The hypermagnetic power spectra and the phases of Sakharov oscillations

TL;DR

This paper investigates how gauge field amplification during inflation influences hypermagnetic power spectra, Sakharov oscillations, and magnetogenesis, highlighting the role of duality symmetry and the timing of modes relative to the Hubble radius.

Contribution

It reveals the impact of duality symmetry on hypermagnetic spectra and clarifies how the timing of modes affects late-time magnetic fields in inflationary magnetogenesis.

Findings

Standing oscillations are overdamped by conductivity after inflation.

Late-time magnetic field strength depends on when modes reach the Hubble radius.

Magnetogenesis constraints vary with post-inflationary expansion rate.

Abstract

If the gauge fields are amplified from the inflationary vacuum, the quantum mechanical initial data correspond to travelling waves that turn asymptotically into standing waves whose phases only depend on the evolution of the gauge coupling. We point out that these gauge analogs of the Sakharov oscillations are exchanged by the duality symmetry and ultimately constrain both the relative scaling of the hypermagnetic power spectra and their final asymptotic values. Unlike the case of the density contrasts in a relativistic plasma, the standing oscillations never develop since they are eventually overdamped by the finite value of the conductivity as soon as the corresponding modes are comparable with the expansion rates after inflation. We show that the late-time value of the magnetic field is not determined at radiation dominance (and in spite of the value of the wavenumber) but it depends on the moment when the wavelengths (comparable with the Mpc) get of the order of the Hubble radius before equality. This means that the magnetogenesis requirements are only relaxed if the post-inflationary expansion rate is slower than radiation but the opposite is true when the plasma expands faster than radiation and the corresponding power spectra are further suppressed. After combining the present findings with the evolution of the gauge coupling we show that these results are consistent with a magnetogenesis scenario where the gauge coupling is always perturbative during the inflationary stage while, in the dual case, the same requirements cannot be satisfied.