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Is there any laboratory demonstration or theoretical model for the proposition that a fundamental attribute of the “fabric of space” is its ability to expand forever just because it got a single expansionary “kick in the pants” from inflation? In other words, why didn’t space stop expanding the instant the cosmic foot came off of the inflaton accelerator?

I’ll use the term “original expansion” to refer to the expansion after inflation ended, and excluding the expansionary contribution of the cosmological constant. As I understand it, mainstream cosmology (e.g., the estimable Prof. Peebles) describes the ongoing original expansion as being the result of space possessing a “kinetic energy of expansion”. In a flat universe (which is what we observe), this kinetic energy must forever exceed the mass/energy of the total matter and radiation contents of the universe. This kinetic energy is “momentum-like”, in that it is not depleted by expanding per se, but only by the drag of gravity tugging against its expansion over time (converting the kinetic energy to potential energy). This mainstream kinetic energy assumption gives rise to several problems. I would appreciate if anyone can explain why these concerns are misconceived, or direct me to literature where these issues are discussed in detail.

1. Why doesn’t the kinetic energy of expansion gravitate? Adding this kinetic energy to the right side of the Friedmann equation would result in a substantially different expansion rate calculation. It is widely held that in general, kinetic energy (heat, pressure stress, electromagnetic energy) gravitates. Kinetic energy of momentum is something of a question mark, because the relativistic mass of momentum depends on the reference frame of the observer. Although as I suggest that expansion energy is “momentum-like”, nothing is actually moving, and the expansion itself looks identical from every frame of reference available to us. (We don’t have the luxury of standing outside the universe looking in). Of course, the cosmological constant clearly is held to gravitate, and so has earned its own home in the right side of the Friedmann equation. I don’t see any impediment to assuming that kinetic energy of expansion has mass/energy and gravitates, and therefore also ought to be accounted for separately in the Friedmann equation.

2. Why doesn’t the expansionary contribution of the cosmological constant have momentum-like characteristics? If space retains the expansionary momentum-like velocity imparted to it by inflation, then one would expect the expansion resulting from the cosmological constant to retain a momentum-like contribution as well. The cosmological constant is considered to impart ongoing expansion energy to space by means of its constant negative pressure (dark energy). This is like an ion engine that provides an ongoing (but small) thrust to continue accelerating a rocket in deep space. The rocket’s velocity at every second builds on the velocity retained from the prior second.

However, the cosmological constant causes space to expand at exactly the escape velocity of its own mass/energy at each instant in time. If space retained that momentum from instant to instant, then in each subsequent instant the total expansion velocity should “build” upon the retained velocity of the prior instant, and so on faster and faster. The cosmological constant does cause the expansion rate to increase over time, but only because the expansion of space generates more cosmological constant, not because of any retained momentum. It is difficult to rationalize why the velocity vector of the cosmological constant is additive to the velocity of expansion at each instant in time, but is not added to the retained momentum-like vector.

3. If the expansion of the universe is thought of as being analogous to an expanding sphere, then ΔVolume / ΔTime (cubic meters/second) seems to me to be the most representative measure of a momentum-like expansion vector. Since volume expansion is proportional to r^3, it’s not terribly surprising to calculate that, at the standard ΔRadius / ΔTime Hubble expansion rate (converted to an absolute meters/second scale), ΔVolume / ΔTime would steadily increase over the Hubble Time, if the cosmological constant is omitted entirely from the Friedmann equation. I don’t see how the original expansion can be considered momentum-like when the expansion vector increases over time.

By comparison, it is easy to demonstrate that the expansion rate caused by the cosmological constant alone, divided by the total volume of the total universe, is constant over time. That rate is 5.80E-18 cubic meters of expansion / second / cubic meter of volume. Note that while the momentum-like vector of the original expansion becomes “diluted” over time as it is spread over an ever-larger volume, that is not true of the expansionary contribution of the cosmological constant. Additional cosmological constant is added to the equation with every passing instant, which exactly offsets the volumetric dilution. So it is all the more surprising that even the "diluted" momentum-like vector of the original expansion increases over time while that of any arbitrarily fixed quantity of cosmological constant does not.

4. As I suggested previously in this forum, the idea that the original expansion retains “momentum-like” kinetic energy seems to require that each of an almost infinite quanta of vacuum retains its own separate kinetic energy level "account balance" that can range anywhere from near the original post-inflation energy, to far below zero. The more intense and prolonged exposure to gravitation an individual quantum of space has experienced, the less kinetic energy it currently retains. There is no reason to imagine that this kinetic energy does not go negative in local regions, signifying a local contraction of space under the influence of strong gravity. (Is kinetic energy allowed to go negative?) This variation in local energy levels seems mandatory, if for no other reason than the event horizons which prevent any causal connection or normalization of kinetic energy across distant regions of the universe.

I recognize that there are many questions in cosmology which don’t currently have definite answers. However, my impression is that the major missing links underlying mainstream cosmology theory get a lot of attention. This expansion problem doesn’t seem to have gotten attention.

Jon

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# Is the Friedmann expansion the ultimate 'free lunch'?

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