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

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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 (${\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{f}}_{0}$ and ${\stackrel{\ifmmode\ddot\else\textasciidieresis\fi{}}{f}}_{0}$) 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 $\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{G}/{G}_{0}\ensuremath{\lesssim}{10}^{\ensuremath{-}6}\text{ }\text{ }{\mathrm{yr}}^{\ensuremath{-}1}$, while the best currently known verification binary will reach $\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{G}/{G}_{0}\ensuremath{\lesssim}{10}^{\ensuremath{-}4}\text{ }\text{ }{\mathrm{yr}}^{\ensuremath{-}1}$. 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 $\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{G}/{G}_{0}\ensuremath{\lesssim}{10}^{\ensuremath{-}11}\text{ }\text{ }{\mathrm{yr}}^{\ensuremath{-}1}$.

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