So, here stands a unitary identification of the dark energy and dark matter of the cosmos as being the singular energetic gravitational field. It was obtained solely by means of an orthodox development of, arguably, the most tested and successful physics theory of all time – general relativity.
New and significant aspects in this explanation include:
1. a single metric – the radially symmetric gravitationally perturbed Robertson-Walker metric - that:
- is applicable at all scales across the universe, smoothly accommodating descriptions in domains of both small and large scale phenomena.
- at large scales, recovers an FLRW line element, the one without curvature, that large-scale observations confirm. Here, in deep space, the metric appears as that of an empty de Sitter space-time.
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 gravitational field.
5. The recognition that the expansion of gravity and 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 attributed separately 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 demonstration that:
- the Hubble parameter, previously only empirically determined at large scales, is a cosmic constant. This is confirmed through the derivation, here, of the Hubble-Lemaître law from the general conditions of gravitational expansion outlined in paragraph 5 above.
- the Hubble constant references a universal maximum magnitude, both of the gravitational pressure and of the gravitational energy density, expressed as \(H^2/2{\kappa}\).
8 . The cosmic scale factor, irrespective of all types of gravitating bodies and radiation, is \(a(t)=e^{cHt}\).
9. The recognition of the historical nature, and the development of the historical forms, of certain laws of nature including expressions for:
- the gravitational pressure and gravitational energy density.
- gravitational acceleration and the velocities of circular orbits.
- gravitational induction.
10. The recognition of the prime position of - the presently unidentified - gravitational energy in the equation of cosmic density parameters of cosmology and astrophysics.
8.0 DISCUSSION
The theoretical results obtained above strongly motivate development of techniques to advance empirical investigations to determine the linearity of the Hubble-Lemaitre at small scales < 5 Mpc \cite{Sandage_2010}This will test the proposal that the Hubble parameter is invariant.
It should be clear, in view of the account given here, that dark matter and dark energy are conceptions created to explain 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 recession of galaxies and the unexpected orbits in galaxies and in their clusters – as being two different entities operating in mutually exclusive regions. These two sets of effects are manifestations of the actions of two coinciding energetic fluxes of gravity – pressure (dark energy) and energy density (dark matter). These fluxes are equal in magnitude everywhere.
This avoids the ‘cosmic coincidence problem', confronting the ΛCDM model, of inexplicably comparable magnitudes of an increasing dark matter density and that of the constant dark energy density in this epoch \cite{Velten_2014}.
It is remarkable that the maximum, and almost average, value here predicted of the energy density of the gravitational field of H2\(\)/2\(\kappa\)≈ 1.52E-27 Kg m-3 is of the same order of magnitude as CDM's current estimate of the cosmic density of ‘dark energy’ ≈ 6.9E-27 Kg m-3.
Thereby, this explanation avoids the ‘cosmological constant problem'\cite{Weinberg_1989} confronting explanations based on particle physics of dark energy as being represented by a hypothetical cosmological constant of a uniformly constant energy density across the cosmos due to hypothetical energetic quantum fluctuations of the vacuum. The problem is that the predicted minimum energy density of physical quantum systems is of an order of magnitude 1E+122 greater than CDM estimates 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’ gradients in the vicinity of the galactic centre. In fact, as the centre is approached, the density declines, as do the predicted velocities of rotation. This decline of velocities, that challenges prominent models of dark matter, is generally empirically confirmed. \cite{de_Blok_2010}