1.0 Discussion of similar ideas regarding Dark Matter and Λ
Hardly an original idea, theories incorporating a negative pressure as a major contributor to the rotation curve of galaxies replacing Dark Matter[1] still postulate a constant and invariant Λ, even when accounting for scale or radius of measurement as a possible factor[2]. A large Λ is postulated in many cases to account for the vacuum energy theorized in quantum mechanics, or as a mechanism in universal expansion and acceleration. A small Λ in other cases is theorized that would have negligible effect in the scale below Kpc, making it difficult to isolate and test local results of the presence of Dark Energy, or to design laboratory scale tests.

Axinides et al[2] infer similarly that scale seems to be a factor if Λ is to be invoked as a contributor to the flat rotational curve of galactic motion, and cluster motion as well, however they instead opt to the side of increased mass over what is predicted from galactic rotation velocities measured for the Milky Way and M31 by 35%, assuming that gr (their term for the repulsive vacuum factor in modifying Newtonian gravitational equations ) is invariant over any property but radius r, and therefore across the radius of a galaxy repulsion would instead serve to fling galaxies apart. Radius of the galaxy, or the distance from center of mass to edge, is important in MoND (Modified Newtonian Dynamics) [3] to explain flat rotational velocities in galaxies. While some correlation of this theory have borne out, other studies of high-surface-brightness ellipticals appear to diverge, maintaining a Keplerian distribution of rotational velocities out to distances further than those predicted by MoND. A variant quantity - locally variable vacuum energy or "quintessence" is posited in other scenarios as the generative force of negative pressure, and also evaluated in terms of coupling to space-time, but eventually tied to long period variations in the gravitational constant, varying across time.[5]

A similar idea for simple modification of the laws of gravitation is proposed by Carroll, Duvvuri, Trodden and Turner ( "Is Cosmic Speed-Up Due to New Gravitational Physics?", 2004 )[4], however it too, while providing a self-accelerating solution and a possible mechanism for inflation does not account for Dark Matter and does not allow for local-space variable values for a "tuned" gravity varying over time. Carroll et al almost approach as close as Moffat, J W in his paper "Modified Gravitational Theory as an Alternative to Dark Energy and Dark Matter"(2004)[13], which, with a replacement for Dark Energy, Dark Matter and Inflation very closely resembles in field equations the general approach of this paper. It is unfortunate that the author of this article cannot grasp Moffat's paper and its implications fully enough to determine what predictions it makes.

1.1 Outline and description of λ, the locally variable negative pressure force.
The primary difference between the theory presented in this paper and many of the cited articles with regard to Λ is one of local variance not in time, and not tied to absolute distances, and no assumption that Λ measured locally is the same as Λ elsewhere except in behavior. This might seem like a violation of the assumptions of the Cosmological Principle and requirements for uniformity in all directions imposed by the Cosmic Microwave Background. Negative gravitation as postulated in this paper is far from being uniform and invariable; it is instead a Casimir-like matter-density dependant force that behaves like an "inverse" gas in terms of pressure increasing with expansion. Therefore, the term λ will be used for locally variable antigravity/negative pressure to distinguish it from Λ or the Cosmological Constant, as while it symbolizes negative gravity λ as referred to in this paper is anything but constant.

With a locally variable λ, it is important to establish under what criteria it can vary, and what essentially the consequences are as λ → ∞ and λ → 0. First, the supposition that λ varies with matter density. As density increases, the average domain size for the vacuum decreases, and it is any difference in mean domain size that gives rise to the λ value for a local measurement. If a mass is between two domains of different volume it will experience a force proportional to the ratio of domain volume, provided domain size has exceeded the parity value or hypothetical ρequilibrium below which λ does not cause expansion and decrease of ρ. The upshot of this is that any Δρ will result in Δλ as the difference in starting or ending ρ over time, or adjacent regions of different ρ will each result in a Δλ proportional to the change.

