Post-Newtonian Gravitational Waves with cosmological constant $\Lambda$ from the Einstein-Hilbert theory

TL;DR

This paper extends the Post-Newtonian framework to include the cosmological constant in Einstein-Hilbert gravity, analyzing its subtle effects on gravitational waves at very low frequencies.

Contribution

It derives the 1PN Lagrangian and waveforms for a two-body system with a cosmological constant, highlighting its negligible impact at higher frequencies.

Findings

Lambda causes slight amplitude reduction at very low frequencies

Effects of Lambda are negligible at higher frequencies

The study provides a framework for including Lambda in gravitational wave models

Abstract

We study the Post-Newtonian approach implemented to the Einstein-Hilbert action adding the cosmological constant $\Lambda$ at 1PN order. We consider very small values of $\Lambda$ to derive the Lagrangian of a two body compact system at the center of mass frame at 1PN. Furthermore, the phase function $\phi(t)$ is obtained from the balance equation and the two polarizations $h_{+}$ and $h_{\times}$ are also calculated. We observe changes due to $\Lambda$ only at very low frequencies and we notice that it plays the role of "stretch" the spacetime such that both amplitudes become smaller; however, given its nearly negligible value, $\Lambda$ has no relevance at higher frequencies whatsoever.