Cosmic Acceleration From Matter-Curvature Coupling
  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.
