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Einstein-deSitter Expansion Questions v.2

  1. Sep 24, 2007 #1
    [NOTE: I did a substantial re-edit on v.2 on 9/25 AM]

    Hi, I'm restarting this discussion as a new thread. I want to sharpen the focus.

    According to current accepted theory, during the period after inflation ended and before the cosmological constant became dominant at about 9.45Gy, the universe acted as an Einstein-deSitter universe. Supposedly, the accumulated "momentum of expansion" left over from inflation continued to drive expansion, while the gravity of radiation, and later matter, acted to slow down the expansion. Shortly after inflation ended, at 3.4e-32 seconds, the universe had a radius of about 3 meters, a mass of about 3.8e+76 kilograms, and an enormous radial expansion rate on the order of e+33 meters/second (equal to the peak rate of inflation). Due to the decelerating effect of gravity, this radial expansion rate continues to slow down (at present, 13.7Gy, it is 9.85e+8 m/s), but not all the way to zero; at some future time, the expansive force added by the cosmological constant will cause the radial expansion rate to speed up again (by 141 Gy, it will be e+11 m/s).

    I have some questions about this theory that space possesses a "momentum of expansion." I will refer to this momentum as if it were a built-in scalar field of the vacuum, and I will call it the vacuum's "Moment of Inertial Expansion." Questions:

    1. Does it act like normal momentum? In other words, is it reasonable to assume that the Moment of Inertial Expansion requires an external force to accelerate it (e.g., inflatons and cosmological constant), and an external force to decelerate it (gravity)? Will it continue expanding forever in the absence of enough gravity to drain its momentum to zero? Is it correct that the Moment of Inertial Expansion has no energy content of its own? (except that expansion momentum can be considered a pseudo-form of kinetic energy. I say "pseudo-" because there is nothing actually moving, and because the expansion is volumetric, not linear.)

    2. Can vacuum have momentum if it doesn't have mass/energy? Recall that Momentum = velocity*mass. (Arguably vacuum does have mass/energy equal to the cosmological constant).

    3. Does each quantum of vacuum have its own Moment of Inertial Expansion, which is independent of that of every other quantum of space? That makes sense. After all, even our observable universe has event horizons, which prevent the distant vacuum in one direction from Earth from having any causal connection with the distant vacuum in the opposite direction.

    4. Can the Moment of Inertial Expansion go negative as well as positive? Presumably it can, as a negative value means that the vacuum is contracting.

    5. If a particular quantum of vacuum is subjected to gravity for a period of time (from a nearby mass), will that vacuum's Moment of Inertial Expansion remain reduced after the mass is removed? Presumably it will, since it operates like a battery, not a generator.

    6. If two quanta of vacuum possessing different Moments of Inertial Expansion are adjacent to each other, will the momentum average out between them, or not? In other words, is it transferable?

    7. Is there any means, even theoretical, to directly measure the Moment of Inertial Expansion of a particular quantum of vacuum?

    8. If some "clouds" of vacuum are expanding at various rates, while others are static or contracting, will photons passing through these differentially-expanding vacuaa experience angular deflection or red/blue shift?

    9. Do expanding clouds of vacuum cause regions of vacuum to have a positive pressure? (And do contracting clouds cause negative pressure?) (If this were actually true, could the net positive pressure of the vacuum be the mass/energy that is the source of the cosmological constant? Just asking!)

    10. Does the Moment of Inertial Expansion possess a separate scalar field, or is it the same scalar field as the inflaton and/or graviton? Does it have its own mediating particle? (which I'll call the "elasticon")

    OK, enough questions for one posting!

