8.0 DISCUSSION 

The theoretical results obtained here strongly motivate further endeavours to advance empirical investigations to determine the linearity of the Hubble-Lemaître law at small scales less than 5Mpc \cite{Sandage_2010} below 0.7 Mpc [9] \citep*{Karachentsev_2009}. At galactic and solar scales ≤ 100 pc, innovative techniques will have to be developed. This will test the proposal that the Hubble parameter is invariant. 
The historical forms of the laws of the field and their influences, given here, may assist in providing the bases for the development of techniques applicable to the determination of the expansion, especially in regions of curvilinear gravity.
Due to its EoS, gravity’s energetic fluxes - pressure (‘dark energy') and energy density (‘dark matter') - are equal in magnitude everywhere. This avoids the ‘cosmic coincidence problem’ confronting the \(\)ΛCDM model, of infinitesimal likelihood, in any single epoch, of the occurrence of comparable magnitudes of a continuously decreasing dark matter density and that of an unchanging dark energy density.
‘This ratio changes from almost infinity to zero in the ΛCDM model' \cite{Velten_2014}.
Given this latitude, the question is: why is it that, in this epoch, this ratio is of an order of magnitude of one.
‘Since the missing energy density and the matter density decrease at different rates as the universe expands, it appears that their ratio must be set to a specific, infinitesimal value in the very early universe in order for the two densities to nearly coincide today, some 15 billion years later’ (Zlatev 1999).
The volumetrically dominant cosmic voids and empty intergalactic spaces [16] are, here, described as domains of maximal gravitational energy density and of approximately flat space-time. This makes for an overall proximate flatness of the field across the cosmos. Furthermore, the growth of the field increases the volumes of these flat regions as it reduces its gradients in the gravitationally curvilinear vicinities of galaxies and, thereby, increases the overall cosmic flatness of the field. 
This avoids the ’flatness problem’ of ΛCDM presented by its requirement that:
“the initial value of the Hubble constant must be fine tuned to extraordinary accuracy to produce a universe as flat (i.e., near critical mass density) as ‘the one we see today (flatness problem)’ “ \cite{Guth_1981}
In ΛCDM, the geometry of the universe depends on the density parameter: ratio of the density of its contents relative to a critical density that is directly proportional to the square of the Hubble parameter. Now, according to ΛCDM if the initial value of the cosmic density parameter was not within the range of 1.0±1.0E-15 at the Big Bang, then there would have been an exponentially fast departure from flatness. Since ΛCDM makes no prediction on the cosmic density at the beginning of the universe and that it predicts widely varying rates of spatial expansion, then, to itself, the initial closeness of the cosmic and critical densities is a mere coincidence.
Here, the geometry of the universe is that of the gravitational field. It is almost flat at large-scales, and curvilinear in the galactic haloes.
It is quite remarkable that the maximum, and approximately average cosmic, value here predicted of the energy density of the gravitational field, H2/2κ \(\)≈ 1.52E-27 Kg m-3 for H = 2.26E-18 s-1, is of the same order of magnitude as ΛCDM's current ‘observed' value of the density of ‘dark energy’ which approximately is 6.9E-27 Kg m-3. This is significant because 'dark energy' is, in ΛCDM, the sole occupant in the cosmic voids. However, by the account given here, the first occupant of the vacuum is the energetic gravitational field that produces the vacuum as its form - space, as opposed to resulting from it.  This shared order of magnitude of energy density of the field and ‘dark energy' supports the identification of the latter as being the gravitational field.
This approximate value, as determined here, of the average cosmic energy density of the gravitational field in the vacuum also avoids the ‘cosmological constant problem' [19] confronting explanations of dark energy based on particle physics. In the  ΛCDM description of dark energy it is represented by a cosmological constant with a uniformly constant energy density. This energy is proposed by particle physicists to be due to energetic quantum fluctuations of the vacuum. The problem is that the predicted minimum energy density of physical quantum processes (electroweak) is of an order of magnitude 1.0E122 greater than ΛCDM estimates of the density of the hypothetical dark energy.
