Small-scale probes of the early universe

Large-scale observations of the Cosmic Microwave Background have provided the most substantial evidence for how the Universe expanded rapidly in the first fraction of a second after the Big Bang. This phase of rapid expansion known as inflation provided the seeds for all of the structure that we see in the Universe today, and therefore understanding its dynamics will provide explanations for why the Universe is the way it is, in both the visible and dark sectors. Constraining the dynamics of inflation is best done with the primordial power spectrum, which measures the overdensities and underdensities left over at the end of inflation. This thesis investigates different probes for measuring and constraining the primordial power spectrum on small scales, where constraints are currently much weaker than those deduced from large-scale measurements. The existence or lack of primordial black holes is primarily investigated as a means for both constraining the primordial power spectrum and hence inflation, as well as due to their interest as a dark matter candidate. Large-amplitude scalar perturbations are usually required for the production of primordial black holes, and therefore observational signatures of such perturbations including spectral distortions, stochastic gravitational waves, and the 21cm signal will be explored as means of detecting them. Constraints and signatures from these observations will be compared with classes of inflationary models so as to understand the inflationary dynamics that would be necessary to produce the results and predictions of multiple current and future experiments.