Post-Newtonian gravitational waves with cosmological constant Λ from the Einstein-Hilbert theory

We study the compact binary dynamics in the post-Newtonian approach implemented to the Einstein-Hilbert action adding the cosmological constant Λ at first post-Newtonian (1PN) order. We consider very small values of Λ finding that it plays the role of a PN factor to derive the Lagrangian of a compact two-body system at the center of mass frame at 1PN. Furthermore, the phase function φ(t) is obtained from the balance equation, and the two polarizations h₊ and h_× are also calculated. We observe changes due to Λ 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, Λ has no relevance at higher frequencies whatsoever.