  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. $T^{\mu}_{\nu ; \mu}
\neq 0$. 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 much larger than the typical $\Omega_M \simeq 0.3$
value inferred from cluster gas mass fraction data.
