Varying gravitational coupling theories and the Generalized Rastall Theory

In this paper, the compatibility of the Dirac cosmological model which leads to gravitational theories with a varying gravitational coupling parameter in the context of the generalized Rastall theory has been studied. Moreover, in this scenario, the problem of the current accelerated expansion of the Universe has been considered. Two different cosmic fluids have been investigated. Generalized Polytropic matter, which leads to an observationally consistent model. Also, considering the generalized Chaplygin gas, it is shown that an astronomically consistent model cannot be obtained. Briefly speaking, we came to the result that the generalized Rastall theory is capable of being matched with the Dirac hypothesis leading to the present accelerated expansion of the Universe.