Classical and quantum dynamics during inflation

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The classical evolution of fields during a period of accelerated expansion in the very early universe("inflation") can establish an idealised homogeneous and isotropic cosmology, but quantumfluctuations inevitably generate inhomogeneities and anisotropies on all observable scales (andbeyond). This project will explore the nature of the fluctuations produced in scalar, vector and tensorfields, including the primordial density field and gravitational waves, and how we may compare thesepredictions against current and future observations to identify the inflationary dynamics and physicaldegrees of freedom present in the very early universe.In particular we will employ the stochastic approach to modelling inflationary dynamics, incorporatingquantum fluctuations as a stochastic noise, and the recently developed non-perturbative techniques tocalculate the full probability distribution function for the primordial density field. We will characterisethe nature of this non-Gaussian distribution, and apply our results to calculate the abundance ofextreme objects such as ultra-compact mini-halos and primordial black holes predicted in somemodels. This project involves a combination of analytic and numerical work.