Generalized Curvature-Matter Couplings in Modified Gravity

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.

f(T,𝒯) gravity and cosmology

“…Thus, one obtains an effective interaction between the dark energy and matter sectors, which is usual in modified matter coupling theories [78][79][80][81][82][83]. Therefore, in the present model the effective dark energy is not conserved alone, and there is an effective coupling between dark energy and normal matter, with the possibility of energy transfer from one component to another.…”

“…The simplest models are those with non-minimally coupled [60][61][62][63] and non-minimal-derivatively coupled [64][65][66][67][68] scalar fields, but one could further use arbitrary functions of the kinetic and potential parts such as in K-essence [69], resulting in the general Horndeski [70] and generalized Galileon theories [71][72][73]. However, since there is no theoretical reason against couplings between the gravitational sector and the standard matter one, one can consider modified theories where the matter Lagrangian is coupled to functions of the Ricci scalar [74][75][76][77], and extend the theory to arbitrary functions (R, L m ) [78][79][80][81][82]. Alternatively, one can consider models where the Ricci scalar is coupled with the trace of the energy momentum tensor T and extend to arbitrary functions, such as in f (R, T ) theory [83][84][85][86][87], or even consider terms of the form R µν T µν [88,89].…”

Spherically Symmetric Solutions of Light Galileon

“…A class of modified theories of gravity has been discovered in which geometry is coupled to the matter field(s) non minimally, via Lagrangian of matter or energy-momentum tensor , with the following general Lagrangian [50]:…”

“…For the simple case of f (R, T µ µ )it has been investigated in several problems from cosmology to black holes [50] - [58]. The new extension of such models has been proposed recently as [59], [60] f (R, R µν T m µν ).…”

Traversable asymptotically flat wormholes in Rastall gravity

“…In the curvature-matter theory of gravity [39][40][41], while the divergence of energy-momentum tensor is not always zero, geometry and matter fields are coupled to each other in a non-minimal way. Indeed, quantum effects in curved spacetimes such as the particle production process [42][43][44][45][46] may motivate us to consider non-divergenceless energymomentum sources and thus modify the general relativity theory.…”