  Regionally averaged relativistic cosmologies have recently been considered as
a possible explanation for the apparent late time acceleration of the Universe.
This contribution reports on a mean field description of the backreaction in
terms of a minimally coupled regionally homogeneous scalar field evolving in a
potential, then giving a physical origin to the various phenomenological scalar
fields generically called quintessence fields. As an example, the
correspondence is then applied to scaling solutions.
