Testing the Starobinsky model of inflation with resonant cavities

We show that the Starobinsky inflation model based on $R^2$ gravity has a special feature that it provides a unique scalaron-two-graviton vertex with a coupling proportional to $1/M_P$. In this model stochastic gravitational waves are produced when the scalaron - which is the massive scalar mode of the metric - decays into gravitons during reheating. This decay is accompanied by decay of scalaron into matter as well through a similar coupling, providing an efficient reheating. The stochastic gravitational waves thus produced have characteristic strain $h_c\sim 10^{-35}-10^{-34}$ in the frequency range $10^{6}-10^{12}\, {\rm Hz}$ which makes them accessible to resonant cavity searches for graviton to photon conversions. The detection of these high frequency gravitational waves would be a significant step in experimentally testing the Starobinsky inflation model.