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 ${10}^4–{10}^5$ solar masses for three years should be able to measure $\dot{G}/G$ at the time of merger to better than ${10}^{-11}{\mathrm{yr}}^{-1}$.

Figure 1

Difference in the GW phase between a ${\dot{G}}_{\mathrm{c}}=0$ evolution and a ${\dot{G}}_{\mathrm{c}}\ne 0$ evolution, as a function of time in units of months. Left panel: Fiducial extreme-mass ratio inspiral with $\eta ={10}^{-5}$ and redshifted mass $M_z≔M(1+z)={10}^6$ in the last stages of coalescence (the orbital radius $r/M\in (6,10)$). Right: Fiducial SMBH inspiral $\eta =1/4$ and $M_z={10}^6$ in the last stages of coalescence (the orbital radius $r/M\in (6,95)$).