Bounds on the possible evolution of the gravitational constant from cosmological type-Ia supernovae

Abstract

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 ${}^{56}\mathrm{Ni}$ synthesized in the supernova outburst. Both effects are related to a change in the Chandrasekhar mass ${M}_{\mathrm{Ch}}\ensuremath{\propto}{G}^{\ensuremath{-}3/2}.$ 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 ${G/G}_{0}\ensuremath{\lesssim}1.1$ and $\ifmmode \dot{G}\else \.{G}\fi{}/G\ensuremath{\lesssim}{10}^{\ensuremath{-}11}{\mathrm{yr}}^{\ensuremath{-}1}$ at redshifts $z\ensuremath{\simeq}0.5.$ These new bounds extend the currently available constraints 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 magnitude in time and distance.