On the propagation of gravitational waves in a ΛCDM universe

We study here how the presence of non-zero matter density and a cosmological constant could affect the observation of gravitational waves in pulsar timing arrays. Conventionally, the effect of matter and cosmological constant is included by considering the redshift in frequency due to the expansion. However, there is an additional interesting effect due to the change of coordinates from the ones describing the geometry of the region where waves are produced to the ones used to measure the pulsar timing residuals. This change of coordinates is unavoidable as the strong gravitational field in a black hole merger distorts clocks and rules. Harmonic waves produced in such a merger become anharmonic when detected by a cosmological observer. The effect is tiny but appears to be nevertheless observable for the type of gravitational waves to which pulsar timing arrays are sensitive and for the favoured values of the cosmological parameters.