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We study the Post-Newtonian approach implemented to the Einstein-Hilbertaction adding the cosmological constant $\Lambda$ at 1PN order. We considervery small values of $\Lambda$ to derive the Lagrangian of a two body compactsystem 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 higherfrequencies whatsoever.

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