Primordial magnetic fields in the $f^{2}FF$ model in large field inflation under de Sitter and power law expansion

TL;DR

This paper investigates the generation of primordial magnetic fields during large field inflation using the $f^{2}FF$ model, analyzing conditions under which scale-invariant fields can form without exceeding inflation energy density, consistent with observations.

Contribution

It demonstrates that scale-invariant primordial magnetic fields can be generated in large field inflation models when certain constraints are relaxed, expanding understanding of magnetogenesis.

Findings

Scale-invariant PMF are not obtained under strict slow roll constraints.

Electric field energy can remain below inflation energy density for specific wavenumber ranges.

Generated PMF ranges are consistent with observational constraints.

Abstract

We use the $f^{2}FF$ model to study the generation of primordial magnetic fields (PMF) in the context of large field inflation (LFI), described by the potential, $V \sim M \phi^{p}$. We compute the magnetic and electric spectra for all possible values of the model parameters under de Sitter and power law expansion. We show that scale invariant PMF are not obtained in LFI to first order in the slow roll approximation, if we impose the constraint $V(\phi=0)\sim 0$. Alternatively, if these constraints are relaxed, the scale invariant PMF can be generated. The associated electric field energy can fall below the energy density of inflation, $\rho_{\rm{Inf}}$ for the ranges of comoving wavenumbers, $ k > 8 \times 10^{-7} \rm{Mpc^{-1}}$ and $ k > 4 \times 10^{-6} \rm{Mpc^{-1}}$ in de Sitter and power law (PL) expansion. Further, it can drop below $\rho_{\rm{Inf}}$ on the ranges, e-foldings $N > 51$, $p<1.66$, $p >2.03$, $l_0 > 3 \times 10^5 {M_{\rm{Pl}}}^{-1} (H_i < 3.3 \times 10^{-6} M_{\rm{Pl}})$, and $M > 2.8 \times 10^{-3} M_{\rm{Pl}}$. All of the above ranges fit with the observational constraints.