Classical and quantum dynamics during inflation

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 quantum
fluctuations inevitably generate inhomogeneities and anisotropies on all observable scales (and
beyond). This project will explore the nature of the fluctuations produced in scalar, vector and tensor
fields, including the primordial density field and gravitational waves, and how we may compare these
predictions against current and future observations to identify the inflationary dynamics and physical
degrees of freedom present in the very early universe.
In particular we will employ the stochastic approach to modelling inflationary dynamics, incorporating
quantum fluctuations as a stochastic noise, and the recently developed non-perturbative techniques to
calculate the full probability distribution function for the primordial density field. We will characterise
the nature of this non-Gaussian distribution, and apply our results to calculate the abundance of
extreme objects such as ultra-compact mini-halos and primordial black holes predicted in some
models. This project involves a combination of analytic and numerical work.