Generation of an electromagnetic field nonminimally coupled to gravity during Higgs inflation

TL;DR

This paper investigates how electromagnetic fields can be generated during Higgs inflation when nonminimal couplings to gravity are considered, analyzing different gravity formulations and estimating the resulting magnetic field strength today.

Contribution

It introduces a detailed analysis of electromagnetic field generation during Higgs inflation with nonminimal couplings, comparing metric and Palatini gravity formulations.

Findings

Magnetic fields with current magnitude of 10^{-14} to 10^{-15} G are possible.

The study derives the effective coupling functions in both gravity formulations.

Electromagnetic helicity and power spectrum are characterized for various coupling parameters.

Abstract

In the framework of Higgs inflation, we consider the electromagnetic field nonminimally coupled to gravity via the parity-preserving $\propto RF^{2}$ and parity-violating $\propto RF\tilde{F}$ terms. Using the perturbation theory to the leading order in these couplings, we study the generation of the electromagnetic field during the inflation stage. We derive the effective kinetic and axial coupling functions arising in the Einstein frame in the usual metric as well as Palatini formulations of gravity. For both formulations, we determine the power spectrum, energy density, and helicality of the generated electromagnetic fields for different values of the nonminimal coupling constants. Finally, we estimate the maximal present-day magnitude of the magnetic field as $10^{-14}-10^{-15}\,$G with the correlation length of order 10 pc.