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f(R) models of dark energy

Since 1980, a variant of the f(R) fourth-order theory of gravity (with small one-loop corrections) was known to provide an internally self-consistent scenario of the early Universe with an initial quasi-de Sitter (inflationary) stage followed by the graceful exit to the radiation-dominated FRW stage via the period of reheating in which all matter in the Universe arises as a result of gravitational particle creation. Its predictions regarding spectra of primordial density perturbations and gravitational waves remain in agreement with the most recent observational data. A few years ago it was proposed to use this class of models for description of dark energy in the present Universe. However, this problem appeared to be more complicated, so many attempts in this direction failed. Still recently some f(R) models of dark energy have been found which can satisfy laboratory, Solar system and cosmological tests. To avoid formation of additional singularities, viable f(R) models of present dark energy should have the same asymptotic behaviour for large R as f(R) models of inflation. Unified description of inflation and present dark energy in f(R) gravity is possible, but leads to completely different reheating after inflation.

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