Abstract
Inflation is a period of rapid, accelerated expansion in the very early universe. It explains the observed homogeneity, isotropy and flatness of our universe. Here we consider inflation driven by a single-scalar field. Primordial density perturbations, needed to seed structure, then originate as microscopic quantum vacuum fluctuations of the field, which are stretched up to macroscopic scales. If large enough, these perturbations can collapse in the very early universe to form primordial black holes, which are a dark matter candidate. This thesis is dedicated to the understanding and numerical computation of these large and rare density perturbations.First, the necessary background on both cosmology and inflation is presented. This includes the fiducial cosmological model and expansion history, as well as cos- mological problems associated with it. We then show how the inflationary paradigm can solve these problems and explain the origin of cosmological perturbations. The theory behind perturbations large enough to form primordial black holes post- inflation is also given.
Second, details of how the numerical computation of large perturbations using stochastic processes and the statistical technique of importance sampling, are given. Importance sampling allows a single CPU to simulate very rare events that pre- viously required supercomputers. Comparison of simulations with analytical test cases are done and limitations discussed.
Third, the instantaneous breakdown is discussed of the separate-universe ap- proach, which gives an intuitive way to understand the evolution of cosmological perturbations in the long-wavelength limit, in models which produce large pertur- bations. This is due to the associated sudden transition. We demonstrate how the separate-universe approach can be applied in piece-wise manner.
Finally, importance sampling is applied to realistic models which produce large perturbations, after a sudden transition, including the full phase space. A new method for modelling the stochastic noise is introduced, along with comparisons with analytical predictions. We finish with conclusions and prospects for future work.
| Date of Award | 19 Mar 2025 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | David Wands (Supervisor), Vincent Vennin (Supervisor) & Kazuya Koyama (Supervisor) |