The possibility of an accelerating cosmology in Rastall's theory

In an attempt to look for a viable mechanism leading to a present day accelerated expansion, we investigate the possibility that the observed cosmic speed up may be recovered in the framework of the Rastall's theory, relying on the non-conservativity of the stress-energy tensor, i.e. Tμv;μ ≠ 0. We derive the modified Friedmann equations and show that they correspond to Cardassian-like equations. We also show that, under suitable assumptions on the equation of state of the matter term sourcing the gravitational field, it is indeed possible to get an accelerated expansion, in agreement with the Hubble diagram of both Type Ia Supernovae (SNeIa) and Gamma Ray Bursts (GRBs). Unfortunately, to achieve such a result one has to postulate a matter density parameter larger than the typical ΩM ≅ 0.3 value inferred from cluster gas mass fraction data. As a further issue, we discuss the possibility to retrieve the Rastall's theory from a Palatini variational principle approach to f(R) gravity. However, such an attempt turns out to be unsuccessful.