On Gravitational Waves in Spacetimes with a Nonvanishing Cosmological Constant

We study the effect of a cosmological constant $\Lambda$ on the propagation and detection of gravitational waves. To this purpose we investigate the linearised Einstein's equations with terms up to linear order in $\Lambda$ in a de Sitter and an anti-de Sitter background spacetime. In this framework the cosmological term does not induce changes in the polarization states of the waves, whereas the amplitude gets modified with terms depending on $\Lambda$. Moreover, if a source emits a periodic waveform, its periodicity as measured by a distant observer gets modified. These effects are, however, extremely tiny and thus well below the detectability by some twenty orders of magnitude within present gravitational wave detectors such as LIGO or future planned ones such as LISA.