Gravitational wave generation in a viable scenario of inflationary magnetogenesis

Abstract

Generation of magnetic fields during inflation is a promising mechanism for the origin of the observed large scale magnetic fields in the universe. Among several attempts, a popular model is one where the inflaton and the electromagnetic field are coupled through a coupling function $f$ leading to a term in the Lagrangian density of the form, $f^2 F^{\mu \nu} F_{\mu\nu}$. A number of potential difficulties with such models have been raised in the literature. In our earlier work, we have suggested viable models of inflationary magnetogenesis which avoid these problems and at the same time can lead to either nonhelical or helical magnetic fields of astrophysical interest. Our models require a low energy scale for inflation and reheating (reheating temperature, $T_R < 10^4$ GeV) and generate a blue spectrum of electromagnetic (EM) field which peaks around the horizon scale of reheating. We show here that the anisotropic stress associated with these EM fields naturally source the production of a stochastic background of Gravitational waves (GW) with frequencies in the range of tens of nano Hertz to milli Hertz. These two extremes of the range can be probed respectively by pulsar timing arrays (PTA) experiments and the upcoming Laser Interferometric Space Array (LISA). The peak value of the GW spectrum energy represented by $d \Omega_{GW}/d \ln k$ is $ 10^{-6} $ for the models which lead to nonhelical primordial fields and $2 \times 10^{-6} $ for the helical case for $T_R=100$ GeV. In this case the spectrum peaks at a frequency $30 \mu$Hz for non helical case and at $40 \mu$Hz for helical case. These values are obtained when the ratio of EM energy density to the cosmological density at reheating $\epsilon \sim 1$ and decrease approximately as $\epsilon^2$ for smaller values.