Spectator field dynamics in de Sitter and curvaton initial conditions

TL;DR

This paper studies how long wavelength spectator scalar fields evolve during inflation, showing that their initial conditions can persist for many e-folds and influence curvature perturbations in the curvaton model.

Contribution

It provides a detailed analysis of the stochastic dynamics of spectator fields with mixed potentials and their impact on initial conditions in inflationary cosmology.

Findings

Spectator fields' probability distributions spread and approach equilibrium over long timescales.

Equilibration timescales can exceed thousands of e-folds, depending on model parameters.

Initial conditions for spectator fields may not be erased during inflation.

Abstract

We investigate the stochastic behaviour of long wavelength modes of light spectator scalar fields during inflation. When starting from a classical field value, the probability distribution for the spectator both spreads out and moves towards an equilibrium distribution. We study the timescales for a mixed quadratic and quartic potential. The timescale of equilibration depends on the parameters of the model, and can be surprisingly large, even much more than thousands of e-folds. These results imply that the initial conditions for spectator fields are not automatically erased during inflation. Applying the results to the curvaton model, we calculate the probability distribution of the curvature perturbation and discuss 'typical' Universes.