Gauss-Bonnet Cosmology Unifying Late and Early-time Acceleration Eras with Intermediate Eras

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In this paper we demonstrate that with vacuum $F(G)$ gravity it is possible to describe the unification of late and early-time acceleration eras with the radiation and matter domination era.

• The Hubble rate of the unified evolution contains two mild singularities, so called Type IV singularities, and the evolution itself has some appealing features, such as the existence of a deceleration-acceleration transition at late times.
• We also address quantitatively a fundamental question related to modified gravity models description of cosmological evolution: Is it possible for all modified gravity descriptions of our Universe evolution, to produce a nearly scale invariant spectrum of primordial curvature perturbations? As we demonstrate, the answer for the $F(G)$ description is no, since the resulting power spectrum is not scale invariant, in contrast to the $F(R)$ description studied in the literature.
• Therefore, although the cosmological evolution can be realized in the context of vacuum $F(G)$ gravity, the evolution is not compatible with the observational data, in contrast to the $F(R)$ gravity description of the same cosmological evolution.