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Void expansion rate and cosmic acceleration.

  1. Apr 21, 2008 #1
    A proliferation of very large voids have been observed recently, at a scale of 250-350 Mpc. Voids are believed to have average densities about 10% of the cosmic average. Voids are conservatively believed to comprise at least 60% of the volume of the observable universe, and perhaps more than 80%.

    Voids are believed to have arisen from gravitational amplification of primordial density fluctuations, for example at the time of last scattering, as reflected by the CMB. The anisotropy of the CMB is measured to be very small, on the order of E-5.

    Therefore, in order to have attained the degree of density inhomogeneity observed today, individual voids must have been expanding at a rate in excess of the average FLRW rate, over the timescale of the expansion.

    Even in an Einstein-de Sitter universe with Lamba (cosmological constant) = 0, it seems to me that the increasing inhomogeneity over time represented by expanding voids would derail the Friedmann equation. As the matter overdensity of void shells is squeezed into a smaller and smaller fraction of the total volume, its influence over the expansion rate of void interiors must decrease as a result of the inverse-square law of gravity. (The gravity source becomes more and more distant from an ever-increasing fraction of the volume.) The equation must depart from equilibrium as the faster expanding regions become an ever larger fraction of the total volume. [For example, if all of the matter of the observable universe were condensed into a single black hole, surely the total expansion rate of the obsvable universe (at its current size) must be faster than the Friedmann equation would calculate for a homogeneous matter distribution.]

    If the matter shells of the voids had been gravitationally bound from the beginning, the void fraction would not have increased over time. I cannot picture any scenario where the void fraction could increase to the extent it has, and then subsequently experience a gravitational collapse. The historical expansion rate of voids leads me to conclude either that total density is below critical density, or alternatively that even it if it is not, the inhomogeneity nevertheless must cause expansion to accelerate rather than decelerate.

    Am I missing something basic here? I'm looking at this from an intuitive perspective rather than from the perspective of particular backreaction models. And I am not assuming that the spatial curvature of voids or of the universe as a whole is negative.

    Last edited: Apr 21, 2008
  2. jcsd
  3. Apr 21, 2008 #2
    A further thought. According to Birkhoff's Theorem, to the extent voids are assumed to be spherical (a not entirely valid assumption), the overdense void shell will exert no gravitational influence over the shell interior.

    Thus, once a spherical void has begun expanding faster than the cosmic-average FLRW rate, and evacuating its matter contents, there is no external or internal influence to impede it from expanding faster than the cosmic-average rate in perpetuity. This should drive the void fraction asymptotically towards 100% over time, squeezing the matter into ever more radially thinned and tranvsersely stretched shells. Over time, this process should result in a noticeable rebiasing of the local Hubble flow in shells, with declining flow in the radial direction and increasing flow in the transverse direction. Over time, the cosmic-average expansion rate should asymtpotically approach the average void expansion rate.

    Metaphorically, the expanding void fraction could be compared to incurable, fast-growing tumors.

  4. Apr 22, 2008 #3
    It strikes me that the void fraction increase in itself might not increase the overall cosmic expansion rate, if one uses the spatial-inflow model of gravity. In that model, matter will suck in and "dispose of" exactly the same volume of space per unit of time, regardless of whether the mass of the observable universe is homogeneously dispersed or concentrated in a single black hole.

  5. Apr 23, 2008 #4
    I've reconsidered this description, and I don't think it's right.

    The expansion of voids faster than the cosmic-average rate does not physically "squeeze" the surrounding overdense void matter shells in the radial direction. The evacuation of the void interior causes evacuated matter to accrete along the inner edge of the shell, actually thickening the shell rather than thinning it. I think the shell material itself can become radially thinner only as a result of its own internal gravitational collapse over time. The expanding void does not "squeeze" the shell thinner, because the expansion of space does not cause any pressure-like effect. Perhaps to a limited degree the accretion of interior matter onto the shell causes the local gravitational collapse rate to increase.

    The shell will be transversely stretched only in the sense that an underdense portion of the void interior actually becomes interposed directly between any two clumps of shell matter. Individual clumps in a single shell which are not gravitationally bound to each other will be physically displaced by the physical intrusion of the void between them; but until the void intrudes, its expansion adjacent to them will not cause two unbound clumps to separate. They should separate only at a local Hubble rate based on the local density.

    Apparently more than 100% of the total cosmic expansion occurs inside the voids. There is a very real displacement of large-scale physical coordinates which results from voids expanding while shells locally collapse gravitationally. Over time, the amount of coordinate space located inside the voids increases, while it decreases inside localized shell clumps. Thus the bulk movement of a shell clump with respect to the CMB rest frame represents a "real" physical displacement.

    For purposes of analyzing cause and effect, it is clearest to start with a background assumption of a "naked" base cosmic expansion rate at a near "empty universe" rate, i.e. near-zero mass density. Then all local differences in expansion rate can be seen to reflect only the degree of local overdensity relative to a near-zero background density. (By definition there is no relative underdensity). In this way the bulk movement can be described as being entirely caused by differentials in local gravitational collapse rates, rather than as some sort of "push" from the expansion of space.

    Last edited: Apr 23, 2008
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