Generalized curvature-matter couplings in modified gravity

TL;DR

This paper reviews modified gravity theories with generalized curvature-matter couplings, highlighting their implications for cosmology, galaxy rotation curves, and dark energy-dark matter interactions, offering a unified framework for various cosmic phenomena.

Contribution

It provides a comprehensive review of curvature-matter coupling models in modified gravity, emphasizing their potential to explain cosmological and galactic observations.

Findings

Curvature-matter couplings induce non-geodesic motion and extra forces.

Models can unify descriptions of different cosmological epochs.

Potential explanation for galactic rotation curves without dark matter.

Abstract

In this work, we review a plethora of modified theories of gravity with generalized curvature-matter couplings. The explicit nonminimal couplings, for instance, between an arbitrary function of the scalar curvature $R$ 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.