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 \nu } F ^ { \mu \nu } 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 ^ { +0.07 } _ { -0.05 } , 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 .