Stability of stealth magnetic field in de Sitter spacetime

TL;DR

This paper analyzes the stability of a de Sitter universe with a homogeneous magnetic field in a specific gauge theory, showing conditions under which such a configuration remains stable, and explores its implications for inflationary magnetogenesis.

Contribution

It provides a detailed stability analysis of a stealth magnetic field in de Sitter spacetime within a scalar-tensor gauge theory, introducing new stable solutions for inflationary magnetogenesis.

Findings

Identified stability conditions for the magnetic field in de Sitter space.

Presented explicit examples satisfying all stability criteria.

Suggested a new mechanism for primordial magnetic field generation during inflation.

Abstract

A detailed stability analysis is presented for the de Sitter solution with a homogeneous magnetic field that was recently found in the context of a $U(1)$ gauge theory nonminimally coupled to scalar-tensor gravity. The magnetic field is `stealth' in the sense that the corresponding stress-energy tensor is of the form of an effective cosmological constant and thus is isotropic despite the fact that the magnetic field has a preferred spatial direction. We study the stability of the solution against linear perturbations in the subhorizon and superhorizon limits. We then present some explicit examples that satisfy all stability conditions. The stable de Sitter solution with a homogeneous magnetic field opens up a new possibility for inflationary magnetogenesis, in which magnetic fields in the Universe at all scales may originate from a classical, homogeneous magnetic field sustained during inflation.