Magneto-reheating constraints from curvature perturbations

TL;DR

This paper derives new constraints on primordial magnetic fields during inflation and reheating by analyzing their impact on curvature perturbations, providing bounds on magnetic field strength, reheating energy scale, and equation of state.

Contribution

It introduces a method to constrain magnetic fields in inflationary models based on curvature perturbation limits, applicable to various inflationary scenarios and magnetic field scaling behaviors.

Findings

Stronger bounds on magnetic field strength than previous backreaction limits.

Massive inflation can produce observable magnetic fields if reheating is matter-dominated at high energies.

For gamma=-1, large magnetic fields are incompatible with massive inflation and matter-dominated reheating.

Abstract

As additional perturbative degrees of freedom, it is known that magnetic fields of inflationary origin can source curvature perturbations on super-Hubble scales. By requiring the magnetic generated curvature to remain smaller than its inflationary adiabatic counterpart during inflation and reheating, we derive new constraints on the maximal field value today, the reheating energy scale and its equation of state parameter. These bounds end up being stronger by a few order of magnitude than those associated with a possible backreaction of the magnetic field onto the background. Our results are readily applicable to any slow-roll single field inflationary models and any magnetic field having its energy density scaling as a^gamma during inflation. As an illustrative example, massive inflation is found to remain compatible with a magnetic field today Bo = 5 x 10^(-15) G for some values of gamma only if a matter dominated reheating takes place at energies larger than 10^5 GeV. Conversely, assuming gamma=-1, massive inflation followed by a matter dominated reheating cannot explain large scale magnetic fields larger than 10^(-20) G today.