be entirely expressed through Minkowski Functionals [@meckeetal] of the boundary of the averaging domain [@buchert:jgrg]. These functionals form a complete basis in the space of (Minkowski–)additive measures for the morphometry of spatial sets.

Motivation: the morphon modeling a cosmological constant
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Let us give a simple example. As shown in [@buchert:static], Subsect. 3.2 (also advanced as a motivation case in [@kolbetal]), the effective source ${\cal Q}_{{\cal D}}$ may act as a cosmological constant. The general condition for the corresponding exact solution of the effective Friedmann equations (\[effectivefriedmann\]) (with $\langle\varrho\rangle_{\cal D}=0$ and $\Lambda = 0$) is ${\left\langle {{\cal R}}\right\rangle_{{\cal D}}}= 6 k_{{{{{\cal D}}_{\rm \bf i}}}} /a_{{\cal D}}^2 -3{\cal Q}_{{\cal D}}$; ${\cal Q}_{{\cal D}}= 
{\cal Q}_{{{{{\cal D}}_{\rm \bf i}}}}$; e.g., for $k_{{{{{\cal D}}_{\rm \bf i}}}} = 0$ we have: $$\label{inflaton1}
{\dot\Phi}_{{\cal D}}= 0\;\;\;;\;\;\; \varrho^{{\cal D}}_{\Phi}= U_{{\cal D}}\;\;\;;\;\;\;p^{{\cal D}}_{\Phi} = -U_{{\cal D}}\;\;\;;\;\;\;U_{{\cal D}}= U_{{{{{\cal D}}_{\rm \bf i}}}}  \;\;.$$ The kinematical backreaction term assumes a constant value ${\cal Q}_{{{\cal D}}}
= 8\pi G U_{{{{{\cal D}}_{\rm \bf i}}}}$, and the morphon potential mimics a (scale–dependent) cosmological constant. Note that the averaged curvature is non–zero, ${\left\langle {{\cal R}}\right\rangle_{{\cal D}}}= -24\pi G U_{{{{{\cal D}}_{\rm \bf i}}}}$, so that simultaneously the morphon unavoidably installs a non–zero averaged scalar 