A generalization to the Rastall theory and cosmic eras

Abstract

A generalized version for the Rastall theory is proposed showing the agreement with the cosmic accelerating expansion. In this regard, a coupling between geometry and the pressureless matter fields is derived which may play the role of dark energy, responsible for the current accelerating expansion phase. Moreover, our study also shows that the radiation field may not be coupled to the geometry in a non-minimal way which represents that the ordinary energymomentum conservation law is respected by the radiation source. It is also shown that the primary inflationary era may be justified by the ability of the geometry to couple to the energy-momentum source in an empty flat FRW universe. In fact, this ability is independent of the existence of the energymomentum source and may compel the empty flat FRW universe to expand exponentially. Finally, we consider a flat FRW universe field by a spatially homogeneous scalar field evolving in potential V(φ), and study the results of applying the slow-roll approximation to the system which may lead to an inflationary phase for the universe expansion.

The commutator algebra of covariant derivative as general framework for extended gravity. The Rastall theory case and the role of the torsion

“…Thus, matter fields and geometry are coupled to each other in a non-minimal way in Rastall theory, and one gets compatibility with some observational data [25]. The replacement (6) permits to replace the matter source with a Rastall effective matter source as…”

“…In the Rastall's approach the standard energy-momentum tensor is replaced by an effective energy-momentum tensor as [10,25] …”

A connection between Rastall-type and f(R, T) gravities

“…Equations (12) and (13) have been written in a suitable form which we need to discuss them in the next section. A modified version of Rastall theory i.e., GRG has been proposed through using a coordinate dependent Rastall parameter [37], as…”

“…Although in the original theory, the Rastall parameter is a constant, some modifications of RG has been proposed e.g., in a recent work [37], the authors have generalized the theory to include a variable Rastall parameter (we hereafter call this theory the Generalized Rastall Gravity GRG). They then investigated cosmological consequences of the model ∇ µ T µν = ∇ ν (λ ′ R), where λ ′ is now a function of spacetime coordinates, and predicted a primary inflationary phase which can exist even in the absence of matter components in a flat FRW spacetime.…”

Gravitational collapse in Rastall gravity

“…As the result of this assumption, the ordinary EMT conservation law, ∇ µ T µ ν = 0, is not valid anymore [26][27][28]. Nevertheless, such a modification of GR is in good agreement with observations as well as theoretical expectations [29,30]. Surprisingly, in comparison to GR, Rastall theory of gravity provides somehow better compatibility with the observational data of the matter dominated era and the helium nucleosynthesis [31].…”