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Galaxies 2014, 2(3), 410-465; doi:10.3390/galaxies2030410
Review

Generalized Curvature-Matter Couplings in Modified Gravity

1
 and
2,*
1 Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK 2 Centro de Astronomia e Astrofísica da Universidade de Lisboa, Campo Grande, Edifício C8 1749-016 Lisboa, Portugal
* Author to whom correspondence should be addressed.
Received: 30 May 2014 / Revised: 7 July 2014 / Accepted: 8 July 2014 / Published: 28 July 2014
(This article belongs to the Special Issue Beyond Standard Gravity and Cosmology)
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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.
Keywords: modified gravity; curvature-matter couplings; cosmology; dark matter modified gravity; curvature-matter couplings; cosmology; dark matter
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Harko, T.; Lobo, F.S. Generalized Curvature-Matter Couplings in Modified Gravity. Galaxies 2014, 2, 410-465.

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