Constraining the evolution of Newton's constant with slow inspirals observed from spaceborne gravitational-wave detectors

TL;DR

This paper develops an analytical method to estimate how well spaceborne gravitational-wave detectors can constrain the time variation of Newton's constant G, using quasi-monochromatic signals from binary systems.

Contribution

It introduces a Fisher-matrix-based approach to estimate constraints on G's evolution from gravitational-wave data, validated by Monte Carlo simulations.

Findings

LISA galactic binaries could constrain ot G/G_0 to 0^{-6} yr^{-1}.

Verification binaries could reach ot G/G_0 \u2264 10^{-4} yr^{-1}.

DECIGO-like detectors could constrain ot G/G_0 to 0^{-11} yr^{-1}.

Abstract

Spaceborne gravitational-wave (GW) detectors observing at milli-Hz and deci-Hz frequencies are expected to detect large numbers of quasi-monochromatic signals. The first and second time-derivative of the GW frequency ($\dot f_0$ and $\ddot f_0$) can be measured for the most favourable sources and used to look for negative post-Newtonian corrections, which can be induced by the source's environment or modifications of general relativity. We present an analytical, Fisher-matrix-based approach to estimate how precisely such corrections can be constrained. We use this method to estimate the bounds attainable on the time evolution of the gravitational constant $G(t)$ with different classes of quasi-monochromatic sources observable with LISA and DECIGO, two representative spaceborne detectors for milli-Hz and deci-Hz GW frequencies. We find that the most constraining source among a simulated population of LISA galactic binaries could yield $\dot G/G_0 \lesssim 10^{-6}\text{yr}^{-1}$, while the best currently known verification binary will reach $\dot G/G_0 \lesssim 10^{-4}\text{yr}^{-1}$. We also perform Monte-Carlo simulations using quasi-monochromatic waveforms to check the validity of our Fisher-matrix approach, as well as inspiralling waveforms to analyse binaries that do not satisfy the quasi-monochromatic assumption. We find that our analytical Fisher matrix produces good order-of-magnitude constraints even for sources well beyond its regime of validity. Monte-Carlo investigations also show that chirping stellar-mass compact binaries detected by DECIGO-like detectors at cosmological distances of tens of Mpc can yield constraints as tight as $\dot G/G_0 \lesssim 10^{-11}\text{yr}^{-1}$.