Inflaton effective potential from fermions for general ε

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 $\ensuremath{\epsilon}(t)$. For $\ensuremath{\epsilon}=0$ our final result agrees with the famous computation of Candelas and Raine done long ago on the de Sitter background [P. Candelas and D. Raine, Phys. Rev. D 12, 965 (1975).], and both computations degenerate to the result of Coleman and Weinberg in the flat space limit [S. R. Coleman and E. J. Weinberg, Phys. Rev. D 7, 1888 (1973).]. Our result contains a small part that depends nonlocally on the inflationary geometry. Even in the numerically larger local part, very little of the $\ensuremath{\epsilon}$ dependence takes the form of Ricci scalars. We discuss the implications of these corrections for inflation.