examples
with spectroscopic redshifts (Wang et al., 2023; Carniani et al., 2024). The
space density of such objects remains uncertain: are they typical, or are they
merely rare extremes?

It is certainly possible to explain the JWST data with some models. Katz et
al. (2023) find a good match of the Sphinx simulation (Rosdahl et al., 2018,
2022) with the cumulative number counts at $9<z<13$. In this case, the test
may come at lower redshift to which it is not yet computationally feasibly to
extend Sphinx. Examination of Fig. 34 of Katz et al. (2023) shows the surface
density $n(z)$ increasing rapidly with decreasing redshift, implying that this
simulation may fit the high redshift data at the risk of overshooting the data
at lower redshift (Sabti et al., 2024) as implied by the evolutionary
trajectories common in simulations (Fig. 3).

Figure 7: The data from Figures 3 and 6 shown together using the same symbols.
The large data points at $z<6$ represent $M^{*}_{*}$ determined from Schechter
fits to many galaxies with spectroscopic redshifts while those at $z>6$ are
individual galaxies observed by JWST. The dashed red line shows the growth
predicted by the Illustris $\Lambda$CDM simulation (Rodriguez-Gomez et al.,
2016) for the typical largest progenitor of a galaxy that reaches a final mass
of a typical local ETG ($9\times 10^{10}\;\mathrm{M}_{\sun}$: Driver et al.,
2022). The solid red line shows the envelope of the most massive objects in
TNG300 (Pillepich et al., 2018). The black lines show equation 5 for
$M_{f}=9\times 10^{10}\;\mathrm{M}_{\sun}$ and $t_{i}=\tau=0.3$, 0.4, and 0.5
Gyr (top to bottom). Star formation histories like those described by equation
5 are consistent with the illustrated data at all epochs — low, intermediate,
and high redshifts — provided that the timescales $t_{i}$ and $\tau$ are both
short.

To make our own assessment, we queried the Illustris TNG50 (Pillepich et al.,
2019) and TNG300 (Pillepich et al., 2018) simulations to find the most massive
model galaxy in terms of stellar mass as a function of redshift. TNG50 has a
higher resolution while TNG300 provides a larger box size. Higher resolution
helps to see the earliest knots that form, while a large box size contains
more rare objects. It is not entirely obvious which of these effects should
win out; Yung et al. (2023) find that resolution pushes there estimate up. In
the case of the Illustris TNG simulations, box size wins: the objects with the
most stellar mass are more massive at every redshift in TNG300 than in TNG 100
than in TNG50. We leave unexamined whether some of these most massive objects
might break up if simulated at higher resolution. The TNG300 result closely
tracks the estimate of Yung et al. (2023) (red line Fig. 6). Consequently,
this line is a conservative estimate of the envelope illustrating a practical
upper limit on stellar mass: objects near this line should be exceedingly
rare, and nonexistent beyond it.

Observed galaxies populate a region of mass-redshift space where they simply
should not be. The assessment of ‘should’ depends on the star formation
efficiency, i.e., how effectively nascent dark matter halos convert their
baryons into stars. This can be treated as a free parameter to ease the
observed tension; perhaps early-forming halos were more efficient at producing
stars. This line of reasoning has a limit, as star formation cannot be more
efficient than 100%: there comes a point when dark matter halos lack enough
baryons to produce the observed stars (Boylan-Kolchin, 2023). A few galaxies
appear to challenge this disallowed region (Fig. 6), albeit not many. These
may prove illusory (Arrabal Haro et al., 2023), but they are noteworthy as
spectroscopic confirmation of truly massive galaxies at these high redshifts
would in principle falsify the $\Lambda$CDM structure formation paradigm.
While it will take some time to assess the severity of this problem, it
certainly appears that structure appeared at an accelerated rate in the early
universe (Castellano et al., 2022, 2023).

Figure 8: The stellar masses of quiescent galaxies from Nanayakkara et al.
(2024). The inferred growth of stellar mass is shown for several cases,
marking the time when half the stars were present (small green circles) to the
quenching time (mid-size orange circles) to the epoch of observation (large
red circles). Illustrative star formation histories following equation 5 are
shown as dotted lines with parameters $t_{i},\tau$ in Gyr noted. We omit the
remaining lines for clarity, as many cross. There is a wide distribution of
formation times from very early ($t_{i}=0.2$ Gyr) to relatively late ($>1$
Gyr), but all of the galaxies in this sample are inferred to build their
stellar mass rapidly and quench early ($\tau<0.5$ Gyr).

