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Galilean genesis is an alternative to inflation, in which the universe startsexpanding from Minkowski with the stable violation of the null energycondition. In this paper, we discuss how the early universe is reheated throughthe gravitational particle production at the trasition from the genesis phaseto the subsequent phase where the kinetic energy of the scalar field isdominant. We then study the consequences of gravitational reheating afterGalilean genesis on the spectrum of primordial gravitational waves. Theresultant spectrum is strongly blue, and at high frequencies $\Omega_{\rmgw}\propto f^3$ in terms of the energy density per unit logarithmic frequency.Though this cannot be detected in existing detctors, the amplitude can be aslarge as $\Omega_{\rm gw}\sim 10^{-12}$ at $f\sim 100\,$MHz, providing a futuretest of the genesis scenario. The analysis is performed within the framework ofgeneralized Galilean genesis based on the Horndeski theory, which enables us toderive generic formulas.

Reheating and Primordial Gravitational Waves in Generalized Galilean Genesis