Potential of radio telescopes as high-frequency gravitational wave detectors

In the presence of magnetic fields, gravitational waves are converted into photons and vice versa. We demonstrate that this conversion leads to a distortion of the cosmic microwave background (CMB), which can serve as a detector for MHz to GHz gravitational wave sources active before reionization. The measurements of the radio telescope EDGES can be cast as a bound on the gravitational wave amplitude, $h_c < 10^{-21} (10^{-12})$ at 78 MHz, for the strongest (weakest) cosmic magnetic fields allowed by current astrophysical and cosmological constraints. Similarly, the results of ARCADE 2 imply $h_c < 10^{-24} (10^{-14})$ at $3 - 30$ GHz. For the strongest magnetic fields, these constraints exceed current laboratory constraints by about seven orders of magnitude. Future advances in 21cm astronomy may conceivably push these bounds below the sensitivity of cosmological constraints on the total energy density of gravitational waves.