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

TL;DR

This paper assesses how future gravitational wave observations with the Einstein Telescope could constrain the No Slip Gravity model, finding that constraints are similar to standard gravity but with degeneracies influenced by redshift data and gravitational wave dimming effects.

Contribution

It provides a forecast analysis of the No Slip Gravity model using third-generation gravitational wave detectors, highlighting parameter degeneracies and the impact of redshift measurements.

Findings

Constraints on dark energy parameters are similar to standard gravity.

Redshift data improves parameter constraints significantly.

Degeneracies exist between modified gravity and cosmological parameters.

Abstract

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.