Fig. 7 combines the data from Figures 3 and 6 to show the stellar mass of
galaxies observed over all of accessible cosmic time. Also illustrated are the
generalized star formation history (eq. 5) and that from Illustris (Rodriguez-
Gomez et al., 2016) and TNG300 Pillepich et al. (2018). Illustris illustrates
the stellar mass growth of the largest progenitor of a typical galaxy that
attains a final mass consistent with $M^{*}_{*}$ for local early type galaxies
(Driver et al., 2022). TNG300 illustrates the most massive model galaxy in
that simulation. These parallel one another; other $\Lambda$CDM models and
simulations follow a similar trajectory with modest variations (Fig. 3). These
variations stem from differences in the implementation of baryonic physics,
not the assembly of mass (Fig. 1).

The most massive progenitors of typical galaxies in $\Lambda$CDM models fall
well short of the data as a function of redshift. This discrepancy is already
perceptible at $z=1$, clear at $z=2$, and glaring for $z>4$. We can imagine
that the anecdotal examples of bright individual galaxies found in early JWST
data at $z>8$ are early adopters, being the brightest beacons that form first
and are the most visible, things like the most massive objects in TNG300.
However, the data do not appear to follow the predicted linear track of
growth, and would grow too massive by low redshift if they did so.

Fig. 7 also illustrates evolutionary tracks for the generalized star formation
history encapsulated by eq. 4. These naturally encompass both high and low
redshift data, and better resemble the distribution of the data than do the
approximately linear tracks of $\Lambda$CDM models. The available data suggest
that there exists a population of galaxies for which both the formation and
quenching timescales are short: $t_{i}\approx\tau\lesssim 0.5$ Gyr. Such an
evolutionary history is consistent with the traditional picture of a
monolithic giant elliptical galaxy.

The problem for $\Lambda$CDM is perhaps most severe at intermediate redshifts
where the luminosity functions of entire populations of galaxies have been
measured, not just a few anecdotal cases. At $z\approx 3$, the universe is
only $\sim 2$ Gyr old (a lookback time in excess of 11 Gyr), but galaxies with
$M_{*}>5\times 10^{10}\;\mathrm{M}_{\sun}$ are already commonplace. At this
time, the typical massive galaxy is predicted by $\Lambda$CDM (Rodriguez-Gomez
et al., 2016) to have assembled an order of magnitude fewer stars. This
discrepancy is not subtle, nor can it be explained away by photometric
redshifts or top-heavy IMFs. The relevant observations are based on
spectroscopic redshifts, and the stellar masses are robust, having been
derived from observations of rest-frame optical and near-infrared emission
rather than the rest frame ultraviolet. These data point to galaxies having
grown too big too fast.

###  4.3 Quenched Galaxies

Another important observation is that of quenched galaxies at $3<z<4$
(Schreiber et al., 2018; Merlin et al., 2019; Nanayakkara et al., 2024;
Glazebrook et al., 2023). These galaxies have observed spectra that show the
classic features of a stellar population aging after intense star formation at
an earlier epoch. Not only do massive galaxies exist by $z\approx 4$, but
there are examples that have stellar populations that are old for the age of
the universe at the redshift of observation. By modeling the observed spectra,
it is possible to estimate the stellar mass at the time of quenching and
roughly when when half the stellar mass was in place in addition to the mass
at the observed redshift. This provides an approximate curve of growth for
each galaxy, as illustrated in Fig. 8.

The growth rates inferred by Nanayakkara et al. (2024) are consistent with the
rapid rate of growth illustrated by the monolithic model (eq. 5). Individual
galaxies vary in mass, but all are consistent with following a similar
evolutionary trajectory. Further examples of such galaxies at still higher
redshift are discussed by Wang et al. (2024). These galaxies grew too big too
fast, well ahead of the expectation in $\Lambda$CDM models.

Galaxies that and formed most of their stars early and then quenched is
consistent with the traditional view of the evolution of monolithic early type
galaxies. That the galaxies observed by Nanayakkara et al. (2024) have masses
consistent with other high redshift galaxies and show the evolved spectra
expected for stellar populations descended from earlier star formation
suggests that the most obvious interpretation of the data is also the most
likely: bright galaxies at high redshift are intrinsically luminous because
they contain lots of stars. They apparently formed as giant monoliths at early
times.

Figure 9: The stellar masses and star formation rates of galaxies from
Nanayakkara et al. (2024, red symbols). Downward pointing triangles are upper
limits; some of these fall well below the edge of the plot so are illustrated
as the line of points along the bottom. Also shown are objects selected from
the TNG50 (Pillepich et al., 2019, solid squares) and TNG300 (Pillepich et
al., 2018, open squares) simulations at $z=3$ to cover the same range of
stellar mass. Simulated objects with stellar masses comparable to real
galaxies are mostly forming stars at a rapid pace. In the higher resolution
TNG50, none have quenched as observed.

