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, according to which dark energy could be an effective source. 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. In particular we focused on voids expanding faster than the background solution. 
Valerio Marra