Five-dimensional metric $f(R)$ gravity and the accelerated universe

Abstract

The metric $f(R)$ theories of gravity are generalized to five-dimensional spacetimes. By assuming a hypersurface-orthogonal Killing vector field representing the compact fifth dimension, the five-dimensional theories are reduced to their four-dimensional formalism. Then we study the cosmology of a special class of $f(R)=\alpha R^m$ models in a spatially flat FRW spacetime. It is shown that the parameter $m$ can be constrained to a certain range by the current observed deceleration parameter, and its lower bound corresponds to the Kaluza-Klein theory. It turns out that both expansion and contraction of the extra dimension may prescribe the smooth transition from the deceleration era to the acceleration era in the recent past as well as an accelerated scenario for the present universe. Hence five-dimensional $f(R)$ gravity can naturally account for the present accelerated expansion of the universe. Moreover, the models predict a transition from acceleration to deceleration in the future, followed by a cosmic recollapse within finite time. This differs from the prediction of the five-dimensional Brans-Dicke theory but is in consistent with a recent prediction based on loop quantum cosmology.

14 pages, 9 figures; Version published in PRD

References in corpus (7)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Dynamics of dark energy
• Dark Energy and the Accelerating Universe
• Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
• Experimental Tests of General Relativity: Recent Progress and Future Directions
• Effective Scenario of Loop Quantum Cosmology
• Five-dimensional PPN formalism and experimental test of Kaluza-Klein theory

Cited by in corpus (10)

• Dark Energy
• Conserved Quantities in $f(R)$ Gravity via Noether Symmetry
• Five-dimensional generalized $f(R)$ gravity with curvature-matter coupling
• Binary Black Hole merger in f(R) theory
• Late-time acceleration in Higher Dimensional Cosmology
• Statefinder Parameters for Different Dark Energy Models with Variable G Correction in Kaluza-Klein Cosmology
• Manifestly Gauge Invariant Perturbations of Scalar-Tensor Theories of Gravity
• Distinguishing f(R) theories from general relativity by gravitational lensing effect
• Higher-order gravity in higher dimensions: Geometrical origins of four-dimensional cosmology?
• Classical Tests of General Relativity: Probing Topologically Charged Black Holes on Brane Worlds in f(R) Bulk