“The universe should expand or contract.” This is Einstein’s famous finding that was at odds with observations. And of course, it is wrong--his “greatest blunder.” So he worked into the equations the now infamous “Cosmological Constant,” to try to make the universe do neither.

“The universe” in the above context refers to any and all possible universes. The simplest universe—two particles—will expand or contract. They will either fly past each other off to infinity—expand—or fall towards each other—contract. (Orbiting counts as contraction because the pair will emit gravitational waves, and the orbit will decay). From the simplest to the most complexest of the infinite possibilities, every starting configuration will end up in one bin or the other. A coin will land heads or tails, and a universe will expand or contract.

So if GR says every starting configuration will expand or contract, how is it possible to build a model universe that is static?

Same way we stand a pencil on its pointed end. Start with a granite slab; a room with no air movement; no vibrations; no thermal gradients; throw out QM (no “random” disturbances); balance the pencil with infinite precision, and it will stand on its pointed end. Building a static universe is similar: it can be done, provided we allow some “kind of artificial” conditions. Some, as we shall see, however, are perfectly natural.

A static model can be built as long as it is:
1) Infinite
2) Homogeneous
3) Isotropic
4) Ruled by Newtonian gravity, not GR
5) Composed entirely of “dark matter”

Reviewing these requirements briefly: to be stable, the universe must be infinite in extent, otherwise it will have a “center of gravity.” If it has a C-of-G, it will be either “hot,” i.e. expanding, like the bomb going off in space; or “cold,” like the dreaded asteroid that falls back together. One or the other. The only way for it to not have a C-of-G is for it to be infinite. The only way to “keep it from falling in on itself” is to make “it” infinite.

The need for homogeneity and isotropy are related to this idea: keeping everything “balanced.”

Newtonian gravity (NG) is specified only in so far as the matter cannot emit gravitational waves. The matter’s “darkness,” the last requirement, must be absolute. If an infinite, homogenous, isotropic universe, composed entirely of dark matter obeying NG could be built, it would neither expand nor contract.

Why does it not expand? Well, it takes energy to expand, to move things apart. And there is no source of energy. There is no dark energy (obviously), nor is there any radiant energy. So it cannot expand.

Why does it not contract? This is the crux of the whole matter: It cannot contract, because in order to contract, it must lose energy. The grid is infinite, and for it to contract, it must lose energy. And the particles cannot lose energy by radiation, because as we have already said, they are dark. This last point is subtle, and is entirely missing from the main stream accounting.

1) No gravitational system can contract without losing energy.
2) No gravitational system can contract without losing angular momentum.

The earth does not fall into the sun, because it cannot radiate away gravitational energy/angular momentum very efficiently. The sun does not fall into the black hole in the center of the galaxy, likewise. Dusty clouds of gas, on the other hand, can radiate away energy relatively efficiently, and in “only” a hundred millions years radiate away enough energy to collapse to the point of thermonuclear ignition. Only those systems which can radiate away energy and angular momentum can contract.

A meteoroid can pin-ball its way through the solar system for billions of years, but it never really “falls” until one day it skims earth’s atmosphere, lighting up the night sky for a moment. And in that glorious moment of lighting up the sky, it radiates away enough energy “to fall.” Ultimately, all its starting energy (wrt earth) is radiated away as heat or light. But until it finds a way to lose energy (running into earth will do), it never “falls.” If a system cannot lose gravitational energy and angular momentum, it cannot contract.

But dark matter has no way to lose energy…by definition. Therefore, nothing ever happens in this model. The dark matter—whatever it is composed of—can be moving this way and that. It can have any temperature; can have elastic collisions, like molecules in the air. Air is “dark” in the casual-sense, i.e. neither absorbs nor emits visible light. If the air you are breathing extended to infinity in all directions--same temperature, pressure and composition--and it was dark in the strictest sense, and there was nothing else in the universe, it would just sit there. It would not expand. It would not contract. Nothing would happen.

There. We did it. We built a model universe that neither expands nor contracts. We had to meet the requirements listed above, but we did it.

