Evolution and constraint equations in F(G) cosmologies

Our aim is to determine what kind of changes and differences the cosmological evolution of the F(G) modified gravitational theories bring with respect to the Standard Cosmology of the General Relativity theory. We will consider the F(G)-gravity theory, which belongs to the class of higher order gravitational theories, with Rab and Rabcd being the Ricci and Riemann curvature tensors, respectively and the Gauss-Bonnet term defined in the form of G , G = R2 4Rab Rab + Rabcd Rabcd in R in terms of the the Ricci curvature scalar. Using the effective fluid description, we will generalize this F(G) cosmology to the evolution and bond equations using the covariant and Tetrad Formalism of Conventional Relativist Cosmology (1+3). For this challenge, we will consider isotropic FLRW models.