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

Abstract

The generalized $f(R)$ gravity with curvature-matter coupling in five-dimensional (5D) spacetime can be established by assuming a hypersurface-orthogonal spacelike Killing vector field of 5D spacetime, and it can be reduced to the 4D formulism of FRW universe. This theory is quite general and can give the corresponding results to the Einstein gravity, $f(R)$ gravity with both no-coupling and non-minimal coupling in 5D spacetime as special cases, that is, we would give the some new results besides previous ones given by Ref.\cite{60}. 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 $\epsilon (t)$, $\varphi (t)$ 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.

arXiv admin note: text overlap with arXiv:0912.4581, arXiv:gr-qc/0411066 by other authors

References in corpus (21)

• Dynamics of dark energy
• Dark Energy and the Accelerating Universe
• Extra force in $f(R)$ modified theories of gravity
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• Are f(R) dark energy models cosmologically viable ?
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Nonminimal coupling of perfect fluids to curvature
• String-inspired Gauss-Bonnet gravity reconstructed from the universe expansion history and yielding the transition from matter dominance to dark energy
• The Cosmology of Modified Gauss-Bonnet Gravity
• Modified gravity with arbitrary coupling between matter and geometry
• Energy conditions in f(R)-gravity
• $f(T)$ models with phantom divide line crossing
• Matter instability in modified gravity
• Growth factor in f(T) gravity
• From inflation to dark energy in the non-minimal modified gravity
• Static Solutions with Spherical Symmetry in f(T) Theories
• A viability criterion for modified gravity with an extra force
• Newton law corrections and instabilities in $f(R)$ gravity with the effective cosmological constant epoch
• Do f(R) theories matter?
• Stability of the Einstein static universe in modified Gauss-Bonnet gravity

Cited by in corpus (1)

• Generalized curvature-matter couplings in modified gravity