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Introduction to modified gravity and gravitational alternative for dark energy. (English) Zbl 1112.83047

Summary: We review various modified gravities considered as gravitational alternative for dark energy. Specifically, we consider the versions of \(f(R), f(G)\) or \(f(R, G)\) gravity, model with non-linear gravitational coupling or string-inspired model with Gauss-Bonnet-dilaton coupling in the late universe where they lead to cosmic speed-up. It is shown that some of such theories may pass the Solar System tests. On the same time, it is demonstrated that they have quite rich cosmological structure: they may naturally describe the effective (cosmological constant, quintessence or phantom) late-time era with a possible transition from decceleration to acceleration thanks to gravitational terms which increase with scalar curvature decrease. The possibility to explain the coincidence problem as the manifestation of the universe expansion in such models is mentioned. The late (phantom or quintessence) universe filled with dark fluid with inhomogeneous equation of state (where inhomogeneous terms are originated from the modified gravity) is also described.

MSC:

83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
83F05 Relativistic cosmology
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