of \( \sim \, 1 0 ^ { 8 - 9 } M _ { \odot } \) do host stars. These halos can be observed as ultrafaint galaxies. These systems are currently the most DM-dominated systems with a ratio of DM to stellar mass significantly exceeding a factor of a hundred. DM halos below this threshold are expected to be depleted of stars and are effectively invisible. Halos at and below the galaxy formation threshold offer a pristine environment in which baryonic physics is subdominant to the dark matter behavior, and hence are substantially less affected by baryonic systematics.

# 5.2 Observational Probes

In the following we list some of the promising current and future probes that can probe the abundance and inner composition of halos in the mass range of \( 1 0 ^ { 6 - 9 } M _ { \odot } \).

# 5.2.1 Ultra-faint galaxies

Ultra-faint dwarf (UFD) galaxies, defined as dark matter-dominated stellar systems with luminosity \( L < 1 0 ^ { 5 } \)\( ; L _ { \odot } \) [435], occupy the smallest dark matter halos that form galaxies, with \( 1 0 ^ { 8 } ~ M _ { \odot } \lesssim M _ { \mathrm { h a l o } } \lesssim 1 0 ^ { 1 0 } ~ M _ { \odot } \)[436, 437]. These systems therefore provide crucial information about the astrophysical processes that govern the faint end of galaxy formation and the dark matter physics that impacts the abundance and properties of halos near the galaxy formation threshold.

To date, ultra-faints have exclusively been detected within distances of ∼ 300 kpc as satellites of the Milky Way. Deep photometric surveys including the Dark Energy Survey have significantly increased the number of known Milky Way satellites in recent years, which now exceeds ∼ 60 systems [438]. Nevertheless, both empirical and theoretical arguments suggest that our census of ultra-faints—even within the Milky Way’s virial radius—is highly incomplete [439–441]. Forthcoming observational facilities including the Vera C. Rubin Ob-servatory and the Nancy Grace Roman Space Telescope are expected to drastically improve upon current ultra-faint detection capabilities. Specifically, Rubin is forecasted to discover the entire population of UFD Milky Way satellites in the Southern hemisphere outside the Galactic disk and with surface brightness down to \( \sim 3 2 \mathrm { m a g ~ a r c s e c } ^ { - 2 } \)[157, 314]. Excitingly, these detections are expected to extend well beyond distances of 300 kpc, allowing UFD populations to be characterized throughout much of the Local Volume [442].

Our understanding of the dark matter halos that host ultra-faints has significantly im-proved over the last decade. In particular, hydrodynamical simulations have started to re-solve the formation and evolution of UFDs in a cosmological context, including as satellites of larger hosts [443–448]. In parallel, semi-analytic and empirical galaxy–halo connection models have been combined with observations to infer ultra-faints’ halo properties; in these models, the number of observable ultra-faints suggests that these systems occupy halos with masses down to \( \sim 1 0 ^ { 8 } \)\( : M _ { \odot } \) (near the “atomic cooling limit”; [436, 437, 449, 450]) or even lower [451, 452]. The fraction of low-mass halos that host UFDs and the scatter in the stellar mass–halo mass relation for these systems are also being studied in order to precisely characterize the properties of halos near the galaxy formation threshold [453–456].

Ultra-faints provide stringent constraints on dark matter particle properties. Specifically, the number of observable UFD Milky Way satellites informs dark matter physics that sup-presses the present-day abundance of dark matter halos with masses of \( \sim 1 0 ^ { 8 } ~ M _ { \odot } \), yielding

lower limits on the mass of thermal relic warm dark matter of ∼ 5 keV [449, 457–466] and on the mass of ultra-light dark matter of \( \sim \, 1 0 ^ { - 2 1 } \) eV [464, 467]. Similar analyses con-strain the strength of dark matter–Standard Model interactions at the \( \sim ~ 1 0 ^ { - 3 0 } \mathrm { { c m } ^ { 2 } } \) level[29, 154, 155, 464] and the dark matter particle lifetime at the ∼ 10 Gyr level [468, 469].Furthermore, stellar velocity dispersion measurements for brighter dwarf galaxies inform the strength and velocity-dependence of dark matter self-interactions, with sensitivity to cross sections of \( \sim 1 \mathrm { c m ^ { 2 } } \) \( \mathrm { g } ^ { - 1 } \)[470, 471], and combining measurements of UFD internal dynamics from upcoming spectroscopic facilities and giant segmented mirror telescopes [472] with their population statistics will further inform self-interacting dark matter models [473–475].

The forthcoming observations discussed above are expected to increase the sample of known UFDs near the galaxy formation threshold, reducing statistical uncertainties and improving the corresponding dark matter constraints. For example, Rubin observations are forecasted to probe halo masses below \( \sim 1 0 ^ { 8 } \; M _ { \odot } \) [157]. If these halos are occupied by ultra-faints, these observations will provide evidence for the existence of galaxies formed through molecular hydrogen cooling; otherwise, they will determine the halo mass threshold and stochasticity associated with galaxy formation. Thus, combining these measurements with purely gravitational probes of small-scale structure will enable the detection of completely dark halos.

# 5.2.2 Lyman-alpha forest

The intergalactic medium (IGM) is the rarefied gas that fills the vast volumes between the galaxies in the Universe. Physical effects, ranging from the nature of dark matter to the radiation from star-forming galaxies and quasars, set the observable properties of the IGM, making the IGM a powerful probe of both fundamental physics and astrophysics. Baryons in the IGM trace dark matter fluctuations on Mpc scales, while on smaller (\( \lesssim \) 100 kpc scales) the \( T \sim 1 0 ^ { 4 } \mathrm { K } \) gas is pressure supported against gravitational collapse. While the IGM is sensitive to the Epoch of Reionization [476–478], complex and poorly understood physical processes related to galaxy formation play only a minor role in determining its structure[479, 480].

Forward modeling the structure of the IGM for a given cosmological and DM scenario is a theoretically well-posed problem, albeit requiring expensive cosmological hydro-dynamical simulations. Despite this apparent simplicity, accurate simulations of the IGM are com-putationally challenging because of the multi-scale nature of the problem [481]. A spatial resolution of \( \approx \) 20 kpc is required to resolve the density structure of the IGM, while a rela-tively large box size is required to capture the large-scale power, to obtain a fair sample of the Universe, and to model the topology of reionization.

These characteristics of the Lyman-\( \alpha \) flux power spectrum have allowed for some of the tightest constraints on the nature of dark matter clustering [482–487]. Current anal-yses have been shown to be sensitive to the scale of either a suppression [488, 489] or an enhancement[490, 491] of the small scale power. These dark matter constraints come from high-quality observations of a the few currently available (∼ 100) high redshift (\( z > \) 4) quasar spectra obtained with high resolution instruments (\( R \sim \) 80, 000) and high signal-to-noise observations (\( S / N \sim \) 100). With these spectra, surveys are able to measure scales to wavenumbers of \( k \sim \) 20 h/Mpc [478, 492]. Notably these surveys are currently limited by