Abstract
We analyse the evolution of primordial magnetic fields in spatially flat Friedmann universes and reconsider the belief that, after inflation, these fields decay adiabatically on all scales. Without abandoning classical electromagnetism or standard cosmology, we demonstrate that this is not necessarily the case for superhorizon-sized magnetic fields. The underlying reason for this is causality, which confines the post-inflationary process of electric-current formation, electric-field elimination and magnetic-flux freezing within the horizon. As a result, the adiabatic magnetic decay is not a priori guaranteed on super-Hubble scales. Instead, after inflation, large-scale magnetic fields obey a power-law solution, where one of the modes drops at a rate slower than the adiabatic. Whether this slowly decaying mode can dominate and dictate the post-inflationary magnetic evolution depends on the initial conditions. These are determined by the evolution of the field during inflation and by the nature of the transition from the de Sitter phase to the reheating era and then to the subsequent epochs of radiation and dust. We discuss two alternative and complementary scenarios to illustrate the role and the implications of the initial conditions for cosmic magnetogenesis. Our main claim is that magnetic fields can be superadiabatically amplified after inflation, as long as they remain outside the horizon. This means that inflation-produced fields can reach astrophysically relevant residual strengths without breaking away from standard physics. Moreover, using the same causality arguments, one can constrain (or in some cases assist) the non-conventional scenarios of primordial magnetogenesis that amplify their fields during inflation. Finally, we show that our results extend naturally to the marginally open and the marginally closed Friedmann universes.
Highlights
The origin of cosmic magnetism remains an essentially open question despite the efforts and the established widespread presence of magnetic (B) fields in the universe [1,2,3,4]
The ideal-MHD limit is the result of causal microphysical processes, which have local range only and cannot dictate the evolution of B-fields with super-Hubble correlations without violating causality. As long as they remain superhorizon-sized, B-fields remain immune to causal physics and they are only affected by the background expansion, just like any other inflation-generated perturbation
The scenarios of cosmic magnetogenesis are typically classified into early-time and late-time mechanisms, according to whether they operate before or after recombination
Summary
The origin of cosmic magnetism remains an essentially open question despite the efforts and the established widespread presence of magnetic (B) fields in the universe [1,2,3,4]. The ideal-MHD limit is the result of causal microphysical processes, which have local range only and cannot dictate the evolution of B-fields with super-Hubble correlations without violating causality Put another way, as long as they remain superhorizon-sized, B-fields remain immune to causal physics and they are only affected by the background expansion, just like any other inflation-generated perturbation. As long as they remain superhorizon-sized, B-fields remain immune to causal physics and they are only affected by the background expansion, just like any other inflation-generated perturbation All these mean that, on scales larger than the horizon, the magnetic flux is not necessarily conserved and the adiabatic (B ∝ a−2 ) decay-law is not a priori guaranteed. A development that could put the question of cosmic magnetism under an entirely new perspective
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