Observational constraints on Gauss–Bonnet cosmology

We analyze a fully geometric approach to dark energy in the framework of $F(R,{\cal G})$ theories of gravity, where $R$ is the Ricci curvature scalar and ${\cal G}$ is the Gauss-Bonnet topological invariant. The latter invariant naturally exhausts, together with $R$, the whole curvature content related to curvature invariants coming from the Riemann tensor. In particular, we study a class of $F(R, {\cal G})$ models with power law solutions and find that, depending on the value of the geometrical parameter, a shift in the anisotropy peaks position of the temperature power spectrum is produced, as well as an increasing in the matter power spectrum amplitude. This fact could be extremely relevant to fix the form of the $F(R, {\cal G})$ model. We also perform a MCMC analysis using both Cosmic Microwave Background data by the Planck (2015) release and the Joint Light-Curve Analysis of the SNLS-SDSS collaborative effort, combined with the current local measurements of the Hubble value, $H_0$, and galaxy data from the Sloan Digital Sky Survey (BOSS CMASS DR11). We show that such a model can describe the CMB data with slightly high $H_0$ values, and the prediction on the amplitude matter spectrum value is proved to be in accordance with the observed matter distribution of the universe. At the same time, the value constrained for the geometric parameter implies a density evolution of such a components that is growing with time.