3 p_{\Phi}^{{\cal D}}\,\right)
= -4\pi G \langle\varrho\rangle_{{\cal D}}+ {\cal Q}_{{\cal D}}\;<\;0\,.$$ While we do not need ‘exotic matter’, the above condition will be ‘violated’ in order to have volume acceleration, ${\cal Q}_{{\cal D}}> 4\pi G\langle\varrho\rangle_{{\cal D}}$ [@kolbetal], [@buchert:static], [*cf.*]{} Subsection \[subsubsect:accelerationconditions\].

Newtonian limit
---------------

In the Newtonian limit [@buchertehlers], the above correspondence persists. The sources of the morphon in the effective Friedmann equations (\[effectivefriedmann\]) are then identified as follows, [*cf.*]{} Eqs. (\[omeganewton\]) and (\[integrabilityintegral\]): $$\begin{aligned}
\label{sourcesnewton}
\varrho^{{\cal D}}_{\Phi N} := \frac{1}{8\pi G}\left[\,\frac{1}{a_{{\cal D}}^2} 
\int_{{{t_{\rm \bf i}}}}^t \rmd t'\ {\cal Q}_{{\cal D}}\frac{\rmd }{\rmd t'} a^2_{{\cal D}}(t')
 -\frac{3k_{{{{{\cal D}}_{\rm \bf i}}}}}{a_{{\cal D}}^2}\,\right]\;\;;\;\;\nonumber\\
p^{{\cal D}}_{\Phi N} := - \frac{1}{24\pi G}\left[\,\frac{1}{a_{{\cal D}}^2} 
\int_{{{t_{\rm \bf i}}}}^t \rmd t'\ {\cal Q}_{{\cal D}}\frac{\rmd }{\rmd t'} a^2_{{\cal D}}(t') 
-\frac{3 k_{{{{{\cal D}}_{\rm \bf i}}}}}{a_{{\cal D}}^2}+2{\cal Q}_{{\cal D}}\,\right]\;\;.\end{aligned}$$ However, Newtonian cosmologies suppress the morphon degrees of freedom on some fixed large scale where the kinematical backreaction term has to vanish identically [@buchertehlers]. In particular, this remark applies to cosmological N–body simulations: by construction, these simulations enforce ‘virial equilibrium’ of the morphon energies on the scale of the simulation box.

The Newtonian framework also offers a concise explanation of our choice ‘morphon field’: the kinematical backreaction term ${\cal Q}_{{\cal D}}$ can 