Abstract: We have great certainty on how gravity works around our solar system, but on large scales we still have a considerable lack of understanding about the constituents of our universe. Furthermore, observational tensions are starting to arise as we enter the era of precision cosmology.

In this talk, I will mention how we can learn more about cosmology with future gravitational wave data. In particular, I will focus on the use of standard sirens for testing cosmology beyond the ΛCDM model. I will show how new physics can change the way gravitational waves propagate and discuss forecasts for binary neutron star mergers with Advanced LIGO. I will show that new physics can bias constraints on the current Hubble rate H0 from standard sirens, and thus it is crucial that we search for these new effects to make robust predictions on sensitive cosmological parameters. Finally, I will discuss the role that lunar laser ranging and binary pulsar data play on the outlook of standard sirens.