We show that the Starobinsky inflation model based on $R^2$ gravity has a special feature that 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 the decay of the scalaron into matter as well through a similar coupling, providing an efficient reheating. The stochastic gravitational waves thus produced have a characteristic strain $h_c\sim {10}^{-35}–{10}^{-34}$ in the frequency range ${10}^6–{10}^{12}\mathrm{Hz}$, 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.

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• Alternative gravity theories
• Gravitational waves
• Inflation