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A generalized version for the Rastall theory is proposed showing theagreement with the cosmic accelerating expansion. In this regard, a couplingbetween geometry and the pressureless matter fields is derived which may playthe role of dark energy responsible for the current accelerating expansionphase. Moreover, our study also shows that the radiation field may not becoupled to the geometry in a non-minimal way which represents that the ordinaryenergy-momentum conservation law is respected by the radiation source. It isalso shown that the primary inflationary era may be justified by the ability ofthe geometry to couple to the energy-momentum source in an empty flat FRWuniverse. In fact, this ability is independent of the existence of theenergy-momentum source and may compel the empty flat FRW universe to expandexponentially. Finally, we consider a flat FRW universe field by a spatiallyhomogeneous scalar field evolving in potential $\mathcal{V}(\phi)$, and studythe results of applying the slow-roll approximation to the system which maylead to an inflationary phase for the universe expansion.

A Generalization to the Rastall Theory and Cosmic Eras