Gravitational Waves from Primordial Magnetic Fields via Photon-Graviton Conversion

We explore a novel process in the early Universe in which thermalized photons are converted into gravitons in the presence of strong primordial magnetic fields. It is found that the frequency of generated gravitational waves (GWs) is typically of order of GHz and their amplitude can be up to ${\mathrm{\Omega }}_{\mathrm{G}\mathrm{W}}{h}^2\sim {10}^{-10}$. If detected with future developments of the technology to explore this frequency region, the produced stochastic GW background enables us to know when and how strong the primordial magnetic fields are generated. From the peak frequency of the GWs, we can also probe the number of relativistic degrees of freedom at that time.