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

We study the compact binary dynamics in the post-Newtonian approach implemented to the EinsteinHilbert action adding the cosmological constant A at first post-Newtonian (1PN) order. We consider very small values of A finding that it plays the role of a PN factor to derive the Lagrangian of a compact twobody system at the center of mass frame at 1PN. Furthermore, the phase function 0ot thorn is obtained from the balance equation, and the two polarizations h thorn and hx are also calculated. We observe changes due to A 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, A has no relevance at higher frequencies whatsoever.