Reconstruction method applied to bounce cosmology and inflationary scenarios in cosmological f(G) gravity

The modified theory of gravity f(G) is addressed in this work where G means the Gauss–Bonnet invariant. We investigate through this paper, some f(G) models susceptible to describe some evolution phase of our universe. Accordingly we introduce a special reconstruction program called reconstruction method and based on the Friedmann space time metric which is an ideal manifold to represent our universe at large scale. Firstly, this reconstruction procedure is developed for f(G) forms that can give rise to scale-factor bounce evolutions. New Gauss–Bonnet modified gravity models with bouncing behavior in the early stages as well the late-time of the universe evolution are provided. The f(G) models near the bounce satisfy some well-known f(G) gravity properties which make them to explain the transition from the matter or radiation domination epoch to the dark matter domination epoch, whereas away from the bounce, only one epoch is recovered. Secondly, we also apply the reconstruction method to the inflationary regime. The quasi de Sitter evolution is involved and from the extraction and analysis of its corresponded Hubble slow-roll parameters, one obtains the appropriate cosmological inflationary f(G) model.