It must be noted that the ‘model’ of ‘dark matter’ presented here – that of the gravitational energy density field – has a galactocentric radial energy density profile that displays no ‘cuspy’ gradient in the vicinity of the galactic centre. In fact, as the centre is approached, the density declines, as do the velocities. This decline of velocities in the galactic core, that challenges prominent models of dark matter [4], is generally empirically confirmed.
It is also clear that the flattened orbits in galaxies and clusters, considered here, do not violate the law of conservation of angular momentum and Einstein’s laws of gravitation. The orbits are displaying the gravitational effects of an unseen energetic field; the gravitational field.
Indeed, it is because all forms of energy are equivalent in inducing gravity - as shown by equation (68) - that the auto-induced energetic gravitational field will appear, purely through its gravitational effects, just as it really is, that is, as an invisible and thereby dark, ‘dissipationless’ and thereby cold, growing and thereby clustering, mass-energy field. So, it is understandable that for Newtonian science - that presumes action-at-a-distance of a massive gravitating body and does not make provisions for the agency, in such matters, of a gravitational field – that these apparently anomalous orbits cannot be due to anything other than the attraction by some cold dark matter.
Subsequent to the failure to identify baryonic dark matter, the search has focussed on non-baryonic dark matter (NBDM), but without success so far \cite{Weinberg_1989}
The NBDM is here identified as the gravitational field.
Phenomena elsewhere attributed separately to ‘dark matter' and ‘dark energy' are here attributed to the common cause of the qualitatively unchanging gravitational field. This explanation, thereby, avoids problematics associated with explanations that are based on particularities, often exotic, of the natures of the variously hypothesized species of matter that commonly occur in speculations concerning both dark energy and dark matter.
It should be clear, in view of the account given here, that dark matter and dark energy are conceptions created to pre-configure explanations of two sets of dynamical manifestations of one and the same thing – the auto-induced expansion of the gravitational field into new spaces that it creates. That is, the expansion of the gravitational field appears, through its different effects – the isotropic recession of galaxies, on one hand, and unexpected orbits in galaxies and in their clusters and gravitational lensing in their haloes, on the other - as being two different entities operating in mutually exclusive regions. So, the auto-inductive gravitational field provides a unifying explanation of phenomena attributed to dark energy and dark matter, without the problematics associated with their models.
The application of the gravitationally perturbed Robertson-Walker metric has been quite productive in this work. It provides a single versatile metric suitable for descriptions of phenomena both in large- and small-scale regions. So, it avoids the challenges of integrating the small-scale curvilinear space-time of galaxies with a spatially flat space-time of the universe at large scales that confronted Einstein and Straus.
It is also interesting to note the appellation - gravitationally perturbed Robertson-Walker metric. It seems to assign to curvilinear gravity – which is associated with such distinctly metric phenomena as orbits, gravitational lensing, and, even with the spatial expansion - the insignificance of merely being a perturbation of the flat cosmic Robertson-Walker metric that underpins FLRW cosmology, as opposed to being an essential structural aspect of the cosmos.
Across the universe, the field appears as being, unintuitively, a high and flat – and, thereby, non-Minkowskian - plateau of energy density pocked by innumerable narrow curvilinear declines into deep gravitational wells - associated with widely isolated baryonic fields - reaching down to zero energy density at event horizons.
The gravitational field manifests two modes of geodesic and metric influences on bodies and radiation: (a) energetically in the inducement of a universal and constant, uniform, isotropic recession, and (b) non-energetically in the inducement of recession-influenced baryonic kinematics and optics – rectilinear in voids and curvilinear in the vicinities of baryons.
