Recent Developments in Stochastic Inflation

TL;DR

This paper reviews recent advances in stochastic inflation, extending Starobinsky's formalism to complex interactions including fermions, photons, and derivative couplings, and discusses limitations of stochastic methods in capturing secular loop effects.

Contribution

It generalizes stochastic inflation formalism to include fermions, photons, and derivative interactions, and analyzes the limitations of stochastic techniques in certain quantum corrections.

Findings

Extended stochastic formalism to fermions and photons

Incorporated derivative interactions like nonlinear sigma models and gravity

Identified secular loop corrections beyond stochastic methods

Abstract

This article is dedicated to the memory of Alexei Starobinsky. I begin with some recollections of him and then review the generalization of his wonderful stochastic formalism from scalar potential models to theories which interact with fermions and photons, and finally to theories with derivative interactions such as nonlinear sigma models and gravity. This entails effective potentials generated by the usual field-dependent masses, as well as by field-dependent field strengths, and by field-dependent Hubble parameters. I also discuss secular loop corrections which cannot be captured by stochastic techniques.