About the propagation of the Gravitational Waves in an asymptotically de-Sitter space: Comparing two points of view

TL;DR

This paper investigates how gravitational waves propagate in an asymptotically de-Sitter space, revealing that the cosmological constant limits detectability and supports the Cosmic No Hair Conjecture.

Contribution

It compares two approaches to include the cosmological constant in gravitational wave propagation and confirms the critical distance limit related to the Cosmic No Hair Conjecture.

Findings

The critical detection distance depends on wave frequency and strain.

The inclusion of $5$ impedes GW detection beyond a certain scale.

Results support the Cosmic No Hair Conjecture.

Abstract

We analyze the propagation of gravitational waves (GWs) in an asymptotically de-Sitter space by expanding the perturbation around Minkowski and introducing the effects of the Cosmological Constant ($\Lambda$), first as an additional source (de-Donder gauge) and after as a gauge effect ($\Lambda$-gauge). In both cases the inclusion of the Cosmological Constant $\Lambda$ impedes the detection of a gravitational wave at a distance larger than $L_{crit}=(6\sqrt{2}\pi f \hat{h}/\sqrt{5})r_\Lambda^2$, where $r_\Lambda=\frac{1}{\sqrt{\Lambda}}$ and f and $\hat{h}$ are the frequency and strain of the wave respectively. We demonstrate that $L_{crit}$ is just a confirmation of the Cosmic No hair Conjecture (CNC) already explained in the literature.