A cosmic equation of state for the inhomogeneous Universe: can a global far–from–equilibrium state explain Dark Energy?

A system of effective Einstein equations for spatially averaged scalar variables of inhomogeneous cosmological models can be solved by providing a ‘cosmic equation of state’. Recent efforts to explain Dark Energy focus on ‘backreaction effects’ of inhomogeneities on the effective evolution of cosmological parameters in our Hubble volume, avoiding a cosmological constant in the equation of state. In this Letter it is argued that, if kinematical backreaction effects are indeed of the order of the averaged density (or larger as needed for an accelerating domain of the Universe), then the state of our regional Hubble volume would have to be in the vicinity of a far– from–equilibrium state that balances kinematical backreaction and average density. This property, if interpreted globally, is shared by a stationary cosmos with effective equation of state p eff = −1/3̺ eff . It is concluded that a confirmed explanation of Dark Energy by kinematical backreaction may imply a paradigmatic change of cosmology. PACS numbers: 04.20.-q, 04.20.-Cv, 04.40.-b, 95.30.-k, 98.80.-Es, 98.80.-Jk 1. Effective Einstein equations and the cosmic equation of state To set notation and to provide the framework for our argument, we recall a set of effective Einstein equations [2]. The argument presented can be carried over to studies of inhomogeneous cosmologies covering the Early Universe and radiation–dominated epochs with the help of the more general effective equations developed in [3]. 1.1. Averaged equations For the sake of transparency we restrict ourselves to the matter model irrotational dust. Adopting a foliation of spacetime into flow–orthogonal hypersurfaces (which is possible for irrotational dust) with the 3–metric gij in the line–element ds 2 = −dt2+gij dX dX, we define spatial averaging of a scalar field Ψ on a domain D with volume VD by: