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 (CMB).} The sensitivity of current day CMB experiments allows to place 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.
We propose a new method to detect observational appearance of Dark Matter axions. The method utilizes observations of neutron stars (NSs) in radio. It is based on the conversion of axions to photons in strong magnetic fields of NSs (Primakoff effect)
. Whether the conversion takes place, the radio spectrum of the object would have a very distinctive feature -- a narrow spike at a frequency corresponding to the rest mass of the axion. For example, if the coupling constant of the photon-axion interaction is $M=10^{10}$ GeV, the density of Dark Matter axions is $rho=10^{-24} {rm g cm^{-3}}$, and the axion mass is $5 {rm mu eV}$, then a flux from a strongly magnetized ($10^{14}$ G) NS at the distance 300 pc from the Sun is expected to be about few tenths of mJy at the frequency $approx 1200$ MHz in the bandwidth $approx 3$ MHz. Close-by X-ray dim isolated neutron stars are proposed as good candidates to look for such radio emission.
