The effect of the cosmological constant on gravitational wave quadrupole signal

Abstract

In this study the effects of a non-zero cosmological constant $\Lambda$ on a quadrupole signal are studied. The linearized approximation of general relativity was used, so the metric can be written as $g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}^{\Lambda}+h_{\mu\nu}^{GW}$ where $h_{\mu\nu}^{GW}$ can be interpreted as gravitational waves and $h_{\mu\nu}^{\Lambda}$ is the background perturbation. The $\Lambda h^{GW}$ term was also included in this study. To derive physically relevant consequences of $\Lambda\neq0$, the Friedmann--Robertson--Walker comoving coordinates are used. In these coordinates, the equations of motion are not self-consistent so the result of the linearized theory have to be transformed to the FRW metric. The luminosity distance and the same order of the magnitude of frequency of the GW150914 was used for the results.