2.0 Dark Matter vs. locally variable λ to explain galactic rotational velocity curves.
Ideally, below this density and in regions of varying density, an anti-gravitational force should be observed. If this force is used in the place of Dark Matter, it would "push" in the direction going from regions of lower density to regions of higher density, as more λ would exist in areas of higher mean domain size/low density (ρ). No force/negative pressure, however, would be apparent in either regions that exceeded ρequilibrium, or within regions where ρ is uniform. Peculiarly, measurements of galactic rotational velocities appear to show a "hole" in the Dark Matter towards galactic center as galaxy size (and core density) increase, to the point that some supermassive elliptical galaxies appear to contain little Dark Matter at all.

"However, other considerations point in a different direction. For instance, maximum disk solutions formally require hollow halos in most galaxies. (The disk is providing all the observed rotation velocity near the galactic center, so the halo has zero mass in its inner regions.) This is clearly unphysical and more realistic models require that the disk in many galaxies has a mass somewhat below the value derived from the maximum disk hypothesis."
Ashman, Keith M., Dark Matter in Galaxies, Publications of the Astronomical Society of the Pacific (1992)[9]

Ongoing results and surveys from later data still appear to support this "hollow" profile for mid-size spirals to large ellipticals apparently rather devoid of Dark Matter. This is at variance with models that rely upon scale, as scale does not account for the apparent drop to zero Dark Matter contribution to galactic rotational velocity near the core and well before it in some cases, while still allowing for Dark Matter contribution at or near the core for dwarf irregular galaxies.[10]. Additionally, supporting the top-down evolution of structure are recent reportings of early development of galaxies, and the "dark" galaxy recently reported, with no stars.

2.1 Extension of λ → ∞ and a new Inflationary model.
For the opposite scenario, where λ → ∞, we'll start with λ > ρequilibrium, where the negative pressure of λ from this minimum domain size necessary to induce expansion in space-time starts to expand due to negative pressure. As the domain starts to expand, it is capable of generating a greater λ or negative pressure versus other regions - and the beginnings of a feedback loop are evident. However, due to the dependance upon mean domain size, expansion is not uniform over smaller scales, and could probably be localized as primarily within the open large scale structure rather than along the implied lines of the Lyman-α outlined structure. This inhomogeneity serves to limit the expansion rate to an extent, but the implications are that without any matter or energy to put constraints upon domain size, a domain would expand to infinity at an ever increasing rate, and we've already answered our question with regard to λ → ∞: domain size → infinity. This scenario, while reminiscent of the "big rip" Dark Energy future, is also reminiscent of the inflationary epoch. With λ → ∞ in the beginnings of the universe, the energies required to generate matter quickly inflate not from a singularity, but from "nothing": a vacuum if you will. The energy and scale of the universe are consequences of the inflationary epoch; similarly, the phase-change that ended the inflationary epoch is postulated to be the sudden emergence of standard energy and matter at a critical λ: the mean domain size is reduced suddenly and drastically, resulting in the currently "slowly" expanding universe. A possible mechansim might be a critical expansion rate at which virtual quark-antiquark and gluon pairs cannot re-combine before they are torn apart with a color tube and trails of quarks and particle jets generated by this action, resulting in matter/antimatter, energy and slowdown of the expansion, similar in mechanism to Hawking's explanation of evaporation in black holes, but ubiquitous and near simultaneous across the entire universe.

The "heating up" of the universe after the inflationary epoch is resolved as instead the initial appearance of matter, the sudden change in the rate of expansion and the cause of inflation are presumed in this model to all be the result of the vacuum and its behavior; the current situation is not sudden or contrived, tuned or anthropocentric, but the logical evolution of a vacuum-dominated universe expanding over time. No extra dimensions, branes, inflaton fields, false vacuums, tachyons, or decaying coupled scalars are required; just an extremely rapid expansion and virtual particle pairs. This is where the "Big Flash" term of the model comes in, as the previous lonely universe expanding to infinity would suddenly flash over, resulting in a new universe full of matter and antimatter.

2.2 Large scale structure and evolution of galaxies and stars.
What of the epoch following inflation? What would be the effect of no Dark Matter and λ variant by density/adjacent mean domain size in this early nearly uniform universe? Similarly to the density-dependant negative pressure pushing nearly uniformly at the outer bounds of galaxies, the λ would have served to clear out areas of low density; both creating and growing quickly areas of high density, negating the need for a Λ to be of an arbitrarily low value during the age of galaxy formation. Reverse hierarchial development would have been the norm, with the large scale structures forming first, then galactic aggregations, then stars. The earliest universe would have resembled a foam of void and atoms. No superstrings or Dark Matter are required in this scenario, which avoids the slow formation of the Hot Dark Matter model and the hundreds of dark dwarf galaxies of the Cold Dark Matter model[6], [7],[8]. The initial structure came from the first moments of the vacuum in its expansion phase as initial fluctuations expanded before critical λ. From these original disparities grew the large scale structure, then galaxies, then the first population of stars.

