Backreaction and the Covariant Formalism of General Relativity
  This thesis is a review of backreaction, which is a possible alternative to
dark energy and modified gravity. We describe in detail the 3+1 covariant
formalism and Frobenius' theorem. We present the averaging procedure developed
by Buchert, the Buchert equations and the generalization of these equations to
the case of general matter. We then generalize to arbitrary number of spatial
dimensions. We focus on the case of 2+1 dimensions, where the relation between
the topology and the geometry of a surface imposes a global constraint on
backreaction.
