Chaplygin gas and effective description of inhomogeneous universe models
  in general relativity
  In the framework of spatially averaged inhomogeneous cosmologies in classical
general relativity, effective Einstein equations govern the dynamics of
averaged scalar variables in a scale--dependent way. A particular cosmology may
be characterized by a cosmic equation of state, closing the hierarchy of
effective equations. In this context a natural candidate is provided by the
Chaplygin gas, standing for a unified description of dark energy and dark
matter. In this paper, we suppose that the inhomogeneous properties of matter
and geometry obey the Chaplygin equation of state. The most extreme
interpretation assumes that both dark energy and dark matter are not included
as additional sources, but are both manifestations of spatial geometrical
properties. This feature is an important conceptual difference in comparison
with the standard approach of a Friedmann-Lema\^itre-Robertson-Walker universe
filled with dust and another fundamental field characterized by the Chaplygin
equation of state. We finally discuss the consequences of the resulting
scenario for effective cosmological parameters in order to establish the
framework of a future confrontation with observations, and we note that the
standard Chaplygin gas may not be ruled out by them.
