Fluctuations of inflationary magnetogenesis

TL;DR

This paper investigates the growth rate of magnetized inhomogeneities during inflation, deriving bounds based on the dynamics of scalar modes and their impact on magnetic spectra, within a two-field inflationary model.

Contribution

It provides new bounds on the growth rate of inflationary magnetogenesis considering a coupled inflaton and spectator field system with gauge-invariant analysis.

Findings

Maximum growth rate of 2.2 in Hubble units for 70 efolds of inflation.

Tighter bounds for shorter inflation durations, looser for longer durations.

Upper bounds imply a lower limit on the magnetic spectral index.

Abstract

This analysis aims at exploring what can be said about the growth rate of magnetized inhomogeneities under two concurrent hypotheses: a phase of quasi-de Sitter dynamics driven by a single inflaton field and the simultaneous presence of a spectator field coupled to gravity and to the gauge sector. Instead of invoking ad hoc correlations between the various components, the system of scalar inhomogeneities is diagonalized in terms of two gauge-invariant quasi-normal modes whose weighted sum gives the curvature perturbations on comoving orthogonal hypersurfaces. The predominance of the conventional adiabatic scalar mode implies that the growth rate of magnetized inhomogeneities must not exceed 2.2 in Hubble units if the conventional inflationary phase is to last about 70 efolds and for a range of slow roll parameters between 0.1 and 0.001. Longer and shorter durations of the quasi-de Sitter stage lead, respectively, either to tighter or to looser bounds which are anyway more constraining than the standard backreaction demands imposed on the gauge sector. Since a critical growth rate of order 2 leads to a quasi-flat magnetic energy spectrum, the upper bounds on the growth rate imply a lower bound on the magnetic spectral index. The advantages of the uniform curvature gauge are emphasized and specifically exploited throughout the treatment of the multicomponent system characterizing this class of problems.