The so-called ‘gravitationally bound’ systems of galaxies and solar systems do not resist the gravitational recession, but participate fully in the cosmic Hubble flow that manifests itself, here, in strange flattened orbits. The term - gravitationally bound - has traditionally been used to infer orbiting bodies or those on course to collide with the gravitating bodies. Such bodies are said to be able to escape their fates if supplied with sufficient energy. However, from the point of view here taken, this energy is that required to take the bound body from the deep gravitational wells of relatively low energy density to the remote regions of higher gravitational energy intensity which are also flat and thereby devoid of orbits. So, they appear unbound. However, these bodies still participate in the recession due to gravity. So, in fact, all bodies are gravitationally bound, hence their universal mutual recession. There is no space outside of gravity.
If the explanation here given proves to be useful, then such an outcome would be consistent with the conjecture that the operational absence of the gravitational field in ΛCDM cosmology has led to its failure to identify the agents of dark energy and dark matter.
Possibly due to the non-locality and non-covariance of its pseudo-tensor, gravitational energy is not given a place in ΛCDM's cosmic density parameters. Here, the non-locality of the pseudo-tensor is consistent with its cosmic application. Yet, inadvertently, ΛCDM grants to gravitational energy, through the proxies of dark energy and dark matter, an allocation of about ninety-five percent of the cosmic mass-energy density.
This work is a proof of principles. As such, it considers an ideal galaxy, one with a dominant central SMBH and infinitesimal baryonic tracers. Applications to more realistic situations involving different types of bound systems - galaxies, clusters, and walls - may not only discern the influence of the cosmic expansion, but also contribute to the comprehension of the formation of their structures.
A useful application of the relationships, such as here developed, is in the mapping of the gravitational field of regions of the observable universe. This would include data from on-going and future sky surveys of the distribution of matter fields; regions of curvilinear gravity (dark matter haloes) as determined by orbital tracers and gravitational lensing; and cosmic voids and walls. Simulations of past and future baryonic trajectories within the developing gravitational field, both at large- and small-scales, will enable a significantly greater comprehension of the universe and its development.

9.0   CONCLUSIONS

So, here stands a derivation of the Hubble-Lemaître law as a law of gravity and a unitary identification of the dark energy and dark matter of the cosmos as being the singular energetic gravitational field.
It is the application of the Hubble-Lemaître law that leads to an explanation of both sets of phenomena separately attributed to dark matter and to dark energy.
New and/or significant aspects in this explanation include: 
1.  A single universal metric – the radially symmetric gravitationally perturbed Robertson-Walker metric - that:
2. The determination, in the space-time defined by this metric, of an equation of state (EoS) of the gravitational field as being: w=-1.
3. The identification of the mechanism of the auto-induction of gravity in Einstein’s theory of general relativity.
4. The recognition that space is the form of the transparent gravitational field embedding baryons and traversed by the radiation emitted and absorbed by the latter.
5. The recognition that the expansion of gravity and so of its form - space - is due to the auto-induction of gravity and the nature of its EoS, under the constraints of conservation of gravitational energy density. The expansion is non-thermal and locally isobaric, with the continuous creation of new gravitational fields in the form of spaces occurring everywhere.
6. A unitary explanation of the cosmic phenomena separately attributed to dark energy and dark matter as being due to the actions of the auto-induced expanding gravitational field on embedded baryonic matter and radiation.
7. The recognition that ‘dark matter haloes’ essentially are regions of curvilinear gravity (of its field components and energetic fluxes) and curvilinear space-time - in the vicinities of baryonic matter fields - with the curvilinear geodesics of orbits and lensing.
8. The demonstration that:
9. The scale factor - independently of the particular qualities of material bodies and radiation, as well as of the curvilinearity of the gravitational field, and so of time and location, thereby being cosmic - is given by\(a(t)=e^{cHt}\).
10. The recognition that the vast empty regions of flat space-time are not those of vanishing fields of gravity, but of the field’s maximal gravitational intensity - pressure and energy density – and are, thereby, non-Minkowskian. 
11. The recognition of the historical nature, and the development here, of certain laws of nature including:
12. The recognition of the prime position of gravity in the equation of cosmic mass-energy density parameters.