Superhorizon magnetic fields

2015/12/31 by Leonardo Campanelli
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Cosmology and Gravitation Theories #Geomagnetism and Paleomagnetism Studies #Omega #Physics #Quantum mechanics #Solar and Space Plasma Dynamics #astro-ph.CO

paper · pdf · doi:10.1103/physrevd.93.063501

published as Phys. Rev. D 93, 063501 (2016) · 15 pages, 1 figure, typo corrected in Eq. (57), to appear in Phys. Rev. D

arxiv created 2016/02/25 · openalex publication_date 2016/03/04 · arxiv updated 2016/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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\ensuremathη_e, n_k, and \mathrm\ensuremathΩ_k, where \ensuremathη_e is the conformal time at the end of inflation, n_k is the number density spectrum of inflation-produced photons, and \mathrm\ensuremathΩ_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_k^\ensuremath-1\ensuremath≪|k\ensuremathη_e|\ensuremath≪1, and three evolutionary scenarios are possible: (i) |\mathrm\ensuremathΩ_k\ensuremath∓\ensuremathπ|=O(1), in which case the evolution of the magnetic spectrum B_k(\ensuremathη) is adiabatic, a²B_k(\ensuremathη)=const, with a being the expansion parameter; (ii) |\mathrm\ensuremathΩ_k\ensuremath∓\ensuremathπ|\ensuremath≪|k\ensuremathη_e|, in which case the evolution is superadiabatic, a²B_k(\ensuremathη)\ensuremath∝\ensuremathη; (iii) |k\ensuremathη_e|\ensuremath≪|\mathrm\ensuremathΩ_k\ensuremath∓\ensuremathπ|\ensuremath≪1 or |k\ensuremathη_e|\ensuremath∼|\mathrm\ensuremathΩ_k\ensuremath∓\ensuremathπ|\ensuremath≪1, in which case an early phase of adiabatic evolution is followed, after a time \ensuremathη_\ensuremath⋆\ensuremath∼|\mathrm\ensuremathΩ_k\ensuremath∓\ensuremathπ|/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.

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