Notes on the compatibility of type Ia supernovae data and varying-G cosmology

Observational data for type Ia supernovae shows that the expansion of the universe is accelerated. This accelerated expansion can be described by a cosmological constant or by dark energy models, like quintessence. An interesting question may be raised here. Is it possible to describe the accelerated expansion of the universe using varying-G cosmological models? Here we shall show that the price for having accelerated expansion in slow-varying-G models (in which the dynamical terms of G are ignored) is to have highly non-conserved matter, and also that it is in contradiction with other data.