Title: The stochastic spectator

Abstract: I shall present our study of the stochastic distribution of spectator fields during inflation in the very early Universe. These are quantum fields that are present during inflation but play no direct part in driving inflation – such as a Higgs field – and can play a crucial role in the origin of structure. Such scenarios are sensitive to the field values acquired at the end of inflation by the spectator and thus can be ruled in and out of favour by statistical inference. Our work specifically focuses on calculating the distribution over field values where inflation is no longer driven by a flat (plateau) potential, but instead with a monomial potential with general power (Large-Field inflation). In this regime the background expansion may vary over time scales that are less than the relaxation time of the spectator field distributions towards the stationary solution. We find that the stationary solution approximation is in fact never a reliable estimate for the typical distribution at the end of inflation for a quadratic spectator during monomial inflation, with some caveats to be discussed.