The fate of a gravitational wave in de Sitter spacetime

Abstract

If we want to explain the recently discovered accelerated stage of the universe, one of the option we have is to modify the Einstein tensor. The simplest such modification, in agreement with all observations, is the positive cosmological constant $\Lambda$. Such a modification will also have its impact on local observables and on the propagation of weak gravitational waves. We show here that the inclusion of a cosmological constant impedes the detection of a gravitational wave if the latter is produced at a distance larger than ${\cal L}_{\rm crit}=(6\sqrt{2}\pi f \hat{h}/\sqrt{5})r_{\Lambda}^2$ where $r_{\Lambda}=1/\sqrt{\Lambda}$ and $f$ and $\hat{h}$ are the frequency and the strain of the wave, respectively. ${\cal L}_{\rm crit}$ is of astrophysical order of magnitude. We interpret the result in the sense that the gravitational wave interpretation is only possible if the characteristic wave properties are smaller than the non-oscillatory solution due to $\Lambda$.