The depiction of evolutionary tracks in Fig. 8 implicitly assumes all the mass
was assembled at an early time. It is also conceivable that the galaxies
observed by Nanayakkara et al. (2024) at $z\approx 3$ to 4 were not individual
objects at the time of quenching or when half the stellar mass had formed.
These events could instead have occurred in protogalactic fragments that
subsequently merged to form the observed galaxies. Since the assembled stars
are old for the epoch of observation, the assembly must occur as dry mergers
devoid of star formation: the stars must be made first in protogalactic chunks
(Newman et al., 2012; Conselice et al., 2022). To check what $\Lambda$CDM
predicts, we have searched the TNG50 and TNG300 simulations (Nelson et al.,
2018, 2019) for model galaxies at $z=3$ with stellar masses in the same range
as the data of Nanayakkara et al. (2024). Many examples of such objects exist
in the simulations, but almost all are actively star forming (Fig. 9).
Quenched galaxies are rare in the simulations at this redshift, with all
branches of the merger trees experiencing high specific star formation rates
at $z>3$ (Fig. 1). So while it is possible to find simulated objects of the
observed stellar mass, their star formation histories are not a good match to
those observed.

It is difficult to avoid the conclusion that observations of the high redshift
universe are genuinely problematic for $\Lambda$CDM (Haslbauer et al., 2022b).
The early appearance of massive galaxies was already apparent in spectroscopic
data (Fig. 2) predating the launch of JWST (Steinhardt et al., 2016; Franck &
McGaugh, 2017). These galaxies are not exceptional individuals, but rather are
typical at intermediate redshifts (Fig. 3). The remarkable discoveries being
made by JWST corroborate and extend this result (Adams et al., 2023; Atek et
al., 2023; Labbé et al., 2023; Naidu et al., 2022; Harikane et al., 2023;
Finkelstein et al., 2022b; Donnan et al., 2023; Nanayakkara et al., 2024).
Many lines of evidence indicate that there exists a population of
exceptionally high mass galaxies in the early universe, galaxies that from the
perspective of $\Lambda$CDM grew too big too fast.

##  5 Accelerated Structure Formation

The discussion to this point has been within the conventional $\Lambda$CDM
framework, for which the results are anomalous. A natural question is how such
anomalies might arise. That structure could and should form at an accelerated
pace was anticipated well in advance by Sanders (1998), McGaugh (1999a),
Stachniewicz & Kutschera (2001), Sanders (2008), and others — see McGaugh
(2015) and references therein. The new physics driving the prediction of early
structure formation is MOND (Milgrom, 1983). MOND has a lengthy track record
of predictive success (Milgrom, 2014), many aspects of which are not
satisfactorily explained by dark matter (McGaugh, 2020). The early formation
of massive galaxies is another predictive success.

###  5.1 Cosmic Context

MOND has been very successful as a theory of galaxy dynamics (Sanders &
McGaugh, 2002; Famaey & McGaugh, 2012; Banik & Zhao, 2022), but has no
completely satisfactory cosmology (Wittenburg et al., 2023). We need a deeper
theory that encompasses both MOND and General Relativity. No completely
satisfactory deeper theory yet exists (Famaey & McGaugh, 2012) just as no
laboratory detection of dark matter has been obtained.

Perhaps the most successful attempt to combine MOND and General Relativity to
date is the Aether-Scalar-Tensor (AeST) theory of Skordis & Złośnik (2019).
AeST has been shown to fit the power spectrum of both the cosmic microwave
background and galaxies at low redshift (Skordis & Złośnik, 2021), but many
details of the theory remain to be explored. One possible shortcoming is an
apparent tension between the parameters required to explain the data at small,
intermediate, and large scales (Mistele et al., 2023).

In this context, it is worth remembering that $\Lambda$CDM works if and only
if some form of invisible non-baryonic mass genuinely exists despite the
persistent laboratory non-detection of the expected candidate particles. From
this perspective, dark matter and dark energy may just be inferences made to
approximate a deeper theory absent the knowledge thereof. While the deeper
theory remains unknown, we know the universe is expanding, and that MOND often
works to describe the dynamics of objects within it. In what follows, we
simply consider what happens to a region within the expanding universe that is
subject to the MOND force law.

###  5.2 Structure Formation in MOND

MOND is inherently nonlinear. The $\sim 10^{5}$ growth factor from $z=1090$ to
$z=0$ is achieved through nonlinear growth (Nusser, 2002; Knebe & Gibson,
2004; Llinares et al., 2008) rather than linear growth with cold dark matter.
Indeed, the usual linear growth rate cannot reconcile the new JWST results
with previous results from HST (Sabti et al., 2024): the data themselves
indicate nonlinearity.

