scale factor $a_{{\cal D}}$ and the volume Hubble functional $H_{{\cal D}}$, we may introduce ‘parameters’ for higher derivatives of the volume scale factor, e.g. the [*volume deceleration functional*]{} $$\label{deceleration}
q^{{\cal D}}:= -\frac{{\ddot a}_{{\cal D}}}{a_{{\cal D}}}\frac{1}{H_{{\cal D}}^2} = \frac{1}{2}
\Omega_m^{{{\cal D}}} + 2 \Omega_{\cal Q}^{{{\cal D}}} - \Omega_{\Lambda}^{{{\cal D}}}\;\;,$$ or [*(volume) state finders*]{} [@sahnietal; @alametal] (see also [@evans] and references therein).

In this paper we shall denote all the parameters evaluated at the initial time by the index ${{{{\cal D}}_{\rm \bf i}}}$, and at the present time by the index ${{{{\cal D}}_{\rm \bf 0}}}$.

More details concerning these equations and their solutions may be found in [@buchert:grgdust; @buchert:grgfluid; @buchert:jgrg; @buchert:static].

The morphon field
=================

In the above–introduced framework we distinguish the averaged matter source and averaged sources due to geometrical inhomogeneities stemming from extrinsic and intrinsic curvature (backreaction terms). The averaged equations can be written as standard Friedmann equations that are sourced by both. Thus, we have the choice to consider the averaged model as a cosmology with matter source ‘morphed’ by a mean field that is generated by backreaction terms. We shall demonstrate below that this introduction of a ‘morphon field’ provides a natural description. We say ‘natural’, because the 