Cosmic acceleration from matter–curvature coupling

Abstract

We consider f (R, T ) modified theory of gravity in which, in general, the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and the trace of the energy-momentum tensor. We indicate that in this type of the theory, the coupling energy-momentum tensor is not conserved. However, we mainly focus on a particular model that matter is minimally coupled to the geometry in the metric formalism and wherein, its coupling energy-momentum tensor is also conserved. We obtain the corresponding Raychaudhuri dynamical equation that presents the evolution of the kinematic quantities. Then for the chosen model, we derive the behavior of the deceleration parameter, and show that the coupling term can lead to an acceleration phase after the matter dominated phase. On the other hand, the curvature of the universe corresponds with the deviation from parallelism in the geodesic motion. Thus, we also scrutinize the motion of the free test particles on their geodesics, and derive the geodesic deviation equation in this modified theory to study the accelerating universe within the spatially flat FLRW background. Actually, this equation gives the relative accelerations of adjacent particles as a measurable physical quantity, and provides an elegant tool to investigate the timelike and the null structures of spacetime geometries. Then, through the null deviation vector, we find the observer area-distance as a function of the redshift for the chosen model, and compare the results with the corresponding results obtained in the literature.

Cosmic acceleration via space-time-matter theory

“…Now, let us compare the above GDE with the corresponding ones in the ΛCDM model and in the minimal coupling model of the f (R, T ) modified gravitational theory, that has been studied in Ref. [14].…”

“…We assume that at z = 0, the deviation vector to be zero and its first derivative to be equal to one. We plot the evolution [14]) has been plotted in this figure, so that the results can be compared with our model. We also obtain the observer area-distance in the STM theory as a measurable quantity.…”

“…Also, to make our investigations more instructive, we study the motion of the time-like and null test particles through the geodesic deviation equation (GDE) of the STM theory and obtain the observer area-distance as a measurable physical quantity. Then, to compare the obtained results with other modified gravitational theories, we choose the ΛCDM model (in which the accelerated expansion of the universe is explained through adding the cosmological constant term into the action) and a particular minimal coupling model of the f (R, T ) gravity [14] (in which the acceleration phase is explained through coupling between the matter source, as a geometrical curvature induction of matter, and the pure geometry).…”

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

“…Recently, it has been shown that observations admit the violation of ordinary energy-momentum conservation law meaning that the energy-momentum sources are nondivergence-free tensors in curved spacetimes [69]. Although this result motivates some physicists to consider the cosmological consequences of this energy conservation violation in f (R,T) gravity [70,71], the idea that the energy-momentum tensor is not conserved in curved spacetime is coming back to Rastall [10]. Recent works in the literature renewed the interest in the Rastall theory [19 -25].…”

Ether and Relativity

“…Even some gravitational theories have been considered in which the Lagrangian of the geometry, that is usually supposed to be the characteristic of the geometry alone, just from the beginning, and indeed a priori, is presented as a function of the geometry and the matter [97]- [105]. Now, inspiring from these types of ideas and theories, and knowing that, in the Mach ideas, the inertia of a body is not just the intrinsic property of that body, but is caused by the cosmic masses via some interactions (where the influence of the distant bodies preponderates), 17 one can perhaps relate this cause to be due to the cosmic background (e.g., the whole geometry of the universe).…”