Gravitational waves in an expanding universe

The propagation of gravitational waves (GW) in an expanding universe, whose composition is dominated by dark energy and dark matter, is usually treated by simply introducing the cosmological red-shift in the frequency. While this is enough for many applications, we have proven that there are other effects that need to be included, in particular a careful treatment of the difference in the reference frames where the waves are produced and detected. This analysis potentially leads to a way of measuring the cosmological constant and other cosmological parameters. In this work we propose to study this in detail. Detection of GW in Pulsar Timing Arrays (PTA) is a possibility and the influence of these effects on the current bounds on the graviton mass is another venue of investigation.