Limits on high-frequency gravitational wave background from its interplay with large scale magnetic fields

In this work, we analyze the implications of graviton-to-photon conversion in the presence of large scale magnetic fields. We consider the magnetic fields associated with galaxy clusters, filaments in the large scale structure, as well as primordial magnetic fields. We analyze the interaction of these magnetic fields with an exogenous high-frequency gravitational wave (HFGW) background which may exist in the Universe. We show that, in the presence of the magnetic fields, a sufficiently strong HFGW background would lead to an observable signature in the frequency spectrum of the cosmic microwave background. The sensitivity of current day cosmic microwave background experiments allows one to place significant constraints on the strength of the HFGW background, Ω_GW≲1. These limits are about 25 orders of magnitude stronger than currently existing direct constraints in this frequency region.