The top panel of Figure 1 shows such a model, only one cube of which is shown. (Suggestion: print it.) It represents infinity by picturing one cube of an infinite number, repeating in all directions without end (post # 24). The dark matter is represented by black dots (tee-he). The outline of the cube is a “tracer” to keep track of things. The model just sits there. Whatever its temperature, pressure, composition and density, as long as these are the same everywhere, it just sits there. Forever. The true Steady State model: the rate-of-change is 0.0.

The bottom panel of Figure 1 shows what happens when you add radiant matter and GR back into the model: it contracts and expands. [Have to switch gears here: now the black dots represent radiant matter; the dark matter is still there—it just cannot be seen...because its dark!] Because “there is light,” matter can radiate away energy. It may start out homogenous, but over time it grows clumpier and clumpier.

Exactly.

The particles in the bottom panel are in a lower energy state than at the start. They have slid “down hill.” Having contracted under their own mutual gravitation, they have radiated away gravitational energy. But where has this energy gone? You might answer: The energy has been radiated into space. Which is true…literally. Remember, every cube off to infinity is also radiating away energy as the matter within it clumps. So there is energy coming and going, from everywhere, to everywhere. When you balance the books, the total energy entering and leaving each cube is the same. The total energy never changes. So as “local” particles lose energy by falling into clumps, the distant clumps gain energy by moving apart. Expansion is a reaction to contraction.

If space cannot expand, then the energy has nowhere to go. This is the paradox Newton puzzled over. Like Einstein, Newton assumed the universe was static, and in his imagination, he built a model like the top panel of Figure 1…infinite in extent. Then he imagined that it would “fracture” into innumerable clumps, such as the stars we see populating the heavens. In order for matter to go from a distributed state to a compact one, it must lose energy, as pointed out above. But where would the energy go? Newton could not imagine. He knew the universe would have to be infinite to keep from falling in on itself, but he also knew that if the universe was infinite, there would be energy coming from everywhere, and going everywhere, in equal proportion, so there could be no net change.

Einstein resolved the paradox by allowing space itself to bend and stretch.

The total energy content of the universe in Figure 1 does not change as it evolves from homogenous to clumpy (top to bottom). What changes is how the energy is distributed. Locally, matter loses energy as it falls downhill into the clumps. Relative to other clumps, however, matter gains energy, going up-hill. The net change is zero. Energy is conserved. Conservation of energy is what “causes” expansion in General Relativity. This has been overlooked again and again to the point of nausea. The talk.origins paper mentions that, “the universe should expand or contract,” but not why any particular universe, say ours, should expand. Do not even bother checking other sources, because no other source mentions the "why" part, either. The "why" part is here. The reason our universe expands is Conservation of Energy. The more bizarre tenets of the theory—that space itself can bend and stretch—are what allow it, but the more mundane principle of energy conservation is what drives it. Space expands in GR in such a way that the total energy content of the universe is constant.

And this is why the expansion is perfectly flat. Like a balloon, which expands in exact proportion to the volume of helium being pumped into it, the universe expands at a rate proportional to the radiant energy driving it.

The earth-moon system makes a perfect analogy. If the earth were not spinning (earth & moon tidally locked, like Pluto & Charon), it would not expand. The spinning earth is the source of energy driving the expansion. The earth-moon system does not expand so fast that the moon will fly off to infinity (“open” in BBT parlance), nor is it expanding so slowly that it will fall back to earth (“closed”). Its expansion is “flat,” perfectly poised betwixt the two. The reason it is “flat” is that it expands at the rate it is being driven. Like the static model above, which neither expands nor contracts (with neither a source of energy nor a means to lose energy), if the earth were not spinning, the earth-moon system would be “static,” or in a “Steady-State.” But it is the earth’s rotation that supplies energy, causing the system to expand at 100 ppt/yr.

Likewise, if there were no radiant energy in the universe, it would not expand, like the static model above. And in analogy with the earth-moon system, the expansion is “perfectly flat,” because it is expanding at the rate it is being driven. “Conservation of helium” is what makes a balloon expands at the rate helium is pumped into it. Conservation of Energy is what makes the universe expand at the observed rate of 73 ppt/yr.