'... I do not understand why only quantities with the transformation characteristics of tensors should be granted physical meaning.'
Albert Einstein, "On Gravitational Waves".
1.0 INTRODUCTION
There is no widely accepted single theory that explains the sets of gravitational phenomena separately attributed to dark energy (DE) and dark matter (DM). So, there occurs a dichotomy within gravitational science. The Friedmann-Lemaître-Robertson-Walker (FLRW) theory of an expanding universe without spatial curvature at very large scales, through its determinations of spatial expansion, continues to be affirmed by observations. However, at small (galactic) scales, it is not applicable.
Theoretical explorations of the relations of spacetimes applicable to galaxies, on one hand, and, on the other, to the FLRW spacetime have not produced very useful results. In fact, in 1945, Einstein and Straus established the conditions for the coexistence of the spherically symmetric curvilinear static Schwarzschild spacetime – that explained significant phenomena at the scale of our solar system – the FLRW spacetime \cite{Einstein_1945}. However, the two had to be mutually excluded in space and only had external relations, with the small-scale Schwarzschild spacetime simply existing within the FLRW spacetime. It has been shown that such coexistence was very fragile for the Schwarzschild spacetime, with instability under isotropic radial changes and vulnerability to non-spherical perturbations \cite{Mars_2013}. So, these spacetimes had to be separated by having the small-scale one existing in a spherical vacuole within the FLRW spacetime \cite{Mars_2013}.