Constraining the time variation of Newton's constant $G$ with
  gravitational-wave standard sirens and supernovae
  The intrinsic peak luminosity of Type Ia supernovae (SNIa) depends on the
value of Newton's gravitational constant $G$, through the Chandrasekhar mass
$M_{\rm Ch}\propto G^{-3/2}$. If the luminosity distance can be independently
determined, the SNIa can be treated as a tracker to constrain the possible time
variation of $G$ in different redshift ranges. The gravitational-wave (GW)
standard sirens, caused by the coalescence of binary neutron stars, provide a
model-independent way to measure the distance of GW events, which can be used
to determine the luminosity distances of SNIa by interpolation, provided the GW
and SNIa samples have similar redshift ranges. We demonstrate that combining
the GW observations of third-generation detectors with SNIa data provides a
powerful and model-independent way to measure $G$ in a wide redshift range,
which can constrain the ratio $G/G_0$, where $G$ and $G_0$ are respectively the
values in the redshift ranges $z>0.1$ and $z<0.1$, at the level of $1.5\%$.
