A history of the universe in primordial black holes

Primordial black holes (PBHs) are a unique type of astrophysical object. Formed in the early universe but persisting to the present day, they offer an incredible probe for studying the physics of both the early and late universe. Additionally, they provide a natural dark matter candidate without requiring physics beyond the standard model, although there are many constraints on the fraction they can contribute across a broad range of PBH masses. In this thesis, PBHs are studied at both early and late times. Their formation from large overdensities is examined and choices in the calculation of their abundance are considered. These choices are shown to have a limited effect on the PBH abundance and mass distribution, although they will become important in the future. Additionally, robust constraints on the primordial power spectrum are calculated for present and future detections. The detailed shape of the PBH mass distribution is important for constraining the population. Fitting late universe observables with the mass distribution calculated from the power spectrum would be computationally expensive, so it is necessary to use simple parametrisations that capture the underlying shape. A number of these parametrisations are tested against the numerical calculation, and it is found that two of these consistently outperform the often-assumed lognormal, at the cost of an extra fitting parameter. Finally, the possibility that PBHs could explain the LIGO merger events is studied by applying a detailed model of the PBH merger rate and the detection probability of the LIGO instrument. Distributions of the merger rate are produced for a number of observables, indicating that the mass ratio could be an important quantity for distinguishing between astrophysical and primordial black hole mergers. A simple statistical test is carried out to demonstrate that PBHs can explain the totality of the LIGO events, with an appropriate abundance and mass distribution.