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

• Published in: The European physical journal. C, Particles and fields Particles and fields, 2017-03, Vol.77 (3), p.1-18, Article 171
• Main Author: Troisi, Antonio
• Format: Article
• Language: English
• Subjects: Astronomy; Astrophysics and Cosmology; Cosmology; Einstein equations; Elementary Particles; Geometry; Gravitation; Hadrons; Heavy Ions; Mathematical models; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Reduction; Regular Article - Theoretical Physics; String Theory; Tensors
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-017-4719-7

Determining the cosmological field equations is still very much debated and led to 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 one to define, at the effective level, Einstein field equations equipped with source-like energy-momentum tensors of geometrical origin. In this paper, the possibility is discussed 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-D to 4-D 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 the gravity model with f ( R ) = f 0 R n the possibility is investigated 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.