Magnetogenesis during inflation and preheating in the Starobinsky model

摘要

By assuming the kinetic coupling $f^{2}(\phi)FF$ of the effective inflatonfield $\phi$ with the electromagnetic field, we explore magnetogenesis duringthe inflation and preheating stages in the Starobinsky model. We consider thecase of the exponential coupling function $f(\phi)=\exp(\alpha\phi/M_{p})$ andshow that for $\alpha \sim 12-15$ it is possible to generate the large scalemagnetic 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 couplingparameter, $\alpha=12-15$, model avoids the back-reaction problem for allrelevant modes.