Metric perturbation from inflationary magnetic field and generic bound on inflation models

TL;DR

This paper investigates how primordial magnetic fields generated during inflation can induce metric perturbations, leading to bounds on inflation models by ensuring these perturbations stay within observational limits.

Contribution

It provides a robust method to constrain inflation models based on metric perturbations sourced by inflationary magnetic fields, linking magnetic field origin to inflation parameters.

Findings

Derived a bound on inflation models from metric perturbation limits

Converted the bound into a lower limit on the Hubble parameter during inflation

Established a connection between primordial magnetic fields and inflationary dynamics

Abstract

There is an observational indication of extragalactic magnetic fields. No known astrophysical process can explain the origin of such large scale magnetic fields, which motivates us to look for their origin in primordial inflation. By solving the linearized Einstein equations, we study metric perturbations sourced by magnetic fields that are produced during inflation. This leads to a simple but robust bound on the inflation models by requiring that the induced metric perturbation should not exceed the observed value 10^-5. In case of the standard single field inflation model, the bound can be converted into a lower bound on the Hubble parameter during inflation.