Constraining the evolutionary history of Newton's constant with gravitational wave observations

Space-borne gravitational wave detectors, such as the proposed Laser Interferometer Space Antenna, are expected to observe black hole coalescences to high redshift and with large signal-to-noise ratios, rendering their gravitational waves ideal probes of fundamental physics. The promotion of Newton's constant to a time function introduces modifications to the binary's binding energy and the gravitational wave luminosity, leading to corrections in the chirping frequency. Such corrections propagate into the response function and, given a gravitational wave observation, they allow for constraints on the first time derivative of Newton's constant at the time of merger. We find that space-borne detectors could indeed place interesting constraints on this quantity as a function of sky position and redshift, providing a constraint map over the entire range of redshifts where binary black hole mergers are expected to occur. A gravitational wave observation of an inspiral event with redshifted masses of 10⁴-10⁵ solar masses for three years should be able to measure Ġ/G at the time of merger to better than 10^-11 yr^-1.