Constraining the Gravitational Wave Speed in the Early Universe via Gravitational Cherenkov Radiation

Scalar particles traveling faster than a subluminal gravitational wave generate gravitons via gravitational Cherenkov radiation. In this paper, we investigate graviton production by the primordial plasma within the framework of modified gravity in the early Universe, generating a relic graviton background. We find that for the minimal model, where only the speed of gravitational waves is modified and a standard model plasma minimally couples to gravity, the relic graviton background can be enhanced by several orders of magnitude, but still agrees with the Big Bang Nucleosynthesis (BBN) bound in most cases. Moreover, we also find that for Horndeski theories, such as Galileon theory, the relic background produced by the thermalized scalar field can reach significant amplitudes, exceeding the BBN bound for a region of the parameter space. By requiring the relic graviton background to remain consistent with the BBN constraint, we derive limits on the gravitational wave speed at early times in these modified gravity theories.