Gravitational waves in the presence of a cosmological constant

We derive the effects of a nonzero cosmological constant Λ on gravitational wave propagation in the linearized approximation of general relativity. In this approximation, we consider the situation where the metric can be written as g_μν=η_μν+h_μν^Λ+h_μνW, h_μν^Λ,W1, where h_μν^Λ is the background perturbation and h_μνW is a modification interpretable as a gravitational wave. For Λ≠0, this linearization of Einstein equations is self-consistent only in certain coordinate systems. The cosmological Friedmann-Robertson-Walker coordinates do not belong to this class and the derived linearized solutions have to be reinterpreted in a coordinate system that is homogeneous and isotropic to make contact with observations. Plane waves in the linear theory acquire modifications of order √Λ, both in the amplitude and the phase, when considered in Friedmann-Robertson-Walker coordinates. In the linearization process for h_μν, we have also included terms of order O(Λh_μν). For the background perturbation h_μν^Λ, the difference is very small, but when the term h_μνWΛ is retained the equations of motion can be interpreted as describing massive spin-2 particles. However, the extra degrees of freedom can be approximately gauged away, coupling to matter sources with a strength proportional to the cosmological constant itself. Finally, we discuss the viability of detecting the modifications caused by the cosmological constant on the amplitude and phase of gravitational waves. In some cases, the distortion with respect to gravitational waves propagating in Minkowski space-time is considerable. The effect of Λ could have a detectable impact on pulsar timing arrays.