Effect of a possible cosmological time dependence of the gravitational parameter G on the peak luminosity of type Ia supernovae

The cosmological expansion of the universe affects the behaviour of all physical systems and, in the case of gravitationally bound ones, could correspond to or mimic a time dependent Newton's constant. Here we discuss the case of a locally spherical mass distribution embedded in a generic Robertson Walker universe. Choosing the most appropriate metric tensor for the problem and assuming that the local time scale is much much lower than the cosmic one, we show that G is practically unaffected thus leaving the absolute magnitude of type Ia supernovae unaltered at all epochs.