Figure 10: The expansion of spherical regions of various masses in MOND as a
function of time (Sanders, 1998). Globular clusters collapse first and form
early. Large galaxies reach maximum expansion after $\sim 3\times
10^{8}\;\mathrm{yr}$; rich clusters of galaxies do so after $\sim 3\times
10^{9}\;\mathrm{yr}$. Laniakea (Tully et al., 2014) and Ho’oleilana (Tully et
al., 2023) may be examples of vast structures near turnaround today. The
redshift scale on the top axis assumes vanilla $\Lambda$CDM for reference, but
the time–redshift relation may differ in MOND.

Calculating the nonlinear growth of structure in MOND is a nontrivial problem
(Sanders, 1998; Stachniewicz & Kutschera, 2001; Sanders, 2001; Nusser, 2002;
McGaugh, 2004; Llinares et al., 2008; Feix, 2016; Wittenburg et al., 2020) and
considerable work remains to be done. Nevertheless, a common feature of these
analyses is a rapid period of structure formation. Indeed, this seems
unavoidable when considering a MONDian region within an expanding background.

Sanders (1998) considered spherical regions in the MOND regime in an expanding
Universe. After first showing that the usual early universe results (e.g., Big
Bang Nucleosynthesis) are retained, Sanders (1998) showed that there is a
characteristic length scale $r_{c}$ below which MOND dynamics should apply.
The value of $r_{c}$ grows with time, with small regions entering the MOND
regime first and larger ones later in a hierarchical sequence, albeit one
greatly accelerated relative to $\Lambda$CDM. On scales larger than $r_{c}$,
the Universe remains homogeneous and isotropic, so the conventional Friedmann
equation may continue to apply. On scales smaller than $r_{c}$, the region
becomes detached from the Hubble expansion and is destined to recollapse under
its own gravity. This process is inevitably inefficient: not all regions of
the universe will be neat spheres that are cleanly in the MOND regime. Those
which are must necessarily collapse rapidly, so there should be a portion of
the galaxy population that forms early.

The governing equation for an initially expanding spherical region in the MOND
regime (Felten, 1984; Sanders, 1998) is

$(\dot{r})^{2}=(\dot{r}_{i})^{2}-\left(\frac{16\pi}{3}\,\mathrm{a}_{0}G\,\rho_{b}r_{0}^{3}\right)^{1/2}\,\ln(r/r_{i}),$
(6)

where $r_{0}$ is the comoving radius of the spherical region, $r_{i}$ and
$\dot{r}_{i}$ are the initial radius and expansion velocity thereof,
$\rho_{b}$ is the baryonic mass density, and $\mathrm{a}_{0}=1.2\times
10^{-10}\;\mathrm{m}\,\mathrm{s}^{-2}$ (Begeman et al., 1991; McGaugh et al.,
2016). The introduction of the dimensional constant $\mathrm{a}_{0}$ makes the
problem scale-dependent (Felten, 1984), so the initial conditions matter.
Fortunately, $r_{i}$ and $\dot{r}_{i}$ have an obvious interpretation: since
this growth can only commence after radiation releases its grip on the
baryons, the initial velocity is simply the cosmic expansion rate at that time
while the initial radius specifies the mass of the object. The precise
redshift when this occurs is sensitive to the cosmology (Sanders, 1998), but
happens early enough ($z\gtrsim 200$) that the net result for galaxy mass
objects is not particularly sensitive to the initial conditions: the start
time is small compared to the subsequent evolution. A region that evolves
according to eq. 6 reaches a mass-dependent maximum radius and recollapses on
a timescale comparable to that of the initial expansion (Fig. 10).

###  5.3 The Early Formation of Massive Galaxies

The early formation of massive galaxies was explicitly predicted by Sanders
(1998): “Objects of galaxy mass are the first virialized objects to form (by
$z=10$), and larger structure develops rapidly.” Contrast this with the
contemporaneous $\Lambda$CDM statement by Mo et al. (1998): “present-day discs
were assembled recently (at $z\leq 1$).” One of these a priori predictions is
consistent with the data.

Since the background cosmology remains unknown in MOND, the time–redshift
relation is not firmly established. The predictions of Sanders (1998) are
based on the dynamical evolution of a spherical top-hat embedded in an
expanding universe. In a pure MOND universe, such a region is destined to
recollapse (Felten, 1984) irrespective of its initial density (eq. 6), with
small regions naturally collapsing faster than large ones. The mass of the
top-hat sets the timescale for decoupling from the Hubble flow (Sanders, 1998)
and recollapse (Stachniewicz & Kutschera, 2001). This predicted timescale is
more fundamental than the corresponding redshift, which is cosmology-dependent
(Clifton et al., 2012; Skordis & Złośnik, 2021). Hydrodynamics is important at
the scale of globular clusters, which briefly delays their collapse
(Stachniewicz & Kutschera, 2001). It is less important at galaxy scales,
collapse is approximately symmetric with the expansion illustrated in Fig. 10.

