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

Recent observational claims of magnetic fields stronger than 10(-16)G in the extragalactic medium motivate a new look for their origin in the inflationary magnetogenesis models. In this work we shall review the constraints on the simplest gauge invariant model f(2)(phi)F mu vF mu v of inflationary magnetogenesis, and show that in the optimal region of parameter space the anisotropic constraints coming from the induced bispectrum, due to the generated electromagnetic fields, yield the strongest constraints. In this model, only a very fine tuned scenario at an energy scale of inflation as low as 10(-2) GeV can explain the observations of void magnetic fields. These findings are consistent with the recently derived upper bound on the inflationary energy scale. However, if the detection of primordial tensor modes by BICEP2 is confirmed, the possibility of low scale inflation is excluded. Assuming the validity of the BICEP2 claim of a tensor-to-scalar ratio r = 0.2(-0.05)(+0.75), we provide the updated constraints on this model of inflationary magnetogenesis. On the Mpc scale, we find that the maximal allowed magnetic field strength from inflation is less than 10(-30) G.