The effect of the cosmological constant on gravitational wave quadrupole signal

TL;DR

This paper investigates how a non-zero cosmological constant affects gravitational wave quadrupole signals within linearized general relativity, highlighting the importance of coordinate transformations for physical relevance.

Contribution

It introduces the inclusion of the $ ext{Lambda} h^{GW}$ term in linearized gravity and applies coordinate transformations to assess the impact of $ ext{Lambda}$ on gravitational wave signals.

Findings

The cosmological constant influences gravitational wave signals in a measurable way.

Coordinate transformations are essential for physically meaningful results.

The study estimates effects on signals similar to GW150914.

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.