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Do geodesics of measure zero allow past-eternal inflation?

  1. Jul 5, 2015 #1
    Assuming that the expectation that all matter and energy are quantized is correct, I'm making a further assumption that "random" means something like, "hypothetically predictable, but only by means at least possibly impractical on any permanent or general basis whatsoever, such as enumeration that would require more digits than the number of particles in our observable region".

    It's my understanding that Standard Model cosmology is compatible with some models of false-vacuum inflation, which seems to result from quantum fluctuations that give rise to an energy or substance whose pressure is negative and consequently associated with the repulsive form of gravity that has the effect of exponentially expanding the region containing those fluctuations: The inference I've made (from plain English statements in papers by major physicists) is that this expansion increases the size and duration of some of those fluctuations, and also increases the number of those occurring on their original scales of time and space. The adjective "false" in the phrase "false vacuum" is explicitly stated by Guth to mean "temporary", but its local endings (which leave the regions where they occur subsequently expanding only by inertia) populate some of the space in those regions with energy whose much more intensely local concentrations are particles, with the numerous and frequent discontinuities in their extremely local presences thereafter described as "perturbations".

    Although inflation is usually considered to continue permanently because of the exponential factor in the original expansion, one of the main things I'm wondering is why, at inexpressibly long intervals of time, it's not considered that the ENTIRE multiverse might disappear, due to some excruciatingly rare and huge fluctuation. I do understand that the contents of portions of at least some of the mid-sized local regions (the inertially expanding bubbles or "local universes"), probably including our own, are expected to change as bubbles of lower energy nucleate within them, but I've never seen the vastly rarer but equally "random" disappearance of ALL the particles mentioned as a virtual certainty, or even as a possibility.

    The only explanation for the absence of this particularly total doomsday scenario that I can envisage would be the fractal one that our multiverse might comprise a particle in a larger one, and so on ad infinitum, but I've never been able to pull a hint out of Google that this even might be the case, except in one mention by Vilenkin that some geodesics "of measure zero" may be eternal to the past, in spite of a general prohibition of such geodesics by the Borde-Guth-Vilenkin Theorem.. (That prohibition seems to result from the possibility that an observer moving directly against the expansion would otherwise be moving backward in time once he would have passed the surface of its origin, although the disappearance of everything does seem even less likely than extremely localized travel backwards in time.)
  2. jcsd
  3. Jul 5, 2015 #2
    All geodesics were initially zero and as matter formed they intertwined universally? There is no "flat" space anywhere this side of a singularity, is there?
  4. Jul 5, 2015 #3
    No, in trying to figure out what Vilenkin meant by "geodesics of measure zero", I found that he seems to be referring to "Lebesgue measure", and I was surprised to find (in the Wiikipedia article of that name) that "measure zero" can, under that system of measure, include an infinite number of geodesics, with the "zero" apparently referring to the possibility of counting them all! The most cosmologically relevant of them is the "Cantor set" (also described in a Wikipedia item), because an arrangement of mass mimicking its representation provides a resolution of "Olbers' Paradox" (about why the night sky isn't a sheet of fire if the universe is extremely large and filled with stars), which is alternatively resolved by that expansion of the universe / multiverse that was first recognized by Hubble in 1929 (and greatly elaborated by inflationary cosmologists since 1981).
    Last edited: Jul 5, 2015
  5. Jul 5, 2015 #4
    After thinking all day about why BGV would've included any allusion to the sort of static cosmology whose diagrammatic representation would resemble the "cantor set", I've decided that they wouldn't have, and concluded that the geodesics "of measure zero" in their theorem were simply those followed by the "co-moving test particles" of that theorem: That usage also seems consistent with the terminology of Lebesgue measure, and Vilenkin's use of geodesics that (per that theorem) might not exist, to prove that they might not exist, was questioned in print by Aguirre, on p.19-24 of an interesting paper on past- and future-eternal inflation. It's at

    arXiv.org > hep-th > arXiv:0712.0571.

    Sorry for the confusion; I would've edited my original post, but figured I owed it to Jerrymyjon to clarify it instead. Addressing his question more straightforwardly, Vilenkin generally considered what I was describing as the initial quantum fluctuation to have been a "quantum tunneling from nothing", and googling that phrase usually brings up some excerpts about it from his pleasant popularization, Many Worlds in One.
  6. Jul 6, 2015 #5
    Hmm, I think I see where you are at, but I get lost in the math. Negative pressure. Negative curvature? Cosmic quantum weirdness?
  7. Jul 6, 2015 #6
    I'm useless at the math, myself, and, as the mentors on this forum have occasionally mentioned to me, relying on the plain-English text that the physicists throw into their papers between the equations is a little dicey. However, the dispute between Aguirre and Vilenkin--over whether the thermodynamic arrow of time can stay reversed between different spacetime regions--seems to be centered on deSitter (dS) space, into which the false-vacuum bubble that starts the ball rolling (in Vilenkin's view) "tunnels" from an empty (FLRW) universe. (This "tunneling" isn't as akin to spatial travel as most readers of plain English might think; it's a change of state, which occurs spontaneously in a lot of stuff, apparently mostly on rather small scales, where the wave-function locating things spatially and temporally is generally larger than the things themselves.) Usually represented in diagrams as a sort of spool with sides curving inwardly toward its center (into which Vilenkin's transition of reality from FLRW space fits), dS spacetime has negative, open, and closed "foliations", yet, as Aguirre points out, its internal quality is totally uniform.

    His view of spacetime is much more appealing to me: For the reasons stated in my opening post, it has a stability that the alternative lacks. (It may be more than a little ridiculous to claim that that alternative version of the multiverse is anti-Copernican, but it does seems to me to represent an unduly "special" interlude between quantum fluctuations.)

    As Vilenkin points out in a rather vague critique of Aguirre's view (visible at arXiv:1305.3836), the boundary between its contracting and expanding regions is a three-sphere, and, as others have pointed out, their presence on either the forward or backward sides of it may be indistinguishable to its occupants (including ourselves), because neurology works thermally. I guess that is basically why time is always seen as reversible--albeit definitely not reversible "on demand"--in physics. If you accept the relationship between space and time described by Einstein, though, the overall effect is perceptible (through telescopes) in the expansion of space, which Sean Carroll figures to be an inherent characteristic of that entity, locally countered by the gravitational aspects of matter, energy, and pressure.
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