Inflaton Effective Potential from Fermions for General $\epsilon$

TL;DR

This paper derives an accurate approximation for the fermion contribution to the inflaton potential during inflation with a general slow roll parameter, extending previous results and exploring implications for inflationary models.

Contribution

It provides a novel approximation for the fermion-induced inflaton potential in general inflationary geometries with arbitrary slow roll parameter $psilon$, generalizing prior de Sitter and flat space results.

Findings

Agreement with known de Sitter results for psilon=0

Inclusion of nonlocal geometric dependence in the potential

Minimal Ricci scalar dependence in psilon corrections

Abstract

We accurately approximate the contribution of a Yukawa-coupled fermion to the inflaton effective potential for inflationary geometries with a general first slow roll parameter $\epsilon(t)$. For $\epsilon = 0$ our final result agrees with the famous computation of Candelas and Raine done long ago on de Sitter background, and both computations degenerate to the result of Coleman and Weinberg in the flat space limit. Our result contains a small part that depends nonlocally on the inflationary geometry. Even in the numerically larger local part, very little of the $\epsilon$ dependence takes the form of Ricci scalars. We discuss the implications of these corrections for inflation.