    Let's briefly consider the cosmological constant. Pursuant to the momentum of expansion theory, it should be considered to imbue the vacuum with built-in momentum, not ongoing energy production. It is helpful to imagine spacial expansion as being like the reproductive growth of a microbe colony -- existing quanta of vacuum beget additional quanta of vacuum, and so on. (As opposed to imagining that there is a single quantum of space which started out at Planck scale and has now stretched monstrously to the size of the universe, without losing its singular identity). Thus each "new" quantum of space is "born" with a tiny Moment of Inertial Expansion, which it is free to lose over time, at its own individual rate, based on how intimately it associates with nearby gravitational mass/energy. If we look at it this way, no individual quantum of space can ever gain momentum, it can only retain or lose its "virgin" momentum.

    If we calculate the observable universe's expansionary momentum at any point in time as being the volumetric rate of expansion divided by the volume (seems as good a formula as any), then we find that expansionary momentum indeed is draining away over time. Expansionary momentum was 4.4e+99 cubic meters/second/cubic meter at 3.6e-32 seconds. By 3.6 seconds it dropped to 3e+3. By 28,000 years, it dropped to 9.2e-13. During most of the Einstein-deSitter period, it was in the range of e-17 and slowly dropping. Presently it is at 6.8e-18. In the future at 141Gy, it will fall slightly further to 5.8e-18.

    It is striking how similar the increase in momentum of the cosmological constant is to that ascribed to inflation. Consider a scenario where the universe first pops into existence as a single quantum of vacuum, with no matter or radiation. Due to its "birthright" Moment of Inertial Expansion, that vacuum reproduces at a geometric rate, just like inflation describes. The only difference is that more time is required (perhaps on the order of a few seconds?) for expansion to reach the peak velocity of e+33 meters/second. If radiation and matter appear at that point in time, then expansion will continue subsequently, arguably exactly as we have observed. Could this be developed as an alternative explanation for inflation? Well, for one thing, a different quantum mechanism would be needed to explain why the expansion "reheated" at its peak velocity and released matter and radiation into the universe.

    Now, for completeness I must mention geometric flatness. The present universe appears to be nearly flat, and current cosmological theory requires that the universe was even more nearly (but not perfectly) flat at the end of inflation. It is extremely important to understand that the definition of flatness simply refers to the equilibrium point where the expansion rate equals the "escape velocity" of the universe's total mass/energy content. If there is any discrepency between those two, then the universe is not perfectly flat. Escape velocity in this context means that if the amount of mass/energy remains constant (a condition which by the way never has and never will occur due to the constantly changing total momentum) then the expansion rate will continue to slow, but never quite reach zero.

    It is intriguing that, in a (nearly) flat universe like ours, expansionary momentum and gravitation are inextricably intertwined, in the sense that the two must always be equal. To achieve that result, current cosmological theory must jump through some hoops. First, space must acquire its enormous initial expansionary momentum by means of the theoretical inflaton starting its "slow roll" down a potential energy "slope" that has a precisely tuned shape. Then these friendly inflatons must self-destruct and release all of the radiation and matter of the universe precisely when the expansion rate equals the escape velocity of this mass/energy. This is described in the literature as "the critical point when the potential energy of the inflaton field drops below its kinetic energy"). Then, as time moves forward, the vacuum must separately possess a cosmological constant, which is now usually referred to as "dark energy". The nature of this dark energy is unknown, but it is believed to possess negative pressure, causing a sort of anti-gravity effect.

    Since the universe apparently is (nearly) flat, one can use the equivalence of mass/energy's escape velocity to the expansion rate as a handy and perfectly accurate shortcut for performing cosmological calculations. Escape velocity is easy to calculate, and it has the handy attribute of being additive no matter how many subunits we may choose to divide the universe into (such as atoms).

    This equivalence demands that we ask the next question -- is it theoretically possible that expansion is CAUSED by gravitation, rather than by an accumulated momentum of expansion?

