Propagation of gravitational waves in a cosmological background
Xian Gao, Xun-Yang Hong
Abstract
We investigate the propagation of gravitational waves in a cosmological background. Based on the framework of spatially covariant gravity, we derive the general quadratic action for gravitational waves. The spatial derivatives of the extrinsic curvature and the parity-violating terms are systematically introduced. Special attention is paid to the propagation speed of the gravitational waves. We find that it is possible to make the two polarization modes propagate in the same speed, which may differ from that of the light, in the presence of parity-violating terms in the action. In particular, we identify a large class of spatially covariant gravity theories with parity violation, in which both the polarization modes propagate in the speed of light. Our results indicate that there are more possibilities in the framework of spatially covariant gravity in light of the propagation speed of the gravitational waves.