Extendedf(R,Lm)gravity with generalized scalar field and kinetic term dependences

Abstract

We generalize previous work by considering a novel gravitational model with an action given by an arbitrary function of the Ricci scalar, the matter Lagrangian density, a scalar field and a kinetic term constructed from the gradients of the scalar field, respectively. The gravitational field equations in the metric formalism are obtained, as well as the equations of motion for test particles, which follow from the covariant divergence of the stress-energy tensor. Specific models with a nonminimal coupling between the scalar field and the matter Lagrangian are further explored. We emphasize that these models are extremely useful for describing an interaction between dark energy and dark matter, 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].…”

Improved constraints on violations of the Einstein equivalence principle in the electromagnetic sector with complementary cosmic probes

“…Particularly, those theories motivated by scalar-tensor theories of gravity, which introduce an additional coupling between the Lagrangian of the usual non-gravitational matter field with a new scalar field [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. In this class of theories, all the electromagnetic sector is affected, leading to a variation in the value of the fine structure constant (α = α 0 ζ(z), where α 0 is the current value) of the quantum electrodynamics [25,26], a non-conservation of the photon number and, consequently, a modification of the expression of the luminosity distance, D L (z), important for various cosmological estimates.…”

Can galaxy clusters, type Ia supernovae, and the cosmic microwave background rule out a class of modified gravity theories?

“…Several alternative models can be described by such a kind of coupling. We can cite string dilaton theories [24] at low energies, theories with additional compactified dimensions as Kaluza-Klein [25], models involving axions [26], cosmologies that consider a varying fine structure constant [27], chameleon-field models [28] or f (R) extended gravity theories [29].…”