  Two recent articles \cite{ashtekar2015general, moncrief2019could} suggested
an interesting dynamical mechanism within the framework of the vacuum Einstein
flow (or Einstein-$\Lambda$ flow if a positive cosmological constant $\Lambda$
is included) which suggests that many closed (compact without boundary)
manifolds that do not support homogeneous and isotropic metrics \textit{at all}
will nevertheless evolve to be asymptotically compatible with the observed
approximate homogeneity and isotropy of the physical universe. These studies
however did not include matter sources. Therefore the aim of the present study
is to include suitable matter sources and investigate whether one is able to
draw a similar conclusion.
