Magnetogenesis in Higgs-Starobinsky inflation

TL;DR

This paper investigates the generation of gauge fields during Higgs-Starobinsky inflation, analyzing their spectra, helicality, and energy densities, and finds challenges in producing large, long-range magnetic fields.

Contribution

It introduces a novel approach to gauge field generation via nonminimal couplings in Higgs-Starobinsky inflation, analyzing spectral properties and their dependence on model parameters.

Findings

Scale-invariant or red-tilted magnetic spectra are possible for certain parameters.

Generated gauge fields tend to decrease in magnitude by the end of inflation.

Large correlation lengths are achievable, but magnitudes remain small.

Abstract

In the framework of mixed Higgs-Starobinsky inflation, we consider the generation of Abelian gauge fields due to their nonminimal coupling to gravity (in two different formulations of gravity -- metric and Palatini). We couple the gauge-field invariants $F_{\mu\nu}F^{\mu\nu}$ and $F_{\mu\nu}\tilde{F}^{\mu\nu}$ to an integer power of the scalar curvature $R^n$ in Jordan frame and, treating these interactions perturbatively, switch to the Einstein frame where they lead to effective kinetic and axial couplings between gauge fields and inflaton. We determine the power spectra, energy densities, correlation length, and helicality of the generated gauge fields for different values of the nonminimal coupling constants and parameter $n$. We analytically estimate the spectral index $n_{B}$ of the magnetic power spectrum and show that for $n>1$ it is possible to get the scale-invariant or even red-tilted spectrum for a wide range of modes that implies larger correlation length of the generated fields. On the other hand, the magnitude of these fields typically decreases in time becoming very small in the end of inflation. Thus, it is difficult to obtain both large magnitude and correlation length of the gauge field in the frame of this model.