# Generalized framework for testing gravity with gravitational-wave propagation. III. Future prospect

## TL;DR

This paper explores how future gravitational-wave detectors can precisely measure properties like amplitude damping and graviton mass, providing new tests for gravity theories and the equivalence principle at cosmological distances.

## Contribution

It introduces a framework for future GW observations to constrain amplitude damping, graviton mass, and gravitational coupling variations, advancing tests of gravity beyond current capabilities.

## Key findings

- Future detectors can measure amplitude damping with 1% accuracy.
- Current universe favors models with less GW damping.
- Future observations can test the equivalence principle at 1% level.

## Abstract

The properties of gravitational-wave (GW) propagation are modified in alternative theories of gravity and are crucial observables to test gravity at cosmological distance. The propagation speed has already been measured from GW170817 so precisely and pinned down to the speed of light, while other properties of GW propagation have not constrained tightly yet. In this paper, we investigate the measurement precisions of the amplitude damping rate (equivalently, the time variation of the gravitational coupling for GWs) and graviton mass in the generalized framework of GW propagation with the future detectors such as Voyager, Cosmic Explorer, and Einstein Telescope. As a result, we show that the future GW observation can reach 1% error for the amplitude damping. We also study the time variation of the gravitational couplings in Horndeski theory by performing Monte Carlo-based numerical simulations. From the simulation results, we find that the current accelerating Universe prefers the models with less damping of GWs and that the equivalence principle can be tested at the level of 1% by the future GW observation.