Stochastic 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 explore recent developments in the stochastic approach to modelling inflationary dynamics, incorporating quantum field fluctuations as a stochastic noise. There are important questions about the connection between the stochastic approach and traditional perturbative approaches in general relativity, including the use of the long-wavelength (or separate universe) approximation. We also want to understand better possible connections to recent quantum field theory results, such as soft de Sitter effective theory. Stochastic fluctuations can be sensitive to ultra-high energy physics so it is interesting to consider if there are observational consequences of the ultra- violet limit, for example, unitary bounds. Ultimately our aim is to apply our results to characterise the full probability distribution function for the primordial fields in inflationary models. This project involves a combination of analytic and numerical work.