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

Troisi A.
  Mercoledì 13/09   09:00 - 13:00   Aula A203   III - Astrofisica
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's 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. 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. 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 counterterms. 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 with simple cases of such higher-dimensional solutions.