Magnetogenesis during inflation and preheating in the Starobinsky model

Abstract

By assuming the kinetic coupling $f^2(\varphi )FF$ of the effective inflaton field $\varphi$ 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 $f(\varphi )=\exp (\alpha \varphi /M_p)$ 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.

10 pages, 5 figures