Spectator electric fields, de Sitter space-time and the Schwinger effect

TL;DR

This paper examines the behavior of spectator electric fields in de Sitter space, highlighting issues with current assumptions and their thermodynamic implications, especially in the context of the Schwinger effect.

Contribution

It critically analyzes the evolution of spectator electric fields in de Sitter space, revealing inconsistencies in common assumptions and their thermodynamic violations.

Findings

Spectator electric fields are constrained by critical density bounds.

Ad hoc currents violate the second law of thermodynamics.

Electric energy density remains unaffected by expansion in certain models.

Abstract

During a de Sitter stage of expansion the spectator fields of different spin are constrained by the critical density bound and by further requirements determined by their specific physical nature. The evolution of spectator electric fields in conformally flat background geometries is occasionally concocted by postulating the existence of ad hoc currents but this apparently innocuous trick violates the second law of thermodynamics. Such a problem occurs, in particular, for those configurations (customarily employed for the analysis of the Schwinger effect in four-dimensional de Sitter backgrounds) leading to an electric energy density which is practically unaffected by the expansion of the underlying geometry. The obtained results are compared with more mundane situations where Joule heating develops in the early stages of a quasi-de Sitter phase.