It is here proposed that the passivity, in ΛCDM cosmology, of the gravitational field is the basis of the persistence of the mysteries of DE and DM.
So, the endeavour, here undertaken, is to develop a unitary explanation, within the paradigm of the gravitational field theory of GR, that explains both sets of phenomena. The intent is to include the universal empirical element of the Hubble expansion of space [18] within a strictly classical GR explanation that treats all matter generically as energy tensors, while generally ignoring other aspects of the various species of matter and radiation, some of which become so important in ΛCDM astrophysical cosmology.
In §2, a generalized FLRW metric determines certain common dynamic attributes of the associated class of fields. In §3, a gravitationally perturbed Robertson-Walker (gpRW) metric is used to develop descriptions of initial states of certain spherically symmetric gravitational systems. Then, in §4 a physical derivation of the Hubble-Lemaître law is presented. Phenomena associated with DM are explained by the Hubble expansion in §5. The recession in cosmic voids is explored in §6. In §7, the Hubble expansion across all scales is explored. In §8, the redshift-distance relation is explored. In §9, a gravitational process proposed to energize the spatial expansion is presented. In §10, there is a discussion of the views presented here and certain aspects of ΛCDM. The explanations given here are summarized in §11.
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. At large scales, the expanding space-time of FLRW theory, without spatial curvature, through its descriptions of spatial expansion, continues to be affirmed by observations. However, at small (galactic) scales, it is not \cite{Demianski_2017}applicable. \cite{Harrison_1993}
Theoretical explorations of the relationships of space-times applicable to galaxies, on one hand, and, on the other, to the FLRW space-time 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 space-time - that explained significant phenomena at the scale of our solar system - and the spatially flat FLRW space-time \cite{Einstein_1945}. However, the two had to be mutually excluded in space and they only had external relations, with the small-scale Schwarzschild space-time simply existing within the FLRW space-time. It has been shown that such coexistence was very fragile for the Schwarschild space-time, with instability under isotropic radial changes and vulnerability to non-spherical perturbations \cite{Mars_2006}. So, these space-times had to be separated by having the small-scale one existing in a spherical vacuole within the cosmic FLRW space-time \cite{Plaga_2005}.
In the absence of a robust coherent connection between the spacetimes of large- and small-scale regions, there has been a reassertion, in the latter, of Newtonian science of gravity in cosmology and astrophysics \citep{Chisari_2011,Chisari_2011a} For, at small scales, it is apparent that Newtonian science of gravity is the normative model applied in analysis and so in simulations. So, though based on Einstein’s theory of gravity, modern cosmology was, in small-scale regions, mainly applying Newton’s methods against the background of a flat space-time. This occurs even though Newtonian physics had already been proven incapable of explaining certain subtle gravitational effects such as the precession of Mercury’s orbit and the deflection of light around massive bodies that were explained by general relativity (GR) in \cite{einstein1952}.
Yet, however contradictory the situation appears, it is quite comprehensible. For, in GR, orbits require inherently curvilinear spacetimes \cite{einstein1952}. So, in GR, orbits are inexplicable in the currently applied FLRW space-time 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.
At large-scale, the Standard Model of Cosmology (\(\)\(\)ΛCDM) proposes the cosmological constant as the agent of the expansion of space. This agent is taken to be an unidentified baryonic or radiation field of a character that permits it to couple with space and to expand it.
So, at both large and small scales, the gravitational field, though theoretically implied in FLRW cosmology, is avoided. Yet, as it relates to physical reality, classical - that is, pre-FLWR - GR, as a theory of gravitation, is distinguished by the central role of a metric defined gravitational field - being the only entity that couples with space - in its development, descriptions, and explanations . So, this effective absence of the gravitational field in FLRW cosmological explanations appears as a peculiarity of fundamental impact within a GR-derived theory.
It is here proposed that this peculiarity - within \(\)ΛCDM cosmology and astrophysics - of the absence of the gravitational field 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, given the tight coupling of gravity with space by means of the metric, that 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}e 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 in the choice of a space-time, 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 the 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.