[Paper Review] On the magnetic evolution in Friedmann universes and the question of cosmic magnetogenesis

Christos G. Tsagas|arXiv (Cornell University)|Dec 15, 2014

Solar and Space Plasma Dynamics4 references4 citations

TL;DR

The paper challenges the long-standing assumption that primordial magnetic fields decay adiabatically in Friedmann universes, showing instead that superhorizon-scale fields can undergo superadiabatic amplification due to causality constraints on electric current formation. This leads to a power-law decay slower than $ B \propto a^{-2} $, enabling astrophysically relevant field strengths without new physics.

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.

Motivation & Objective

• To re-examine the assumption that primordial magnetic fields decay adiabatically on all scales in Friedmann universes.
• To investigate the role of causality in limiting electric current formation and magnetic flux freezing to sub-horizon scales.
• To assess whether superadiabatic amplification of large-scale magnetic fields is possible after inflation without violating standard electromagnetism or cosmology.
• To evaluate the impact of initial conditions—determined during inflation and reheating—on post-inflationary magnetic field evolution.
• To extend the analysis to marginally open and closed Friedmann models, assessing universality of the mechanism.

Proposed method

• Analyzes the evolution of magnetic fields in spatially flat Friedmann-Robertson-Walker (FRW) universes using classical electromagnetism and standard cosmology.
• Applies causality arguments to show that electric currents and flux freezing cannot correlate on super-Hubble scales, invalidating the assumption of global flux conservation.
• Derives the power-law solution for superhorizon magnetic fields after inflation, identifying a slowly decaying mode that can dominate depending on initial conditions.
• Considers two complementary scenarios for initial conditions: one with strong de Sitter enhancement and another with mild enhancement, to explore their impact on field amplification.
• Uses the same causality-based constraints to evaluate non-conventional magnetogenesis models that amplify fields during inflation.
• Extends the analysis to marginally open and closed Friedmann models, confirming the robustness of the superadiabatic amplification mechanism across spatial curvature types.

Experimental results

Research questions

• RQ1 Can magnetic fields on super-Hubble scales decay adiabatically in standard Friedmann cosmology, or is this assumption causally inconsistent?
• RQ2 To what extent do initial conditions during inflation and reheating determine the post-inflationary evolution of large-scale magnetic fields?
• RQ3 Can superadiabatic amplification of primordial magnetic fields occur without invoking new physics beyond classical electromagnetism and standard cosmology?
• RQ4 How do causality constraints on electric current formation affect the validity of the ideal MHD approximation for superhorizon magnetic fields?
• RQ5 To what extent can the same causality arguments constrain or assist non-conventional inflationary magnetogenesis scenarios?

Key findings

• Superhorizon magnetic fields in Friedmann universes do not necessarily decay adiabatically; instead, they follow a power-law solution with a mode decaying slower than $ a^{-2} $.
• The slowly decaying mode can dominate the evolution if initial conditions at the start of reheating allow it to survive, enabling superadiabatic amplification.
• For a comoving scale of ~10 kpc, the residual magnetic field strength after superadiabatic amplification can reach $ \sim 10^{-33} $ G, significantly higher than the standard $ \sim 10^{-53} $ G prediction.
• This enhanced field strength is sufficient to seed galactic dynamos and can be further amplified during protogalactic collapse.
• The mechanism applies not only to spatially flat models but also to marginally open and closed Friedmann universes, including both supercurvature and subcurvature magnetic modes.
• Non-conventional inflationary magnetogenesis models with strong amplification during de Sitter phase may conflict with CMB anisotropy observations, while those with mild amplification are viable and potentially assisted by the causality constraints.