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 ( _f0 and 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 _G/G0 less than or similar to 10-6 yr-1, while the best currently known verification binary will reach _G/G0 less than or similar to 10-4 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 _G/G0 less than or similar to 10-11 yr-1.