    I call this idea "gravitational expansion." It would simply require that the stress-energy tensor of mass/energy's gravity both curve space, and simultaneously cause that space to expand at the escape velocity of the mass/energy. In order for gravitational expansion to retain equivalency, space cannot have an inherent propensity to expand, and cannot store up expansionary momentum. At every instant in time, expansion must rely on the presence of nearby gravity in order to continue expanding. Note that gravitational expansion provides a logical explanation for the cosmological constant -- space expands simply because it possesses mass/energy that self-gravitates. No need for dark energy or other exotic theories. And gravitational expansion might possibly also be adaptable to explain inflation, in the manner I outlined above.

    Because both metrics produce identical mathematical results, I think it will be difficult to detect which one is the better description of reality. I can think of three things that might distinguish the two approaches:

    1. The expansionary momentum theory requires that space presently be nearly flat, but not precisely flat. In fact it must be quite a bit less flat than it was at the end of inflation. On the other hand, gravitational expansion by definition requires that space always be perfectly flat. No deviation, no matter how tiny, is ever permitted. If we can ever measure flatness to sufficient accuracy, perhaps we can discern if one of the approaches can be ruled out.

    2. As pointed out earlier, quanta of vacuum should be permanently drained of their Momentum of Expansion if they have spent enough time in close proximity to strongly gravitating masses. This means that the more that galaxies, etc. experience peculiar movement (meaning their movement through space relative to each other and the CMB), the more the total momentum of space will be reduced, because each galaxy will "power down" more and more "virgin" vacuum as it passes through. Perhaps this effect could be estimated, and someday measured to detect if total expansionary momentum is in fact lower than it would be if there were no peculiar movement. [On further thought, I'm not sure this idea is fruitful. Even if a mass remains stationary forever, it will cause the Moment of Inertial Expansion of local space to go increasingly negative. This means that the local space will contract, and in effect be replaced by nearby "virgin" vacuum, which in turn will be "powered down", and so forth indefinitely. So the total effect on the expansion rate probably is identical regardless of the amount of peculiar motion]

    3. Perhaps observations of supermassive black holes could detect whether the nearby space appears to be contracting (expansionary momentum) or expanding (gravitational expansion). I'm not sure how to discern the one from the other, however.

    Any other ideas on how we can test the currently accepted theory of expansionary momentum?

    Last edited: Sep 25, 2007
  2. jcsd
  3. Sep 26, 2007 #2

    I need to delete the paragraph that suggests that the cosmological constant could provide an alternative to the standard theory of inflation. The expansion rate would be much, much slower than I had guessed. So I have to go calculate that.

    Also, in my post I suggested (change in volume)/(volume) as the best metric to measure the total Moment of Inertial Expansion. On further thought, I realize that this metric actually measures the average Moment of Inertial Expansion per unit of volume. It is an interesting metric in the sense that it demonstrates that new units of vacuum are "born" with a cosmological constant that even today is lower than the average residual momentum left over from inflation. Thus, the average momentum naturally drops as the intense initial inflationary momentum gets diluted by the increasing volume of space.

    The volume expansion rate caused by the cosmological constant is 5.8e-18 cubic meters/second/cubic meter of volume. So, a more interesting momentum metric is to multiply that rate by the volume, and subtract the product from the absolute volume expansion rate/second, at any point in time. This metric is the ABSOLUTE amount of momentum left over from inflation at any given time, as a standalone value, and without any diluting effect from the increase in total volume or the cosmological constant.

    Clearly, this leftover absolute momentum should decrease substantially over time as it is drained away by the accumulated deceleration caused by gravity. But this does not appear to be the case! My spreadsheet says that this leftover momentum is at 5.7e+53 at 3.6 seconds, increasing to 9.4e+57 at 28,000 years, increasing further to 3.4e+62 at present, and increasing slowly in the future, e.g. to 3.7e+62 at 141 Gy. Unless I find a math error or other explanation, I think this calculation raises a valid question as to whether the momentum of expansion theory can be correct. Momentum doesn't increase by itself! (Remember, I've already subtracted the additional "new" momentum added by the cosmological constant).

    Last edited: Sep 26, 2007
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