# The effect of the gravitational constant variation on the phase of gravitational waves

## TL;DR

This paper uses LIGO-VIRGO-KAGRA data to explore how variations in the gravitational constant G affect gravitational wave phases, providing constraints on G' over G with current and future detector sensitivities.

## Contribution

It introduces a method to constrain G' over G using gravitational wave phase data, highlighting the importance of phase correction in current and future observations.

## Key findings

- Phase correction becomes feasible with increased signal-to-noise ratio.
- Current data requires a significant increase in event distance or SNR for phase-based G' constraints.
- Electromagnetic counterparts help neglect phase correction in G' constraints.

## Abstract

We have previously investigated the effect of the gravitational constant variation on the gravitational wave propagation. Pure theoretical analysis indicates that the leading order effect of the gravitational constant variation corrects the amplitude of gravitational waves, and the second order effect corrects the phase of gravitational waves. As the matched filtering technique is used by gravitational wave data analysis, the phase is more important than the amplitude. In the current paper we use LIGO-VIRGO-KAGRA data to constrain the gravitational constant variation. Our findings indicate that we need to wait until the distance of the detected gravitational wave events and/or the signal-to-noise ratio increases by $2n$ orders compared to the current detection state, and then we can use phase correction to get constraint $|\frac{G'}{G}|<10^{-n}$/yr for gravitational wave events without electromagnetic counterparts. For gravitational wave events with electromagnetic counterparts which provide the information of source's luminosity distance, the phase correction can almost always be neglected to constrain $\frac{G'}{G}$.