The effect of the gravitational constant variation on the propagation of gravitational waves

TL;DR

This paper explores how variations in the gravitational constant affect gravitational wave propagation, leading to amplitude corrections and new constraints on gravity deviations at cosmological scales.

Contribution

It extends the gravitational wave propagation equations to include variable gravitational constants and derives constraints on Yukawa gravity parameters from GW170817.

Findings

Amplitude of gravitational waves is corrected by variable G.

Estimated source distances may be biased if G variation is ignored.

Constraints on Yukawa gravity parameters at 10 Mpc scale.

Abstract

Since the first detection of gravitational waves, they have been used to investigate various fundamental problems, including the variation of physical constants. Regarding the gravitational constant, previous works focused on the effect of the gravitational constant variation on the gravitational wave generation. In this paper, we investigate the effect of the gravitational constant variation on the gravitational wave propagation. The Maxwell-like equation that describes the propagation of gravitational waves is extended in this paper to account for situations where the gravitational constant varies. Based on this equation, we find that the amplitude of gravitational waves will be corrected. Consequently the estimated distance to the gravitational wave source without considering such a correction may be biased. Applying our correction result to the well known binary neutron star coalescence event GW170817, we get a constraint on the variation of the gravitational constant. Relating our result to the Yukawa deviation of gravity, we for the first time get the constraint of the Yukawa parameters in 10Mpc scale. This scale corresponds to a graviton mass $m_g\sim10^{-31}$eV.