A Back-Reaction Approach to Dark Energy

This thesis is mainly about how to set up and carry out in a physically meaningful way the idea of back-reaction, which is an alternative theory to a theory where dark energy is fundamental. There are, broadly speaking, two distinct approaches. One is focused on how cosmological observables are affected by inhomogeneities, while the other is focused on a theoretical description of the inhomogeneous universe by means of a mean-field description. Both approaches, however, share the idea of smoothing out inhomogeneities. We developed this duality in the interpretation of the back-reaction by means of toy models based on the Lemaitre-Tolman-Bondi solution of Einstein's equations.