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The Einstein Telescope and other third generation interferometric detectorsof gravitational waves are projected to be operational post $2030$. Thecosmological signatures of gravitational waves would undoubtedly shed light onany departure from the current gravitational framework. We here confront aspecific modified gravity model, the No Slip Gravity model, with forecastobservations of gravitational waves. We compare the predicted constraints onthe dark energy equation of state parameters $w_0^{}-w_a^{}$, between themodified gravity model and that of Einstein gravity. We show that the No SlipGravity model mimics closely the constraints from the standard gravitationaltheory, and that the cosmological constraints are very similar. The use ofspectroscopic redshifts, especially in the low--redshift regime, lead tosignificant improvements in the inferred parameter constraints. We test howwell such a prospective gravitational wave dataset would function at testingsuch models, and find that there are significant degeneracies between themodified gravity model parameters, and the cosmological parameters thatdetermine the distance, due to the gravitational wave dimming effect of themodified theory.

Cosmology with the Einstein Telescope: No Slip Gravity Model and Redshift Specifications