Constraining the time variation of Newton's constant \(G\) with gravitational-wave standard sirens and supernovae

Abstract

The intrinsic peak luminosity of Type Ia supernovae (SNe Ia) 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 \(d_{\rm L}\) can be independently determined, the SNe Ia 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 SNe Ia by interpolation, provided the GW and SN Ia samples have similar redshift ranges. We demonstrate that combining the GW observations of third-generation detectors with SN Ia 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 \(1.5\%\).