Abstract:

The success and the shortcomings of the standard cosmological model are discussed in view of the most recent theoretical and observational constraints. The motivations for considering extensions and/or modifications of General Relativity are taken into account, with the possibility to describe the gravitational dynamics under different frameworks. A powerful approach to discriminate among competing cosmological scenarios is given by the cosmographic method. After reviewing the main features of standard cosmography,we highlight how to overcome the convergence issue jeopardizing current low redshift-cosmographic distances by means of rational polynomials. Based on numerical bounds over the cosmographic series, we investigate the origin of cosmic acceleration and the possibility of going beyond the standard cosmological model to explain the dark energy problem.