Cosmology with the Einstein Telescope: No Slip Gravity Model and
  Redshift Specifications
  The Einstein Telescope and other third generation interferometric detectors
of gravitational waves are projected to be operational post $2030$. The
cosmological signatures of gravitational waves would undoubtedly shed light on
any departure from the current gravitational framework. We here confront a
specific modified gravity model, the No Slip Gravity model, with forecast
observations of gravitational waves. We compare the predicted constraints on
the dark energy equation of state parameters $w_0^{}-w_a^{}$, between the
modified gravity model and that of Einstein gravity. We show that the No Slip
Gravity model mimics closely the constraints from the standard gravitational
theory, and that the cosmological constraints are very similar. The use of
spectroscopic redshifts, especially in the low--redshift regime, lead to
significant improvements in the inferred parameter constraints. We test how
well such a prospective gravitational wave dataset would function at testing
such models, and find that there are significant degeneracies between the
modified gravity model parameters, and the cosmological parameters that
determine the distance, due to the gravitational wave dimming effect of the
modified theory.
