In this contribution we summarize two recent applications of a correspondence between backreaction terms in averaged inhomogeneous cosmologies and an effective scalar field (the 'morphon'). Backreaction terms that add to the standard sources of Friedmannian kinematical laws and that emerge from geometrical curvature invariants built from inhomogeneities, can be interpreted in terms of a minimally coupled scalar field in the case of a dust matter source. We consider closure conditions of the averaged equations that lead to different evolution scenarii: a) the standard Chaplygin equation of state imposed as an effective relation between kinematical fluctuations and intrinsic curvature of space sections, and b) an inflationary scenario that emerges out of inhomogeneities of the Einstein vacuum, where averaged curvature inhomogeneities model the potential of an effective classical inflaton.