Coincidence problem and holographic f(R) gravity in spatially flat and curved universes

Y. Bisabr1

Abstract

The f(R) gravity models formulated in the Einstein conformal frame are equivalent to Einstein gravity with a minimally coupled scalar field. The latter couples to the matter sector, the coupling term being given by a conformal factor. We apply the holographic principle to such an interacting model in spatially flat and curved universes. We show that the model leads to a constant ratio of energy densities of dark matter to dark energy in a spatially flat universe. In a spatially curved universe, the ratio is not a constant, and the evolution seems to be model-dependent. However, we argue that any cosmologically viable f(R) model can lead to a nearly constant ratio of energy densities and therefore alleviate the coincidence problem.

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