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Observational data for type Ia supernovae, shows that the expansion of theuniverse is accelerated. This accelerated expansion can be described by acosmological constant or by dark energy models like quintessence. Aninteresting question may be raised here. Is it possible to describe theaccelerated expansion of universe using varying--$G$ cosmological models? Herewe shall show that the price for having accelerated expansion inslow--varying--$G$ models (in which the dynamical terms of $G$ are ignored) isto have highly non--conserved matter and also that it is in contradiction withother data.

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