can indeed be made responsible for the late–time acceleration of the Universe, then the effort spent on quintessence models and other approaches [@copeland] can be fruitfully exploited in terms of the proposed rephrasing. Fourth, since the underlying effective equations are general and do not invoke perturbative assumptions, the scalar field cosmology provides access to the whole solution space, notably to the non–perturbative regime. Finally, subcases of exact solutions include a cosmological constant, which therefore can or cannot be included in Einstein’s equations; the cosmological constant is a particular solution of the averaged inhomogeneous model without necessarily being present in Einstein’s equations.

Since the scalar field introduced in this way stems from averaged geometrical degrees of freedom, i.e. kinematical backreaction terms encoded in the extrinsic curvature of spatial hypersurfaces, as well as their scalar curvature, we call it the [*morphon field*]{}: it effectively models the inhomogeneities [*shaping*]{} the structure in the Universe and capturing the total effect of kinematical backreaction, i.e. the effect leading to a deviation from the kinematics of the standard model. Speaking in terms of geometry, we may roughly say that the morphon models the geometrical vacuum degrees of freedom in Einstein’s theory, which are neglected when modeling 