Halo Formation in Self-Interacting Dark Matter Models

The standard model of cosmology assumes that dark matter (DM) is cold and collisionless. This collisionless Cold Dark Matter (CDM) model has been extremely successful in explaining various observational phenomena on mass scales larger than galaxies. Despite the successes on large scales, the CDM model faces several challenges on smaller scales that have remained unanswered for several years. One of the most intriguing discrepancies between CDM predictions and observations stems from the DM content in dwarf and spiral galaxies. While CDM predicts radially divergent DM density (cusps) at the halo centers, many observations suggest constant DM density cores. Abundance of the observed Milky Way satellites has also been at odds with the predictions from CDM. While observations suggest ≤ 100 luminous Milky Way satellites, CDM N-body simulations predict 1-2 orders of magnitude more subhalos for a Milky Way-like galaxy.As an alternative to CDM, self-interacting dark matter (SIDM) models are proposed as potential solutions to some of these cosmological issues. In this class of DM models, DM-DM scatter- ing leads to a re-distribution of energy at the center of the halo such that after a few dynamical times, the halo reaches in-equilibrium isothermal state. This results in the re-distribution of DM particles, which, in principle, can form constant density cores opposite to the cuspy profiles predicted by the CDM model. The interaction between dark matter particles may be extended to the scenarios where DM scatters off from some other relativistic dark sector particles (e.g. dark photons), leading to suppressions in the matter power spectrum. This results in the depletion of DM halos in the regime corresponding to this cutoff in the matter power spectrum, which pro- vides another channel to address the tension between theoretical predictions and observations.In this dissertation, I study the impact of non-gravitational interactions in the dark sector on the distribution and evolution of DM halos. I find that when entangled with the baryonic physics, SIDM models possess rich phenomenology for the formation of structures in the uni- verse. For the dark matter halos in isolation with low baryonic content, DM-DM interactions lead to a cored DM density profile (e.g. dwarf-sized galaxies), as expected from the isothermal behavior of SIDM. On the other hand, in isolated halos with a more significant contribution of baryons (e.g. closer to the mass scale of the Milky Way), a phase of core-contraction is triggered, leading to a high central density. Furthermore, the environmental effects, such as tidal stripping and tidal shocking, can dramatically change the fate of these objects. While gravitational tides remove mass from outskirts of the satellite halos, the heat transport due to the DM self-interactions results in a faster “core-collapse.” The transition from core-expansion to core-collapse is controlled by the orbit and pre-infall halo parameters.In the DM models where DM experiences interactions with dark photons, the suppression in the matter power spectrum causes a depletion of DM halos in the regime of dwarf galaxies. In this dissertation, I develop an analytical Press-Schechter approach to compute halo abundance for SIDM models in a computationally efficient way that is not possible for the conventional numerical simulations. I calibrate and test this analytical model with cosmological simulations, and show that it is robust over different SIDM models, halo mass regimes, and cosmological time-scales. I use this formalism to put a constraint on the parameter space of DM-dark photon interactions that is consistent with previous measurements