The salient prediction Sanders (1998) made is that “Massive galaxies
($10^{11}\;\mathrm{M}_{\sun}$) reach the point of maximum expansion at
$t=3\times 10^{8}$ years.” Collapse happens in a similar time for objects of
this mass (Stachniewicz & Kutschera, 2001), so in principle a massive
protogalaxy can be assembled in 600 Myr. Wittenburg et al. (2020) consider
slightly lower mass objects, and find that “after approximately 0.5 Gyr the
spheres collapse and form a rotating dense, thin disk.” This is the timescale
for forming galaxies in MOND. This corresponds to $z\approx 8$ in
$\Lambda$CDM, and still higher redshift in the low density, baryon-only FLRW
cosmologies considered by Sanders (1998) (see also Stachniewicz & Kutschera,
2001; Sanders, 2001; McGaugh, 2004; Sanders, 2008; Llinares et al., 2008;
McGaugh, 2018).

Globular cluster mass ($\sim 10^{5}\;\mathrm{M}_{\sun}$) objects collapse very
quickly, in a few tens of millions of years (Stachniewicz & Kutschera, 2001).
This is so fast that they will have ages that are practically
indistinguishable from that of the universe itself (Ying et al., 2023). A
large range of masses can collapse within the first Gigayear: this is the
epoch of galaxy formation in MOND. This provides a natural explanation for the
remarkably early formation times $t_{i}$ inferred in Fig. 7. Structure
formation is hierarchical insofar as globular clusters form more quickly than
massive galaxies, but the pace is accelerated to the point that it appears
nearly monolithic after many billions of years.

###  5.4 Larger Structures

Accelerated formation applies to all structure in MOND, not just individual
galaxies. Larger structures like massive clusters of galaxies should also form
earlier than in $\Lambda$CDM. Indeed, the entire cosmic web should emerge
earlier (McGaugh, 2015), and should be perceptible in the distribution of high
redshift quasars. Indications to this effect already exist (e.g., Shen et al.,
2007; Eilers et al., 2024; Pizzati et al., 2024).

A region destined to become a cluster of galaxies will reach maximum expansion
after 2 – 3 Gyr (Sanders, 1998), so clusters should also emerge as
recognizable objects fairly early in the development of the universe, and
certainly earlier than anticipated in $\Lambda$CDM where they are the last
bound structures to form. Kravtsov & Borgani (2012) show that a $\sim
10^{15}\;\mathrm{M}_{\sun}$ cluster is barely getting started at $z=3$ (see
their Fig. 6). Note that in MOND there is no cold dark matter, so the
equivalently massive clusters is of order $10^{14}\;\mathrm{M}_{\sun}$.
Sanders (1998) predicts “that by $z=3$ not only do massive galaxies exist but
they are also significantly clustered (the density of the
$10^{14}\;\mathrm{M}_{\sun}$ region would be enhanced by a factor of 6.5 over
the mean at this redshift).”

Figure 11: Measured velocity dispersions of protocluster candidates (Franck &
McGaugh, 2016a, b) as a function of redshift. Point size grows with the
assessed probability that the identified overdensities correspond to a real
structure: all objects are shown as small points, candidates with $P>50\%$ are
shown as light blue mid-size points, and the large dark blue points meet this
criterion and additionally have at least ten spectroscopically confirmed
members. The MOND mass for an equilibrium system in the low acceleration
regime is noted at right; these are comparable to cluster masses at low
redshift.

Franck & McGaugh (2016a, b) identify dozens of protocluster candidates at
redshifts $2<z<6.6$ (Fig. 11). Of these, the sixteen most reliable candidates
have $N\geq 10$ spectroscopically confirmed members with overdensities ranging
from 5 to 20 with a median $\delta=9.5$. Similar structures have recently been
identified by Shah et al. (2024), including six massive protoclusters around
$z\approx 3$. This is consistent with the findings of Franck & McGaugh (2016b)
and the predictions of MOND, but rather higher than expected in $\Lambda$CDM
(Kravtsov & Borgani, 2012; Mortonson et al., 2011).

