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Post inflationary evolution of inflation-produced, large-scale magnetic fields using a generalised cosmological Ohm's law and both standard and modified Maxwell's equations

In most of the literature on evolution of cosmological magnetic fields, it is found that large-scale magnetic fields evolve as $B^{2}\propto a^{-4}$ (adiabatic magnetic decay) where $a$ is the cosmological scale factor and $B$ is the cosmological magnetic field. This rapid decay has been considered as the main obstacle against magnetic fields produced during the inflationary epoch from surviving until today and seeding the observed fields. However, recent reports of first ever detection of intergalactic fields, with strengths around $10^{-6}G$ are a mystery [1-4]. One possible explanation is that large-scale magnetic fields could have been superadiabatically amplified in their evolutionary history. Superadiabatic amplification may mean that there is an actual increase in the strength of the magnetic field or that magnetic decay-rates are slower than the standard adiabatic magnetic decay rate [5] . This can be demonstrated if we use the generalised cosmological Ohm's law and both standard and modified Maxwell field equations; this is the goal of this study.