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In this work, we analyze the implications of graviton to photon conversion inthe presence of large scale magnetic fields. We consider the magnetic fieldsassociated with galaxy clusters, filaments in the large scale structure, aswell as primordial magnetic fields. {We analyze the interaction of thesemagnetic fields with an exogenous high-frequency gravitational wave (HFGW)background which may exist in the Universe. We show that, in the presence ofthe magnetic fields, a sufficiently strong HFGW background would lead to anobservable signature in the frequency spectrum of the Cosmic MicrowaveBackground (CMB).} The sensitivity of current day CMB experiments allows toplace significant constraints on the strength of HFGW background,$\Omega_{GW}\lesssim1$. These limits are about 25 orders of magnitude stronger{than currently existing direct constraints} in this frequency region.

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