A Suggested Model for Dark Energy

The following is an analogical approach to explaining Dark Energy, with two suggested formalizations.

Dark Energy, or the mystery force causing the accelerated expansion of the universe, is one of the prime mysteries of modern physics. The approach I suggest here, which I believe to be novel, is essentially to model spacetime as imperfectly compressible (contrary to the standard implicit assumption of perfect compressibility) and identify Dark Energy as the corresponding and proportional ‘pushback’ connected with gravity’s compression of spacetime.

To approach this explanation via analogy– if we take spacetime to be like the surface of a balloon upon which we live, the gravitational compression from aggregated clumps of matter (stars, galaxies, black holes, etc) are like fingers pushing into the balloon. Matter compresses spacetime. It’s natural for the balloon to bulge where it’s not being compressed. Furthermore, though its volume stays ~constant[1] as we squeeze it, the balloon (like the universe) appears to expand: its total surface area increases in relation to how unevenly compression is applied.

To help quantify what this means, my prediction is that we should expect a special-case universe composed of 0% energy, 100% homogeneously distributed matter to neither contract nor expand[2] (contrary to the standard theory of contraction due to gravity), much like how a balloon filled with incompressible liquid pushed equally from all sides would stay roughly in equilibrium. Once matter starts to ‘clump up’, however (and it invariably would due to quantum effects), the surface area of the universe would start to expand, just like the surface area of a balloon increases if we squeeze only one side of it (or poke narrow fingers into it– e.g., stars and black holes).

Timeline and predictions:

The timeline of massive expansions due to Dark Energy seems to correlate with what we can guess about major thresholds in the de-homogenization of matter distribution. We would expect a massive initial de-homogenization right after the Big Bang due to quantum effects, then another when particles are able to form, another when large-scale matter structures are able to form, and another as matter organizes into very large scale structures such as galaxies, clusters, and superclusters. As we improve both our models of matter formation and aggregation in the early universe, and our empirical measurements of the changing contribution of Dark Energy, I anticipate these timelines to increasingly correlate.

Looking forward, Dark Energy will contribute to expansion until gravitational entropy is exhausted (e.g., matter stops getting further clumped together), which is to say for an extremely long but finite amount of time. At this point the analogy would be that our fingers have stopped pushing deeper into the balloon, and so its surface area has stopped expanding.

An alternate, particle approximation of this would be roughly as follows: within any specific range of times, the amount of Dark Energy should be equal to:

Gr(a)*S(a) – Gr(h)*S(h), where

Gr(a) is the actual number of gravitational carrier particles (gravitons) exchanged in the universe;

Gr(h) is the hypothetical number of gravitons which would be exchanged in a universe of the current size if matter and energy were distributed homogeneously (necessarily equal to or lesser than Gr(a));

S(a) is the scaling factor of how much the average graviton bends spacetime in the current universe;

S(h) is the scaling factor of how much the average graviton would bend spacetime in a hypothetical universe of the current size but where matter and energy were homogeneously distributed– presumably differing from S(a) due to differences in average graviton longevity.

Discussion:

- The particle approximation involves many ambiguities and really dodges the issue of *why* this would occur. Also, generally speaking, we don’t know enough about the mechanics of gravitons (still purely hypothetical) to speak with much confidence on the difference between S(a) and S(h), and it’s unclear how this force would make itself felt. A new carrier particle? A non-localizable property of spacetime? A MOND-like modification of gravity? An emergent property of entropy? I include the particle approximation as an alternate, semi-quantitative description, not a proper explanation.

- There are many metaphysical questions raised by the geometric formulation of this model. In the above balloon analogy, the liquid inside the balloon is incompressible and thus creates the pushback. What, precisely, would be surrounding or enclosed by spacetime such as to create the pushback? Or is it something inherent to the ‘fabric’ of spacetime?

[1] There are really three options here- that spacetime is perfectly compressible, imperfectly compressible, or perfectly incompressible. My theory merely requires that it is not perfectly compressible.

[2] This statement would not be exactly correct, as it would depend upon the formalization used. In the geometric formalization, even a universe with homogeneously distributed matter would have a small dark energy component, because only a universe with homogeneously distributed compression would not. But if matter was truly distributed homogeneously this component would presumably be very small and would not be a dehomogenizing force.

I’ll admit the formalizations are rough. But I think the core approach elegantly arises from one assumption, is relatively clear and intuitive, and in principle is quite testable.

Edit, 8-21-10: A recent survey of multiple data sets has better quantified the magnitude of what we’re calling Dark Energy. Via Ars, “The end result: at a 99 percent confidence, the matter density is between 0.23 and 0.33, while the cosmological constant is between -1.12 and -0.82.“

(Original paper)

Visual aids:

Timeline of the universe's expansion (credit: NASA)

"In this artist's conception, dark energy is represented by the purple grid above, and gravity by the green grid below." (credit: NASA)