Bounds on the possible evolution of the Gravitational Constant from Cosmological Type-Ia Supernovae

Recent high-redshift Type Ia supernovae results can be used to set new bounds on a possible variation of the gravitational constant $G$. If the local value of $G$ at the space-time location of distant supernovae is different, it would change both the kinetic energy release and the amount of $^{56}$Ni synthesized in the supernova outburst. Both effects are related to a change in the Chandrasekhar mass $M_{Ch} \propto G^{-3/2}$. In addition, the integrated variation of $G$ with time would also affect the cosmic evolution and therefore the luminosity distance relation. We show that the later effect in the magnitudes of Type Ia supernovae is typically several times smaller than the change produced by the corresponding variation of the Chandrasekhar mass. We investigate in a consistent way how a varying $G$ could modify the Hubble diagram of Type Ia supernovae and how these results can be used to set upper bounds to a hypothetical variation of $G$. We find $G/G_0 \la 1.1$ and $G'/G \la 10^{-11} yr^{-1}$ at redshifts $z\simeq 0.5$. These new bounds extend the currently available constrains on the evolution of $G$ all the way from solar and stellar distances to typical scales of Gpc/Gyr, i.e. by more than 15 orders of magnitudes in time and distance.