A number of the best candidate clusters of Franck & McGaugh (2016a, b) are at
$z\sim 3$. The median velocity dispersion of candidate clusters is $\sim
600\;\mathrm{km}\,\mathrm{s}^{-1}$ (Fig. 11). This is about twice that of
equivalent systems found in lookback cones in $\Lambda$CDM simulations
(Franck, 2018). That is, protocluster candidates identified as spikes in
$N(z)$ have larger velocity dispersions in the data than in simulations at the
same redshift. This is another indication that the discrepancy is one in mass,
not just luminosity. These systems should not yet be bound in $\Lambda$CDM,
but it is possible that they have already formed in MOND (Fig. 10).

The median observed velocity dispersion of intermediate redshift cluster
candidates corresponds to a mass of $\sim 10^{14}\;\mathrm{M}_{\sun}$ for
systems in dynamical equilibrium in the deep MOND regime (Milgrom, 2018, 2019,
2021). These numbers are very much in line with the long-standing prediction
of Sanders (1998), and are similar to the masses inferred for clusters in MOND
at low redshift (McGaugh, 2015; Li et al., 2023; Tian et al., 2024). Galaxy
clusters are known to display a residual mass discrepancy in MOND of about a
factor of two (Sanders, 2003, 2007; Angus et al., 2008), so there is an
apparent need for an extra mass component, possibly in the form of undetected
baryons (Milgrom, 2008; Kelleher & Lelli, 2024). We are thus in the curious
situation that the masses of galaxy clusters remain problematic for MOND at
the factor of two level, but their formation time is potentially problematic
for $\Lambda$CDM, as are other properties like cluster collision speeds (Angus
& McGaugh, 2008; Katz et al., 2013) and the largest mass objects (Asencio et
al., 2021).

Sanders (1998) notes that the largest structures nearing turnaround today
would be superclusters (Sankhyayan et al., 2023). These are not expected to be
simple objects, as they are inevitably far from the simple spherical
approximation of eq. 6. Indeed, it was recognized early (Felten, 1984) that
MOND would induce anisotropy on unexpectedly large scales. These
considerations anticipate the size and complex kinematics of objects like
Laniakea (Tully et al., 2014) and Ho’oleilana (Tully et al., 2023), and
motivate searches for anisotropy in the expansion rate.

###  5.5 Other Indications

The morphology of cosmic structure is similar in $\Lambda$CDM and MOND
(Llinares et al., 2008; McGaugh, 2015), but accelerated structure formation of
MOND pushes all benchmarks for structure formation to earlier times in cosmic
history. The cosmic web emerges early, providing a natural explanation for the
clustering of high-redshift quasars (Clowes et al., 2013) and other very large
features (Horváth et al., 2014, 2015; Balázs et al., 2015; Lopez et al.,
2022). Indeed, one can see indications of the clustering of protoclusters at
high redshift (Franck & McGaugh, 2016b), which is visible in Fig. 11 as the
multiplicity of objects at similar redshift. These features are larger than
expected in $\Lambda$CDM, but quite natural in MOND. MOND is also effective
(Llinares et al., 2008; McGaugh, 2015) at making large, empty voids (Nusser et
al., 2005; Peebles & Nusser, 2010).

At still higher redshift, other natural consequences of early structure
formation include early reionization (McGaugh, 1999b) and an enhanced ISW
effect (McGaugh, 2004), for which there is some evidence (Granett et al.,
2008; Nadathur et al., 2012; Kovács et al., 2020). Predictions for 21 cm
absorption at cosmic dawn and during the dark ages are discussed by McGaugh
(2018). The depth of the absorption signal can be deeper than in $\Lambda$CDM
at both epochs ($z\approx 17$ and $z\approx 100$). Due to the nonlinear growth
of structure, one expects less power in fluctuations entering the dark ages
($z\sim 150$) but more by their end ($z\sim 50$) than in $\Lambda$CDM. This is
the epoch when the seeds of structure planted by MOND begin to sprout.

At late times, it becomes difficult for a MOND universe to remain isotropic
(Felten, 1984). This would go some way to explain the tension between the
dipole anisotropy of number counts of distant sources and the cosmic microwave
background (Secrest et al., 2021, 2022; Domènech et al., 2022) and perhaps
lead to an anisotropy in cosmic expansion (Colin et al., 2019). It seems that
many of the puzzling observations in cosmology may be attributed to MOND.
Indeed, many of these things were predicted a priori.

##  6 Summary

We have examined evidence concerning the evolution of galaxies across a large
range of redshifts for which data are available. There appears to be a
population of bright galaxies that formed early and grew rapidly. There is
copious photometric evidence that indicates the existence of this population,
and important corroborative evidence from kinematics.

