On the Evolution of Cosmological Type Ia Supernovae and the Gravitational Constant

There are at least three ways in which a varying gravitational constant $G$ could affect the interpretation of the recent high-redhisft Type Ia supernovae results. If the local value of $G$ at the space-time location of distant supernovae is different, it would change both the thermonuclear energy release and the time scale of the supernova outburst. In both cases the effect is related to a change in the Chandrasekhar mass $M_{\rm Ch}\propto G^{-3/2}$. Moreover the integrated variation of $G$ with time would also affect cosmic evolution and therefore the luminosity distance relation. Here we investigate in a consistent way how these different effects of a varying $G$ could change the current interpretation of the Hubble diagram of Type Ia supernovae. We parametrize the variation of $G$ using scalar-tensor theories of gravity, such as the Jordan-Brans-Dicke theory or its extensions. It is remarkable that Dirac's hypothesis that $G$ should decrease with time can qualitatively explain the observed $\Delta m \simeq 0.2$ mag decrease at $z\simeq 0.5$ (with respect to a decelerating universe) and, at the same time, reduce the duration of the risetimes of distant Type Ia supernovae as recently reported.