Reheating and Primordial Gravitational Waves in Generalized Galilean
  Genesis
  Galilean genesis is an alternative to inflation, in which the universe starts
expanding from Minkowski with the stable violation of the null energy
condition. In this paper, we discuss how the early universe is reheated through
the gravitational particle production at the trasition from the genesis phase
to the subsequent phase where the kinetic energy of the scalar field is
dominant. We then study the consequences of gravitational reheating after
Galilean genesis on the spectrum of primordial gravitational waves. The
resultant spectrum is strongly blue, and at high frequencies $\Omega_{\rm
gw}\propto f^3$ in terms of the energy density per unit logarithmic frequency.
Though this cannot be detected in existing detctors, the amplitude can be as
large as $\Omega_{\rm gw}\sim 10^{-12}$ at $f\sim 100\,$MHz, providing a future
test of the genesis scenario. The analysis is performed within the framework of
generalized Galilean genesis based on the Horndeski theory, which enables us to
derive generic formulas.
