Five-dimensional generalized $$f(R)$$ f ( R ) gravity with curvature–matter coupling

Ya-Bo Wu,Jun-Wang Lu,Yue-Yue Zhao,Jia-Wei Qiao,Xue Zhang,Cheng-Yuan Zhang

doi:10.1140/epjc/s10052-014-2791-9

Ya-Bo Wu, Jun-Wang Lu + Show 4 more

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https://doi.org/10.1140/epjc/s10052-014-2791-9

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Abstract

The generalized $f(R)$ gravity with curvature–matter coupling in five-dimensional (5D) spacetime can be established by assuming a hypersurface-orthogonal space-like Killing vector field of 5D spacetime, and it can be reduced to the 4D formalism of FRW universe. This theory is quite general and can give the corresponding results for Einstein gravity, and $f(R)$ gravity with both no-coupling and non-minimal coupling in 5D spacetime as special cases, that is, we would give some new results besides previous ones given by Huang et al. in Phys Rev D 81:064003, 2010. Furthermore, in order to get some insight into the effects of this theory on the 4D spacetime, by considering a specific type of models with $f_{1}(R)=f_{2}(R)=\alpha R^{m}$ and $B(L_{m})=L_{m}=-\rho $, we not only discuss the constraints on the model parameters $m,n$, but also illustrate the evolutionary trajectories of the scale factor $a(t)$, the deceleration parameter $q(t)$, and the scalar field $\epsilon (t),\phi (t)$ in the reduced 4D spacetime. The research results show that this type of $f(R)$ gravity models given by us could explain the current accelerated expansion of our universe without introducing dark energy.

Highlights

Another interesting alternative modified theory of gravity is f (R) gravity
As a result of the coupling the motion of the massive particles is nongeodesic, and an extra force, orthogonal to the four-velocity, arises
Different forms for the Lagrangian density of matter Lm, and the resulting extra force, were considered in [36], and it was shown that more natural forms for Lm do not imply the vanishing of the extra force

Summary

Introduction

Another interesting alternative modified theory of gravity is f (R) gravity (see, for instance, Ref. [27] for reviews). 4, the accelerated universe in reduced generalized f (R) gravity will be investigated by a numerical analysis of the evolutionary trajectories of the scale factor a(t), the deceleration parameter q(t), and the scalar field (t), φ(t). We consider the generalized f (R) gravity studied in [46,47,48,49], in which the coupling style between matter and geometry is arbitrary and the Lagrangian density of matter only appears in coupling term. Where fi (R)(i = 1, 2) and B(Lm) are arbitrary functions of the Ricci scalar R and the Lagrangian density of matter, respectively It follows that when f2(R) = 1 and B(Lm) = Lm, Eq (2) can be reduced to Eq (1). The dynamical equations of , φ, and the scale factor a(t) can be obtained by means of the above equations as well as Eqs. (11) and (12):

Rφ κ

FGCMC FGNMC FGNC EG