Gauge Invariant Wave Equations in Curved Space-Times and Primordial Magnetic Fields

TL;DR

This paper investigates how breaking conformal invariance via curvature interactions in curved spacetime can amplify primordial magnetic fields during the universe's reheating phase, potentially explaining observed galactic magnetic fields.

Contribution

It introduces a gauge-invariant wave equation incorporating curvature interactions, demonstrating magnetic field amplification during reheating but not during de Sitter inflation.

Findings

Magnetic fields are amplified during reheating due to curvature interactions.

No magnetic field growth occurs during the de Sitter epoch.

Primordial magnetic fields of astrophysical relevance can be generated.

Abstract

The inflationary production of magnetic field seeds for galaxies is discussed. The analysis is carried out by writing the wave equation of the electromagnetic field in curved spacetimes. The conformal invariance is broken by taking into account of the interaction of the electromagnetic field with the curvature tensor of the form $\lambda R_{\alpha\beta\gamma\delta} F^{\alpha\beta} F^{\gamma\delta}$. Such a term induces an amplification of the magnetic field during the reheating phase of the universe, but no growth of the magnetic field occurs in the de Sitter epoch. The resulting primordial magnetic field turns out to have strengths of astrophysical interest.