Inflaton Effective Potential from Fermions for General $\epsilon$

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.

25 pages, 9 figures, uses LaTeX2e. Version 2 (32 pages, 11 figures) substantially revised to provide a detailed comparison between the effective potential and the classical potential, and to explain the tendency for smooth potentials to favor high reheat temperatures

References in corpus (9)

• The Standard Model Higgs boson as the inflaton
• Stochastic Inflationary Scalar Electrodynamics
• Leading Log Solution for Inflationary Yukawa
• Reheating temperature from the CMB
• Reheating Closed String Inflation
• Bose-Fermi Cancellation of Cosmological Coleman-Weinberg Potentials
• Ricci Subtraction for Cosmological Coleman-Weinberg Potentials
• The Inflaton Effective Potential for General $\epsilon$
• Inflaton Effective Potential from Photons for General $\epsilon$

Cited by in corpus (5)

• Coincident Massless, Minimally Coupled Scalar Correlators on General Cosmological Backgrounds
• When tadpoles matter: One-loop corrections for spectator Higgs in inflation
• Reheating with Effective Potentials
• Perturbative Quantum Gravity Induced Scalar Coupling to Electromagnetism
• K-Essence Induced by Derivative Couplings of the Inflaton