###  6.1 Photometric Evidence

The galaxy population that grew too big too fast has photometric properties
that suggest it is

  * •

luminous, with apparent magnitudes considerably brighter than anticipated by
contemporaneous $\Lambda$CDM models (Fig. 2);

  * •

massive, with typical examples approaching the mass of a local $L^{*}$ galaxy
already by $z\approx 3$ when the universe was only $\sim 2$ Gyr old (Fig. 3);

  * •

old, with stellar populations consistent with forming at high redshift
$z_{f}\gtrsim 10$ (Figs. 7 and 8) and quenching early (Fig. 9);

  * •

common in clusters at $z\lesssim 3$ and already clustered in protoclusters at
$z\lesssim 6$ (Fig. 11); and

  * •

consistent with the population of bright galaxies observed by JWST at $z>10$
(Fig. 7) where bright galaxies are more common than anticipated (Figs. 5 and
6).

These observed properties do not sit well with the predictions of hierarchical
$\Lambda$CDM models, which predict that local massive galaxies were divided
into many progenitor protogalaxies at the observed redshifts (Fig. 1). They
are instead consistent with a population of galaxies that formed early as
massive quasi-monoliths, i.e., the traditional picture of giant elliptical
galaxies that form early and quench rapidly, following something like an
exponential star formation history (Figs. 2 and 3).

$\Lambda$CDM galaxy formation models failed to anticipate the bright galaxies
that are observed at both intermediate and high redshift. Forming enough stars
is not the problem. The problem is assembling them into a single object. The
presence of these quasi-monolithic objects appears to violate the hierarchical
assembly paradigm (Fig. 1).

Since there is little flexibility to adjust the mass assembly history in
$\Lambda$CDM, one might instead consider adjusting the efficiency of early
star formation, thus making small mass protogalaxies brighter than nominally
expected. This may be a viable approach at $z>10$, but does not provide a
satisfactory explanation for the bright galaxies observed at intermediate
redshift ($2<z<6$). These objects have spectroscopic redshifts and good multi-
band photometry covering the rest frame optical portion of the spectrum, so
neither their cosmic distances nor their stellar masses can be sufficiently in
error as to explain the large discrepancy. Moreover, they are common enough to
define a value for $L^{*}$ that is much brighter than the predictions of
$\Lambda$CDM models (Steinhardt et al., 2016; Franck & McGaugh, 2017).

The observation of bright galaxies by JWST at still higher redshifts, $z>10$,
came as a surprise because that is clearly not what $\Lambda$CDM predicts
(Fig. 1). This high redshift problem seems more tenable than that at
intermediate redshift since we are more reliant on photometric redshifts and
UV luminosities that are notoriously difficult to relate to stellar mass.
Though this leaves room for flexibility in modeling, the observed UV
luminosity function hardly evolves at $z\gtrsim 10$ where the dark matter halo
mass function should be evolving rapidly (Fig. 5). In order to explain the
data by adjusting the efficiency of star formation or UV light production,
there must be a fine-tuning to reconcile these very different evolutionary
behaviors over a small portion of cosmic time ($<2\times 10^{8}$ Myr).

A more natural interpretation is that galaxies are bright at high redshift
because they had already grown large. This provides an evolutionary trajectory
that maps nicely between observations at low, intermediate, and high redshift.
Note that it is not necessary for all galaxies to form early and follow such a
trajectory, just enough of them to define a bright $L^{*}$ in early ($z\approx
3$) clusters (Franck & McGaugh, 2017). This population was not anticipated by
$\Lambda$CDM models and is not easily reconciled with them: these galaxies
grew too big too fast.

The discrepancy between the stellar masses of intermediate and high redshift
galaxies and the prediction of $\Lambda$CDM is not subtle: galaxies became too
big too fast by a large factor. It is common to see galaxies at $z\approx 3$
(when the universe was $\sim 2$ Gyr old) that have a stellar mass that is
already approaching that of $L^{*}$ galaxies at $z=0$. In contrast,
$\Lambda$CDM models consistently predict that the largest progenitor of such
galaxies should have a rather smaller fraction of their final stellar mass in
place at this early time (Fig. 3): FIRE (Anglés-Alcázar et al., 2017) predicts
$\sim 10\%$, Illustris $\sim 3\%$ (Henriques et al., 2015; Rodriguez-Gomez et
al., 2016). This poses a challenge to the assembly history of mass in the
$\Lambda$CDM structure formation paradigm, not just the evolution of the
luminous component.

