So, in GR, orbits are inexplicable in the currently applicable FLRW space-time (that is spatially flat) since the latter may, simply by means of a time coordinate transformation, be shown to become, thereby, a Minkowskian flat space-time. So, GR cannot be applied to explain galactic orbits in the GR-derived FLRW theory of a spatially flat universe. However, since Newton’s science of gravity applies only to flat space and, moreover, is the only alternative to Einstein’s, then its reassertion is fundamentally unavoidable in FLRW cosmology. This situation amounts to an internal theoretical incongruity in modern cosmology and astrophysics.
It is here proposed that this fundamental incongruity within cosmology and astrophysics is the primary cause of the persistence of the mysteries of dark energy and dark matter.
So, I seek to develop a unitary explanation within the paradigm of the gravitational theory of GR that explains both sets of phenomena. The desire is to include only the universal empirical element of the Hubble expansion of space \citep*{Riess_2001} within a strictly classical GR explanation that treats all matter generically as energy tensors, while generally ignoring the other aspects of the different species of matter, some of which become so important in FLRW cosmology.
Furthermore, it was recognized that in developing his general field equations, Einstein had invoked a feedback mechanism in the induction of gravity \cite{einstein1952}. It seemed that, given the tight coupling of gravity with space by means of the metric, such a mechanism had the potential to explain spatial expansion.
It was clear that the assumed homogeneity in FLRW cosmology is only approximated at very large scales in the universe. So, in order to accommodate small-scale < 3Mpc phenomena \citep*{Karachentsev_2009}principle of homogeneity had to be surrendered.
However, the universe still appears fairly isotropic \cite{Hu_2003}as observed from within our solar system and since galaxies display galactocentric kinematics and distributions of matter, then a radially symmetric metric seemed appropriate. Most important, however, is the fact that the cosmic expansion is isotropic.
The rigidity of an absolutely flat spatial manifold was abandoned for clearly that does not apply within galaxies with their strongly curvilinear geodesics.
Finally, the large-scale curvature of space is not observationally supported and was not pursued here.
So, it was that I chose to combine a generalized form of FLRW metric with a scale factor, but without a curvature term. The generalization was intended to relax the constraints applied in the FLRW metric so as to widen the scope of candidate space-times for theoretical exploration.