Correspondence between kinematical backreaction and scalar field cosmologies - the 'morphon field'

Spatially averaged inhomogeneous cosmologies in classical general relativity can be written in the form of effective Friedmann equations with sources that include backreaction terms. In this paper, we propose to describe these backreaction terms with the help of a homogeneous scalar field evolving in a potential; we call it the 'morphon field'. This new field links classical inhomogeneous cosmologies to scalar field cosmologies, allowing to reinterpret, e. g., quintessence scenarios by routing the physical origin of the scalar field source to inhomogeneities in the universe. We investigate a one-parameter family of scaling solutions to the backreaction problem. Subcases of these solutions (all without an assumed cosmological constant) include scale-dependent models with Friedmannian kinematics that can mimic the presence of a cosmological constant or a time-dependent cosmological term. We explicitly reconstruct the scalar field potential for the scaling solutions and discuss those cases that provide a solution to the dark energy and coincidence problems. In this approach, dark energy emerges from morphon fields, a mechanism that can be understood through the proposed correspondence: the averaged cosmology is characterized by a weak decay (quintessence) or growth (phantom quintessence) of kinematical fluctuations, fed by 'curvature energy' that is stored in the averaged 3-Ricci curvature. We find that the late-time trajectories of those models approach attractors that lie in the future of a state that is predicted by observational constraints.