Warm Inflation with Pseudo-scalar Couplings

TL;DR

This paper examines how pseudo-scalar inflaton couplings during warm inflation influence thermal bath properties, revealing the necessity to correct existing models to include chemical potentials affecting fluctuations and friction.

Contribution

It identifies and corrects the treatment of chemical potentials in models of warm inflation with pseudo-scalar couplings, showing their impact on thermal fluctuations and friction.

Findings

Chemical potentials modify the fluctuation-dissipation relation.

Corrected models account for non-zero chemical potentials affecting friction.

Boltzmann and thermal expectation approaches yield consistent results.

Abstract

Inflaton couplings during warm inflation result in the production of a thermal bath. Thermal friction and fluctuations can dominate the standard de Sitter analogues, resulting in a modified slow-roll scenario with a new source of density fluctuations. Due to issues with back-reaction, it is advantageous to consider inflaton couplings with the thermal bath that are pseudo-scalar in nature, e.g., derivative interactions or topological $F \tilde F$ couplings. We demonstrate that {\it every single} existing model of warm inflation utilizing pseudo-scalar couplings needs to be corrected to properly account for all of the chemical potentials that the thermal bath acquires in response to the inflaton coupling. These chemical potentials are for non-conserved charges, and are non-zero only because of the applied inflaton couplings. The model-dependent chemical potentials modify the fluctuation-dissipation theorem, making the relationship between the thermal friction and thermal fluctuations model-dependent. In extreme cases, these chemical potentials can cause the friction term to vanish while thermal fluctuations remain non-zero. In the context of a simple example, we demonstrate how to calculate the chemical potentials, thermal friction, and thermal fluctuations using both the Boltzmann equations and by calculating thermal expectation values, showing explicitly that the two approaches give the same result.