Cosmology with gravitational waves and gravitational waves with cosmology

In this talk I will present some of the cosmological implications of future gravitational wave observations, focusing in particular on the eLISA mission. I will first describe how massive black hole binary mergers can be used as accurate distance indicators at very high redshift (standard sirens). 
Using realistically simulated data for eLISA, including the modelling and detection by future telescope facilities of electromagnetic counterparts, I will then present forecast constraints on the cosmological parameters of standard and alternative cosmological models, such as early and interacting dark energy. Furthermore I will consider the effect of cosmic matter inhomogeneities on the propagation of gravitational waves, showing how this modifies the measured waveform by a small frequency dependent contribution which could bias the eLISA parameter estimation of slowly evolving, stellar mass black hole binaries.