Illuminating the Cosmos: Dark matter, primordial black holes, and cosmic dawn

The $\Lambda$-CDM model of cosmology has done much to clarify our picture of the early universe. However, there are still some questions that $\Lambda$-CDM does not necessarily answer; questions such as what is the fundamental nature of dark matter? What is its origin? And what causes the intriguing measurements that we are seeing from cosmic dawn? In this thesis, I will describe three directions in which I have pushed forward our understanding of how fundamental physics manifests in cosmology. First, I have studied the signatures of exotic energy injection in various astrophysical and cosmological probes, including the Lyman-$\alpha$ forest, the blackbody spectrum of the cosmic microwave background, the power spectrum of the cosmic microwave background, and the formation of the earliest stars in our universe. Second, I have investigated the formation of primordial black hole dark matter in a general model for inflation with multiple scalar fields. I have identified the space of models that can generate primordial black holes while remaining in compliance with observational constraints using a Markov Chain Monte Carlo, and also showed that future gravitational wave observatories will be able to further constrain these models. Finally, I have developed an analytic description of signals from 21\,cm cosmology using methods inspired by effective field theory. This method includes realistic observational effects and has been validated against state-of-the-art radiation hydrodynamic simulations, including those with alternative dark matter scenarios. With these recent efforts, we are advancing the frontiers of dark matter phenomenology and cosmology, thereby paving the way towards illuminating the remaining mysteries of our cosmos and drawing closer to a comprehensive understanding of the universe.