correspondence the backreaction effect is formally equivalent to the dynamics of a homogeneous, minimally coupled scalar field. Given this correspondence we can try to reconstruct the potential in which the morphon field evolves. Note that there are two equations of state in this approach, one for the morphon, $w^{{\cal D}}_{\Phi}: = p^{{\cal D}}_{\Phi}/\varrho^{{\cal D}}_{\Phi}$, and the total ‘cosmic equation of state’ including the matter source term, $w^{{\cal D}}_{\rm eff}:= p^{{\cal D}}_{\rm eff}/\varrho^{{\cal D}}_{\rm eff}$.

It is also worth noting that a usual scalar field source in a Friedmannian model, attributed e.g. to phantom quintessence that leads to acceleration, will violate the [*strong energy condition*]{} $\varrho + 3p >0$, i.e.: $$\label{energyconditionF}
3\frac{\ddot a}{a} = -4\pi G (\varrho + 3p) = -4\pi G 
(\varrho_H + \varrho_{\Phi} + 3 p_{\Phi}) \;> 0\;\;,\qquad$$ and actually also the [*weak energy condition*]{} $\varrho + p >0$, while for a morphon field both are not violated for the true content of the Universe, that is ordinary dust matter. It is interesting that we can write a ‘strong energy condition’ for the effective sources, i.e.: $$\label{energyconditionQ}
\fl
3\frac{{\ddot a}_{{\cal D}}}{a_{{\cal D}}} =  - 4\pi G (\varrho^{{{\cal D}}}_{\rm eff}
+3{p}^{{{\cal D}}}_{\rm eff}) =- 4\pi G\left(\, \langle\varrho\rangle_{{\cal D}}+ 
\varrho_{\Phi}^{{\cal D}}+ 