Inflationary magnetogenesis without the strong coupling problem II: constraints from CMB anisotropies and B-modes

Abstract

Recent observational claims of magnetic fields stronger than $10^{-16}$ G in\nthe extragalactic medium motivate a new look for their origin in the\ninflationary magnetogenesis models. In this work we shall review the\nconstraints on the simplest gauge invariant model $f^2(\\phi)F_{\\mu \\nu}F^{\\mu\n\\nu}$ of inflationary magnetogenesis, and show that in the optimal region of\nparameter space the anisotropic constraints coming from the induced bispectrum,\ndue to the generated electromagnetic fields, yield the strongest constraints.\nIn this model, only a very fine tuned scenario at an energy scale of inflation\nas low as $10^{-2}$ GeV can explain the observations of void magnetic fields.\nThese findings are consistent with the recently derived model independent\nconstraints. However, if the detection of primordial tensor modes by BICEP2 is\nconfirmed, the possibility of low scale inflation is excluded. Assuming the\nvalidity of the BICEP2 claim of a tensor-to-scalar ratio\n$r=0.2^{+0.07}_{-0.05}$, we provide the updated constraints on inflationary\nmagnetogenesis. On the Mpc scale, the maximal allowed magnetic field strength\nfrom inflation is less than $10^{-30}$ G.\n