Leading Log Solution for Inflationary Yukawa

TL;DR

This paper extends Starobinskii's stochastic approach to analyze a massless scalar-fermion Yukawa interaction in de Sitter space, deriving nonperturbative results and exploring implications for the cosmological constant.

Contribution

It introduces a stochastic framework for scalar-fermion Yukawa interactions in de Sitter space, including passive fields, and provides explicit solutions and nonperturbative stress tensor results.

Findings

Derived a stochastic formulation for Yukawa interactions in de Sitter.

Validated the approach with a two-loop explicit computation.

Obtained a nonperturbative leading log stress tensor result.

Abstract

We generalize Starobinskii's stochastic technique to the theory of a massless, minimally coupled scalar interacting with a massless fermion in a locally de Sitter geometry. The scalar is an ``active'' field that can engender infrared logarithms. The fermion is a ``passive'' field that cannot cause infrared logarithms but which can carry them, and which can also induce new interactions between the active fields. The procedure for dealing with passive fields is to integrate them out, then stochastically simplify the resulting effective action following Starobinski\u{\i}. Because Yukawa theory is quadratic in the fermion this can be done explicitly using the classic solution of Candelas and Raine. We check the resulting stochastic formulation against an explicit two loop computation. We also derive a nonperturbative, leading log result for the stress tensor. Because the scalar effective potential induced by fermions is unbounded below, back-reaction from this model might dynamically cancel an arbitrarily large cosmological constant.