###  6.2 Kinematic Evidence

Photometric observations are complemented by kinematic observations that trace
the mass, not just the light. JWST observations show that morphologically
mature spiral galaxies are common at early times (Ferreira et al., 2022,
2023). Kinematic observations to date (section 3.3) show that rotationally
supported galaxies

  * •

formed early, by $z\gtrsim 6$ (Smit et al., 2018; Rowland et al., 2024; Xu et
al., 2024) when $z\leq 1$ had been the nominal expectation (Mo et al., 1998);

  * •

rotate fast, with circular speeds in excess of
$250\;\mathrm{km}\,\mathrm{s}^{-1}$ (Rizzo et al., 2021; Lelli et al., 2021),
comparable to massive local spirals;

  * •

obey the Baryonic Tully-Fisher relation (Lelli et al., 2019; Nestor Shachar et
al., 2023); and

  * •

obey the dark matter fraction–surface brightness relation (Fig. 4).

These observations show that at least some spiral galaxies formed early and
became massive rapidly. Note that kinematic observations imply a large
dynamical mass: it is not just a matter of stars producing more light per unit
dark matter halo mass. Moreover, galaxies appear remarkably mature. In
addition to their morphologies, scaling relations like the Baryonic Tully-
Fisher and the dark matter fraction–surface brightness relation are already in
place at early times. This clearly was not anticipated by models that expect
disk galaxies to settle down only at later times. Not only were these scaling
relations established early, they appear to have evolved little over most of
cosmic time (the past $\sim 11$ Gyr back to $z\approx 2.5$). This does not sit
comfortably with the gradual assembly predicted by hierarchical galaxy
formation (Fig. 1).

###  6.3 Structure Formation in MOND

The early formation of massive galaxies was explicitly predicted a quarter of
a century ago by Sanders (1998). The new physics driving this prediction of
accelerated structure formation is MOND, a theory that has had many other
predictive successes (e.g., Sanders & Verheijen, 1998; McGaugh & de Blok,
1998; McGaugh, 2011; McGaugh & Milgrom, 2013a, b; Milgrom, 2015; Sanders,
2019a; McGaugh, 2020; Mistele et al., 2024a, b). The nonlinearity of MOND
causes growth to occur at a much higher rate early than expected with linear
growth in $\Lambda$CDM (Sanders & McGaugh, 2002).

MOND makes a number of long-standing predictions about early structure
formation:

  * •

an early cosmic dawn (McGaugh, 2018, $z\approx 17$);

  * •

massive galaxies at $z\gtrsim 10$ (Sanders, 1998, 2008);

  * •

early emergence of the cosmic web (by $z\approx 5$: Llinares et al., 2008);

  * •

rich clusters of galaxies form by $z\approx 2$ (Sanders, 1998);

  * •

an enhanced ISW effect (McGaugh, 2004);

  * •

large voids swept clear by low redshift (McGaugh, 2015);

  * •

the largest scales forming at the present time (Sanders, 1998) were
anticipated to be comparable to Laniakea (Tully et al., 2014);

  * •

the universe may depart from the isotropic ideal of the cosmological principle
at late times (Felten, 1984).

A number of puzzling observations in cosmology were anticipated by MOND,
including the early formation of massive galaxies. The predictive power of
MOND is not limited to the dynamics of individual galaxies.

Despite the predictive successes of MOND, we do not yet know how to construct
a cosmology based on it. Perhaps the most promising theory to date is AeST,
which has demonstrated the ability to fit the power spectrum (Skordis &
Złośnik, 2019) of both the cosmic microwave background and the large scale
structure traced by galaxy redshift surveys. This is a significant
accomplishment, since it had been thought that this was impossible without
cold dark matter. Considerable work remains to be done to see if AeST can be a
fully satisfactory theory.

In contrast, $\Lambda$CDM provides a good fit to a wide range of cosmological
observables, but does not provide a satisfactory explanation of the many
phenomena that were predicted by MOND (Famaey & McGaugh, 2012), nor is it
clear that it can do so (Kroupa, 2015; Sanders, 2019b; McGaugh, 2020; Merritt,
2020, 2021; Roshan et al., 2021; Haslbauer et al., 2022a, b; Kroupa et al.,
2024; Oehm & Kroupa, 2024). We find ourselves caught between two very
different theories that seem irreconcilable despite applying to closely
related yet incommensurate lines of evidence (McGaugh, 2015). The simple force
law hypothesized by MOND has made enough successful a priori predictions that
it cannot be an accident, and must be telling us something. What that is
remains as mysterious as the composition of dark matter.

This research has made use of data from a wide variety of sources, themselves
enabled by great observatories like the Hubble Space Telescope, Spitzer, and
JWST. We gratefully acknowledge the community and society that make these
investigations possible. We also acknowledge conversations with many people,
in particular Sara Tosi, Frances Duey, Konstantin Haubner, Tiffany Visgaitis,
Tobias Mistele, Pengfei Li, and Marcel Pawlowski.

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