We propose a method to constrain the variation of the gravitational constant $G$ with cosmic time using gravitational-wave (GW) observations of merging binary neutron stars. The method essentially relies on the fact that the maximum and minimum allowed masses of neutron stars at a particular cosmic epoch has a simple dependence on the value of $G$ at that epoch. GWs carry an imprint of the value of $G$ at the time of the merger. Thus, if the value of $G$ at merger is significantly different from its current value, the masses of the neutron stars inferred from the GW observations will be inconsistent with the theoretically allowed range. This enables us to place bounds on the variation of $G$ between the merger epoch and the present epoch. Using the observation of the binary neutron star system GW170817, we constrain the fractional difference in $G$ between the merger and the current epoch to be in the range $-1 lesssim Delta G/G lesssim 8$. Assuming a monotonic variation in $G$, this corresponds to a bound on the average rate of change of $-7 times 10^{-9}~mathrm{yr}^{-1} le dot{G}/G le 5 times 10^{-8}~mathrm{yr}^{-1}$ between these epochs. Future observations will put tight constraints on the deviation of $G$ over vast cosmological epochs not probed by other observations.
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