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

Author:

Ricardo Escobedo, Claudia Moreno, Rafael Hernández-Jiménez

Keyword:

General Relativity and Quantum Cosmology, General Relativity and Quantum Cosmology (gr-qc)

journal:

date:

2023-08-23 16:00:00

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.

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