Constraining models of Inflationary Magnetogenesis with NANOGrav

Generation of magnetic field during inflation can explain its presence over a wide range of scales in the Universe. In Ref.\cite{sharma2017}, we proposed a model to generate these fields during inflation. These fields have nonzero anisotropic stress which lead to the generation of a stochastic background of gravitational waves (GW) in the early universe. Here we show that for a scenario of magnetogenesis where reheating takes place around QCD epoch, this stochastic GW background lies in the $95\%$ confidence region of the GW signal probed by NANOGrav collaboration. This is the case when the generated electromagnetic field (EM) energy density is $3-10\%$ of the background energy density at the end of reheating. For this case, the values of magnetic field strength $B_0 \sim (3.8-6.9) \times 10^{-11}$G and its coherence length $\sim 30$ kpc at the present epoch. These values are for the models in which EM fields are of nonhelical nature. For the helical nature of the fields, these values are $B_0 \sim (1.1-1.9) \times 10^{-9}$G and its coherence length $\sim 0.8$ Mpc.