Friedmann's Universe Controlled by Gauss-Bonnet Modified Gravity

The accepted idea that the expansion of the universe is accelerating needs, for compatibility to general relativity, the introduction of some unusual forms of matter. However, several authors have proposed that instead of making weird hypothesis on some yet unobservable species of matter, one should follow the original idea of the first Einstein's paper on cosmology and consider that in the cosmic scene one has to modify the equations that controls the gravitational metric. This possibility led us to re-examine the evolution of the topological invariant containing two duals in a dynamical universe, the so called Gauss-Bonnet topological invariant. The particular interest on this invariant is due to the fact that in a homogeneous and isotropic universe this invariant drives the cosmic acceleration. In a decelerating scenario and as a necessary previous condition of an ulterior acceleration this invariant must have an extremum identified to its maximum value. We will examine the conditions for this to occur, and a description of the universe with epochs of accelerated and decelerated expansion.