Inflationary magnetogenesis, derivative couplings and relativistic Van der Waals interactions

TL;DR

This paper investigates how derivative couplings in inflationary models can generate large-scale magnetic fields, analyzing their spectra, parameter constraints, and the role of susceptibilities and gauge couplings.

Contribution

It introduces a new time parametrization and systematic duality analysis to study magnetogenesis with derivative couplings during inflation.

Findings

Magnetic fields of a few hundredths of a nG are generated on Mpc scales.

Explicit parameter regions satisfy backreaction, bounds, and naturalness constraints.

Weakly coupled initial conditions are favored when gauge couplings are similar at inflation's end.

Abstract

When the gauge fields have derivative couplings to scalars, like in the case of the relativistic theory of Van der Waals (or Casimir-Polder) interactions, conformal invariance is broken but the magnetic and electric susceptibilities are not bound to coincide. We analyze the formation of large-scale magnetic fields in slow-roll inflation and find that they are generated at the level of a few hundredths of a nG and over typical length scales between few Mpc and $100$ Mpc. Using a new time parametrization that reduces to conformal time but only for coincident susceptibilities, the gauge action is quantized while the evolution equations of the corresponding mode functions are more easily solvable. The power spectra depend on the normalized rates of variation of the two susceptibilities (or of the corresponding gauge couplings) and on the absolute value of their ratio at the beginning of inflation. We pin down explicit regions in the parameter space where all the physical requirements (i.e. the backreaction constraints, the magnetogenesis bounds and the naturalness of the initial conditions of the scenario) are jointly satisfied. Weakly coupled initial data are favoured if the gauge couplings are of the same order at the end of inflation. Duality is systematically used to simplify the analysis of the wide parameter space of the model.