# Magnetogenesis during inflation and preheating in the Starobinsky model

## TL;DR

This paper investigates the generation of large-scale magnetic fields during inflation and preheating in the Starobinsky model, using a kinetic coupling function, and finds conditions under which significant magnetic fields can be produced without back-reaction issues.

## Contribution

It introduces a specific exponential kinetic coupling in the Starobinsky model to generate magnetic fields during inflation and preheating, avoiding back-reaction problems for certain parameter ranges.

## Key findings

- Magnetic fields with strength >10^{-15} Gauss can be generated.
- The magnetic field spectrum is blue with spectral index n=1+s, s>0.
- The model avoids back-reaction issues for coupling parameter α=12-15.

## Abstract

By assuming the kinetic coupling $f^{2}(\phi)FF$ of the effective inflaton field $\phi$ with the electromagnetic field, we explore magnetogenesis during the inflation and preheating stages in the Starobinsky model. We consider the case of the exponential coupling function $f(\phi)=\exp(\alpha\phi/M_{p})$ and show that for $\alpha \sim 12-15$ it is possible to generate the large scale magnetic fields with strength $\gtrsim 10^{-15}$ Gauss at the present epoch. The spectrum of generated magnetic fields is blue with the spectral index $n=1+s$, $s>0$. We have found that for the relevant values of the coupling parameter, $\alpha=12-15$, model avoids the back-reaction problem for all relevant modes.