Higher-order gravity in higher dimensions: Geometrical origins of four-dimensional cosmology?

Abstract

Determining cosmological field equations represents a still very debated matter and implies a wide discussion around different theoretical proposals. A suitable conceptual scheme could be represented by gravity models that naturally generalize Einstein Theory like higher order gravity theories and higher dimensional ones. Both of these two different approaches allow to define, at the effective level, Einstein field equations equipped with source-like energy momentum tensors of geometrical origin. In this paper, it is discussed the possibility to develop a five dimensional fourth order gravity model whose lower dimensional reduction could provide an interpretation of cosmological four dimensional matter-energy components. We describe the basic concepts of the model, the complete field equations formalism and the 5-Dim to 4-Dim reduction procedure. Five dimensional $f(R)$ field equations turn out to be equivalent, on the four dimensional hypersurfaces orthogonal to the extra-coordinate, to an Einstein like cosmological model with three matter-energy tensors related with higher derivative and higher dimensional counter-terms. By considering a gravity model $f(R)=f_0{R}^n$ it is investigated the possibility to obtain five dimensional power law solutions. The effective four dimensional picture and the behaviour of the geometrically induced sources are finally outlined in correspondence to simple cases of such higher dimensional solutions.

18 pages, 4 figures; accepted for publication in EPJC

References in corpus (23)

• Dynamics of dark energy
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R,T) gravity
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Cosmological Constraints from the SDSS Luminous Red Galaxies
• Disappearing cosmological constant in f(R) gravity
• Extra force in $f(R)$ modified theories of gravity
• Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Temperature Analysis
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Measuring the Baryon Acoustic Oscillation scale using the SDSS and 2dFGRS
• Avoiding Dark Energy with 1/R Modifications of Gravity
• Low surface brightness galaxies rotation curves in the low energy limit of $R^n$ gravity : no need for dark matter?
• The Newtonian Limit of F(R) gravity
• Energy conditions in f(R)-gravity
• Dark energy and dark matter as curvature effects
• Theoretical Models of Dark Energy
• Fourth order gravity: equations, history, and applications to cosmology
• A viability criterion for modified gravity with an extra force
• Some remarks on the dynamical systems approach to fourth order gravity
• Constraints on cosmological parameters in power-law cosmology
• Five-dimensional generalized $f(R)$ gravity with curvature-matter coupling
• Diversity of universes created by pure gravity
• Modified Brans-Dicke theory of gravity from five-dimensional vacuum

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