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