Gravitational waves in the presence of a cosmological constant

We derive the effects of a non-zero cosmological constant \(\Lambda\) 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 \(g_{\mu\nu}= \eta_{\mu\nu}+ h_{\mu\nu}^\Lambda + h_{\mu\nu}^W\), \(h_{\mu\nu}^{\Lambda,W}