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Minimizing the energy of a many-body system is a fundamental problem in many fields. Although we hope a quantum computer can help us solve this problem better than classical computers, we have a very limited understanding of where a quantum advantage may be found. In this talk, I will present some recent theoretical advances that shed light on quantum advantages in this domain. First, I describe rigorous analyses of the Quantum Approximate Optimization Algorithm applied to minimizing energies of classical spin glasses. For certain families of spin glasses, we find the QAOA has a quantum advantage over the best known classical algorithms. Second, we study the problem of finding a local minimum of the energy of quantum systems. While local minima are much easier to find than ground states, we show that finding a local minimum under thermal perturbations is computationally hard for classical computers, but easy for quantum computers.

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Primordial black holes (PBHs) have long been considered a promising candidate or an important component of dark matter (DM). Recent gravitational wave (GW) observations of binary black hole (BH) mergers have triggered renewed interest in PBHs in the stellar-mass (∼ 10 − 100 Msun) and supermassive regimes (∼ 10^7 − 10^11 Msun). Although only a small fraction (≲ 1%) of dark matter in the form of PBHs is required to explain observations, these PBHs may play important roles in early structure/star formation. We use cosmological zoom-in simulations and semi-analytical models to explore the possible impact of stellar-mass PBHs on first star formation, taking into account two effects of PBHs: acceleration of structure formation and gas heating by BH accretion feedback. We find that the standard picture of first star formation is not changed by stellar-mass PBHs (allowed by existing observational constraints), and their global impact on the cosmic star formation history is likely minor. However, PBHs do alter the properties of the first star-forming halos and can potentially trigger the formation of direct-collapse BHs in atomic cooling halos. On the other hand, supermassive PBHs may play more important roles as seeds of massive structures that can explain the apparent overabundance of massive galaxies in recent JWST observations. Our tentative models and results call for future studies with improved modeling of the interactions between PBHs, particle DM, and baryons to better understand the effects of PBHs on early structure/star formation and their imprints in high-redshift observations.

Current and upcoming James Webb Space Telescope (JWST) imaging surveys hold enormous potential for uncovering the faint low-mass galaxy population, which could provide constraints on alternative DM (altDM) models. In this talk I will investigate the impact of altDM models that exhibit small-scale suppression of the matter power spectrum, namely warm dark matter (WDM), fuzzy dark matter (FDM), and interacting dark matter (IDM) with strong dark acoustic oscillations (sDAO) on the properties of galaxies in the EoR. In altDM scenarios, both the halo mass functions and the ultraviolet luminosity functions at z ≳ 6 are suppressed at the low-mass/faint end, leading to delayed global star formation and reionization histories. However, strong non-linear effects enable altDM models to 'catch up' with cold dark matter (CDM) in terms of star formation and reionization. The specific star formation rates are enhanced in halos below the half-power mass in altDM models. This enhancement coincides with increased gas abundance, reduced gas depletion times, more compact galaxy sizes, and steeper metallicity gradients at the outskirts of the galaxies. These changes in galaxy properties can help disentangle altDM signatures from a range of astrophysical uncertainties. However, we uncover significant systematic uncertainties in reionization assumptions on the faint-end luminosity function. This underscores the necessity of accurately modeling the small-scale morphology of reionization in making predictions for the low-mass galaxy population.

Cosmology can give insights on the self-interactions of Dark Matter. In this talk we analyze how long range forces acting solely in the Dark Sector imprint on the distribution of galaxies, the so-called Large Scale Structure (LSS). First we show how BOSS data can complement CMB information and give the strongest constraint on the strength of the self interaction. In particular we discuss how the long range force affects the galaxy power spectrum and how the theory of LSS is changed in its presence. Finally we forecast that data from future surveys (Euclid, MegaMapper) can improve the bound by roughly one order of magnitude. We also mention how higher point statistics can potentially contain relevant information on the enhanced clustering.

I describe an analytic, timescale-based model for the formation of the first stars in the center of collapsing primordial gas clouds. Despite its simplicity, the model reproduces the stellar mass scale and its parameter dependences observed in state-of-the-art cosmological zoom-in simulations, while clarifying the essential underlying physics. The model provides an inexpensive tool for studying the influence of exotic dark matter on early star formation.

Recent work on the formation of the first dark matter halos suggests they may have had systematically different density profiles, with stronger cusps and higher densities than those predicted at low redshift. I will review recent work on the first generation(s) of dark matter halos, and discuss the implications for dark matter annihilation and structure formation in general.