Abstract
I investigate solutions to challenges the standard Lambda Cold Dark Matter (ΛCDM) cosmological model faces on small scales and in the measured expansion rate of the universe. On small scales, I examine the central density structure of dwarf galaxy dark matter halos in cold dark matter (CDM) and self-interacting dark matter (SIDM) models using simulations from the Feedback In Realistic Environments (FIRE) project. While both baryonic feedback and dark matter self-interactions can convert central cusps into cores, it remains an open question whether the two processes are distinguishable. I will demonstrate that SIDM-induced cores in dwarf galaxies transition more quickly between the constant density central region and the falling density at the outer region, relative to feedback-induced cores. I will separately discuss the mismatch between local and cosmological measurements of the Hubble constant and introduce promising cosmological solutions to this tension.