Using LIGO/Virgo/KAGRA data, the phase correction from a varying gravitational constant is undetectable today, and constraints would improve only as the square root of the distance-times-SNR product.
Asteroseismic constraints on the cosmic-time variation of the gravitational constant from an ancient main-sequence star
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abstract
We investigate the variation of the gravitational constant $G$ over the history of the Universe by modeling the effects on the evolution and asteroseismology of the low-mass star KIC 7970740, which is one of the oldest (~11 Gyr) and best-observed solar-like oscillators in the Galaxy. From these data we find $\dot{G}/G = (1.2 \pm 2.6) \times 10^{-12}~\text{yr}^{-1}$, that is, no evidence for any variation in $G$. We also find a Bayesian asteroseismic estimate of the age of the Universe as well as astrophysical S-factors for five nuclear reactions obtained through a 12-dimensional stellar evolution Markov chain Monte Carlo simulation.
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The effect of the gravitational constant variation on the phase of gravitational waves
Using LIGO/Virgo/KAGRA data, the phase correction from a varying gravitational constant is undetectable today, and constraints would improve only as the square root of the distance-times-SNR product.