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