Year: 2016
Type: article
Abstract: We analyze the evolution of superhorizon-scale magnetic fields from the end of inflation till today. Whatever is the mechanism responsible for their generation during inflation, we find that a given magnetic mode with wave number $k$ evolves, after inflation, according to the values of $k{\ensuremath{\eta}}_{e}$, ${n}_{\mathbf{k}}$, and ${\mathrm{\ensuremath{\Omega}}}_{k}$, where ${\ensuremath{\eta}}_{e}$ is the conformal time at the end of inflation, ${n}_{\mathbf{k}}$ is the number density spectrum of inflation-produced photons, and ${\mathrm{\ensuremath{\Omega}}}_{k}$ is the phase difference between the two Bogoliubov coefficients which characterize the state of that mode at the end of inflation. For any realistic inflationary magnetogenesis scenario, we find that ${n}_{\mathbf{k}}^{\ensuremath{-}1}\ensuremath{\ll}|k{\ensuremath{\eta}}_{e}|\ensuremath{\ll}1$, and three evolutionary scenarios are possible: (i) $|{\mathrm{\ensuremath{\Omega}}}_{k}\ensuremath{\mp}\ensuremath{\pi}|=\mathcal{O}(1)$, in which case the evolution of the magnetic spectrum ${B}_{k}(\ensuremath{\eta})$ is adiabatic, ${a}^{2}{B}_{k}(\ensuremath{\eta})=\text{const}$, with $a$ being the expansion parameter; (ii) $|{\mathrm{\ensuremath{\Omega}}}_{k}\ensuremath{\mp}\ensuremath{\pi}|\ensuremath{\ll}|k{\ensuremath{\eta}}_{e}|$, in which case the evolution is superadiabatic, ${a}^{2}{B}_{k}(\ensuremath{\eta})\ensuremath{\propto}\ensuremath{\eta}$; (iii) $|k{\ensuremath{\eta}}_{e}|\ensuremath{\ll}|{\mathrm{\ensuremath{\Omega}}}_{k}\ensuremath{\mp}\ensuremath{\pi}|\ensuremath{\ll}1$ or $|k{\ensuremath{\eta}}_{e}|\ensuremath{\sim}|{\mathrm{\ensuremath{\Omega}}}_{k}\ensuremath{\mp}\ensuremath{\pi}|\ensuremath{\ll}1$, in which case an early phase of adiabatic evolution is followed, after a time ${\ensuremath{\eta}}_{\ensuremath{\star}}\ensuremath{\sim}|{\mathrm{\ensuremath{\Omega}}}_{k}\ensuremath{\mp}\ensuremath{\pi}|/k$, by a superadiabatic evolution. Once a given mode reenters the horizon, it remains frozen into the plasma and then evolves adiabatically till today. As a corollary of our results, we find that inflation-generated magnetic fields evolve adiabatically on all scales and for all times in conformal-invariant free Maxwell theory, while they evolve superadiabatically after inflation on superhorizon scales in the nonconformal-invariant Ratra model, where the inflaton is kinematically coupled to the electromagnetic field. The latter result supports and, somehow, clarifies our recent claim that the Ratra model can account for the presence of cosmic magnetic fields without suffering from both backreaction and strong-coupling problems.
Author: Leonardo Campanelli
Institution: University of Bari Aldo Moro
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2198059599