appears in the relations among the cosmological parameters, discussed after the next subsection.

Discussion of the scaling solutions
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The solution (\[ndiffpsolution\]) corresponds to the case where the backreaction and the averaged scalar curvature evolve independently, leading to an averaged curvature similar to a constant ‘Friedmannian curvature’ and an additional term that scales as $\langle\varrho\rangle_{\cal D}^2$. As the universe model expands, this solution is rapidly equivalent to a pure constant curvature term, we may say that this solution represents (and maintains) a near–Friedmannian state (${\cal Q}_{{\cal D}}$ decays much more rapidly $\propto V_{{\cal D}}^{-2}$ compared with the averaged density $\propto V_{{\cal D}}^{-1}$). Therefore, we shall not model this solution by a scalar field when describing the late–time dust–dominated Universe. It is interesting to note that this solution exhibits the same late–time behavior as the long–wavelength part of the solution found through the gradient expansion approximation scheme in [@kolbetal].

On the contrary, the solutions (\[backreactionparameter\]) entail a strong coupling between kinematical backreaction and averaged scalar curvature. The coupling itself must be considered a generic property; it has been identified as being responsible for a much slower decay of kinematical fluctuations in an expanding universe model on the cost of averaged scalar 