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

Space-borne gravitational-wave (GW) detectors observing at millihertz and decihertz frequencies are expected to detect large numbers of quasimonochromatic signals. The first and second time derivative of the GW frequency (${\dot{f}}_0$ and ${\ddot{f}}_0$) can be measured for the most favorable 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 quasimonochromatic sources observable with LISA and DECIGO, two representative space-borne detectors for millihertz and decihertz GW frequencies. We find that the most constraining source among a simulated population of LISA galactic binaries could yield $\dot{G}/G_0\lesssim {10}^{-6}{\mathrm{yr}}^{-1}$, while the best currently known verification binary will reach $\dot{G}/G_0\lesssim {10}^{-4}{\mathrm{yr}}^{-1}$. We also perform Monte Carlo simulations using quasimonochromatic waveforms to check the validity of our Fisher-matrix approach, as well as inspiralling waveforms to analyse binaries that do not satisfy the quasimonochromatic 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 $\dot{G}/G_0\lesssim {10}^{-11}{\mathrm{yr}}^{-1}$.