2.3 Prediction for the universe as acceleration due to hypothetical λ increases with domain size.
The future of this model appears to be a variation on the "Big Rip" - but with a peculiar twist. λ exists at ρ higher than equilibrium, but no longer has enough energy in these smaller domains to bend space-time as in gravitational wells, and hence not enough energy to therefore cause expansion. The future of this universe is island galaxies eventually lost over the horizon of accelerating expansion faster than light until λ in these superdomains reaches the critical energy to cause effectively a new inflationary epoch, and "Big Flash." Whether or not the remnants of the old universe will actually "see" any of the new epoch is uncertain, and equally uncertain is whether island galaxies from previous inflationary epochs would be detectable in the current universe; it is unlikely given the presumed superluminal expansion of the horizon, however some fossil elements from the previous epoch might have served to seed the current universe both with empty spaces and with more matter than antimatter.

3.0 Extension and speculation on other effects of this model of vacuum domain dependant λ.
Still other implications and suppositions are problematic and pending examination in this body of theorem. In presuming this density-dependant λ, we have still not addressed moving bodies or rotating bodies on scales smaller than the Lyman-α or galactic. Take a moving body of mass m travelling at velocity v in this new model of vacuum. The mass can be resolved to a higher ρ section of space time: one with smaller domains than its surroundings, which are assumed to not be a perfect hard vacuum but a much lower ρ section of space-time/vacuum: one with larger domains. As the mass moves, it essentially causes a Δρ in the direction of movement and away from the direction of movement, requiring energy to overcome the λ that results pushing against the forward progress, at the same time "gaining" energy from the &lambda that results away from the direction of movement. These amounts should be equal; however, to change velocity v will require energy, as the mass is currently in a feedback loop of Δλ due to Δρ, resembling inertia. Despite a thorough search, I was unfortunately unable to come across a non-Higgs non-String non-Brane theory for mass and inertia for comparison, or a plain language description of the momentum mechanism in any of these theories.

This follows for smaller particles, but other effects exist once one reaches the quantum scale. The ideal point particle is far from the true description of atoms in the universe, and it might be expected that even the smallest change in location of an atom would alter multiple domains nearby. This in turn would generate a change in the ρ or mean domain size and cause a chain reaction in any region of space of reasonable density. Reasonably, a particle at rest or in motion might be expected to continue in that direction, except that at the quantum scale uncertainty creeps in, and the discrete motion of large numbers of particles is no longer an apt description of variable ρ traveling at velocity v. Hiccups occur as Δρ occur due to uncertainty, push at the atom, resulting in a jittering even at extremely low nanoKelvin temperatures resembling Zitterbewegung: vaccuum-matter interaction due to non-point particles being unable to settle into a "rest" state due to the peculiarities of atoms and &lamda;.

4.0 Proposals for testing these conjectures in simple empirical evaluations
If there is any merit to this λ of the vacuum, it would be possible to measure a negative pressure on a test mass suspended within and off-center in a vacuum chamber of large volume cooled to microkelvin to nanokelvin temperatures. If this theory has any merit, a force similar to a Casimir effect should be measured that results in displacement of the acceleration of gravity from no other source than the vacuum. Change in position should result in change in this effect, and control experiments conducted in similar circumstances both without the vacuum and without a test mass should verify this effect. There is some question as to whether a vacuum chamber could affect the curvature of space significantly and distinguish this effect from the Casimir effect by effectively altering the curvature of space near the test chamber while functioning. The magnitude of this effect should be rather small, and precision measurements will be required as well as control experiments to rule out local gravitational anomalies. The scale required for any functional use of an "antigravitational" effect would be prohibitive; on the order of earth itself most likely simply to produce enough negative pressure to achieve 9.8 Newtons.