Nonminimal Derivative Coupling Cosmology and the Speed of Gravitational Waves

Abstract

The so-called Nonminimal Derivative Coupling (NDC) is an alternative to General Relativity, which produces an asymptotic inflationary mechanism when applied to cosmology. The detection of gravitational waves in the last decade has imposed very stringent constraints over gravitational theories, which gave rise to a massive revision of those theories, in order to investigate the compatibility between them and that observational data. In this paper, we review NDC and address the question if it is compatible with gravitational waves or not. We show that the very existence of gravitational waves in this theory is restricted to a limited range in phase space and there are no accelerated solutions compatible with the present day data for the speed of such waves. This last result is alleviated by the fact that we did not detect primordial gravitational waves so far. Those conclusions are based on the comparison between the expression for the speed of tensor perturbations and the phase space. Finally, some possible scenarios and solutions are considered.