Magnetogenesis by non-minimal coupling to gravity in the Starobinsky inflationary model

TL;DR

This paper investigates the potential for magnetic field generation during inflation in the Starobinsky model with non-minimal curvature-electromagnetic couplings, finding limited amplification due to back-reaction effects.

Contribution

It introduces and assesses the effects of parity-preserving and parity-violating non-minimal couplings in the Starobinsky inflationary model on magnetogenesis.

Findings

Parity-preserving couplings produce negligible magnetic field amplification.

Axial couplings face back-reaction issues, limiting amplification to about 10^5.

Magnetogenesis is significantly constrained by back-reaction effects in this model.

Abstract

The $R^2$ term in the Starobinsky inflationary model can be regarded as a leading quantum correction to the gravitational effective action. We assume that parity-preserving and parity-violating (axial) non-minimal couplings between curvature and electromagnetic field are also present in the effective action. In the Einstein frame, they turn into non-trivial couplings of the scalaron and curvature to the electromagnetic field. We make an assessment of inflationary magnetogenesis in this model. In the case of parity-preserving couplings, amplification of magnetic field is negligibly small. In the case of axial couplings, magnetogenesis is hampered by strong back-reaction on the inflationary process, resulting in possible amplification of magnetic field at most by the factor $10^5$ relative to its vacuum fluctuations.