Unimodular $f(G)$ gravity

In this paper we study a modified version of unimodular general relativity in the context of $f(G)$, $G$ denoting the Gauss-Bonnet invariant. We attach attention to Bianchi-type I and Friendmann-Robertson-Walker universes and search for unimodular $f(G)$ models according to the de Sitter and power-law solutions. Assuming unimodular $f(G)$ gravity as perfect fluid and making use of the slow-roll parameters, inflationary model has been reconstructed in concordance with the Planck observational data. Moreover, we investigate the realization of the bounce and loop quantum cosmological ekpyrotic paradigms. Assuming suitable and appropriated scale factors, unimodular $f(G)$ models able to reproduce superbounce and ekpyrotic scenarios have been reconstructed.