F. S. N. Lobo
In this work, we review a plethora of modified theories of gravity with generalized curvature-matter couplings. The explicit non-minimal couplings, for instance, between an arbitrary function of the scalar curvature and the Lagrangian density of matter, induces a non-vanishing covariant derivative of the energy-momentum tensor, implying non-geodesic motion and consequently leads to the appearance of an extra force. Applied to the cosmological context, these curvature-matter couplings lead to interesting phenomenology, where one can obtain a unified description of the cosmological epochs. We also consider the possibility that the behavior of the galactic flat rotation curves can be explained in the framework of the curvature-matter coupling models, where the extra-terms in the gravitational field equations modify the equations of motion of test particles, and induce a supplementary gravitational interaction. In addition to this, these models are extremely useful for describing dark energy-dark matter interactions, and for explaining the late-time cosmic acceleration.
3rd International Winter School-Seminar on Gravity, Astrophysics and Cosmology “Petrov School 2017”
Institute of Physics of Kazan Federal University, Kazan, Russia