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Hubble expansion inside a contracting supercluster

  1. Jan 1, 2008 #1
    The purpose of this thread is to further discuss the concept of the Hubble expansionary flow in our local region -- which is too small to be considered homogeneous for the purposes of the Friedmann equations, say up to a radius of 100 Mpc from us. (A megaparsec (Mpc) equals about 3.25 million light years or 3E+22 meters). I have read a dozen papers on this subject by Chernin, Karachentsev, Teerikorpi, et all, as well as Sandage et al’s http://http://arxiv.org/PS_cache/astro-ph/pdf/0603/0603647v1.pdf" [Broken].

    According to Sandage, a regular Hubble flow of expansion is observed over the range from 4 to 200 Mpc from the center of our Local Group. Observations of a handful of nearby dwarf galaxies suggest that this Hubble flow also remains regular to within 2 Mpc of the center of our Local Group. Our Local Group, comprised of the binary formation of the Milky Way (MW) and Andromeda (M31) massive galaxies, also contains a few small galaxies, 36 or so dwarf galaxies, and numerous star clusters which altogether add little to the total mass of the group. The MW and M31 galaxies are about .7 Mpc apart and are approaching each other at about -120km/s. At that rate they are expected to merge in 5-6Gy. The total mass of the Local Group is estimated at around 1.3E+12 solar masses. Chernin says observations of the dwarf galaxies which early in their existence gained escape velocity from the Local Group (due to the ‘Little Bang’), show that the Hubble expansion flow begins at slightly above 1 Mpc from the Local Group center, that is, just at the outskirts of the group. By about 2 Mpc from the center, the regular Hubble linear velocity-distance trend emerges. (Chernin describes this as the solution to the Sandage-de Vaucouleurs paradox).

    Chernin starts with the mainstream premise that dark energy smoothly pervades all vacuum space. Dark energy’s omega = [tex]\omega = -1[/tex] equation of state creates a local effective “antigravitating” density of [tex]\rho_{v} + 3P_{v} = -2\rho_{v}.[/tex] The gravity of matter dominates at small distances, and the total acceleration is negative (inward). At large distances, the antigravity of dark energy dominates, and acceleration is positive (outward). Gravity and antigravity balance each other, with zero net acceleration, at the “zero gravity surface, which has the radius:

    [tex] R _{v} = \left(\frac{3M}{8 \pi \rho_{v}}\right)^{\frac{1}{3}} [/tex]

    The zero gravity surface is very close to spherical now, and has been roughly spherical over its 12.5 Gy history. When escaped particles (such as the dwarf galaxies) move beyond the zero gravity surface, the dark energy antigravity accelerates their recession, while simultaneously “cooling” their peculiar velocities. This has caused the dispersion of peculiar velocities to become quite narrow in the region.

    Observations of other nearby galaxy groups show the same sort of local Hubble flow as our Local Group. There are papers dedicated to the M81/M82 group, the Centaurus A/M83 group, and the IC342-Maffei group. Chernin suggests that the same unitary zero gravity surface concept also applies to much larger rich galaxy clusters. He suggests that such clusters could have zero gravity surfaces up to 10-20 Mpc radius. There is a footnote in Teerikorpi’s paper saying “However, for a large cluster or a supercluster, the [zero gravity] spheres contain a progressively smaller fraction of the volume.”

    Chernin has created a non-Friedmann equation (which is structured very similar to Friedmann) to model non-homogeneous static space-time.

    [tex]\frac{1}{2}\dot{r}^{2} = GM/R + \frac{1}{2}(r/A)^{2} + \overline{E} [/tex]

    where [tex]A= \left(\frac{8 \pi G}{3}\rho_{v} \right) ^{-\frac{1}{2}} [/tex]

    and [tex]\overline{E} \left( \chi \right) [/tex] is the Lagrangian coordinate [tex]\chi[/tex] per its unit mass.

    He points out that since the vast majority of space is dominated by a very uniform dark energy density, the universe really is much more uniform at local scales than it would appear to be based solely on matter distribution. He demonstrates that his local space-time model can be neatly embedded into the global Friedmann space-time in General Relativity, with the local universe being described as a “spherical vacuole” according to the Einstein-Straus solution. He says [Chernin 3/06]:

    “… one can imagine that the whole Universe may contain not one, but many (or an infinite number) of vacuoles of various sizes and masses. Moreover, a picture is theoretically possible in which vacuoles fill almost all cosmic space without intersecting each others. Such a complex non-uniform expanding structure is exactly (!) described by the equations above. Obviously in this picture the tiny contribution of uniform matter distribution between vacuoles can be neglected, and one obtains a highly non-uniform, but completely regular, cosmological model. The model describes the global expansion in terms of the relative motions of discrete masses which are in the centres of the vacuoles. The masses move apart from each others on the uniform vacuum background, in accordance with the Hubble law and the expansion factor given by the Friedmann theory…. In fact, because the zero-gravity radius is inside the vacuole in such a model, each vacuole expulses every other one and the expansion is generally accelerating…”

    The part of Chernin et al’s model which I find most difficult to conceptualize (probably because they don’t focus much discussion on it) is the scenario in which a local Hubble expansion occurs inside a gravitationally bound structure. This apparently is recognized to be the case for our Local Group, which according to Karachentsev et al is being pulled gravitationally towards the Virgo cluster at around 140 km/s, and towards the Great Attractor at around 290 km/s. It also is moving peculiarly away from the Local Void at around 200 km/s, and residually (compared to the CMB dipole) in yet another direction at around 170 km/s (towards or away from what, isn’t known). In the concordant models, all calculations of the isotropic local Hubble flow are actually adjusted to subtract out these peculiar bulk flows. This is a very significant adjustment, considering how much larger magnitude these bulk flows are than the local Hubble flow (but the adjustment for peculiar flows becomes relatively insignificant at very large distances, e.g. 1000 Mpc). In any event, my interpretation is that this adjustment is the standard treatment: gravitational peculiar flows and Hubble flows are both simply subtractions from the “real” net CMB dipole flow.

    So for example, I interpret this to mean that even though our Local Group is embedded in a local region which is undergoing regular Hubble expansion, that local region also is gravitationally embedded in our Local (Virgo) supercluster, which is gravitationally contracting. This vividly demonstrates how expansion and contraction are in constant dynamic contention with each other at virtually every point in the universe. Although Hubble expansion “dominates” the local region around our Local Group, that entire region is in turn “dominated” by gravitational contraction of the Local Supercluster, which contains many regions like ours which are expanding at the Hubble rate. Thus when the expansion and contraction are netted against each other, the net flow within our local region is contractive, but at a lesser rate of contraction than would exist if the region were not simultaneously undergoing a Hubble expansion.

    I would appreciate any comments or questions.

    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Jan 3, 2008 #2
    Jon, Hi. Just wanted to thankyou for your post which has put to rest my own general deductions/assumptions along the lines you have described... I had no idea they were 'legitimate'. Similarly your use of the word 'flow'. Clearly I am more ignorant than I thought!!

    I'll leave it there so as not to contaminate the thread :smile:(for now)
  4. Jan 3, 2008 #3
    Hi Muccasen,

    Thanks for the encouraging words. This concept of dynamic local contention between expansion and contraction seems implicit in mainstream cosmology, so I've been surprised to find so little written directly on point. Chernin et al's work is a tremendous contribution (in my opinion), first because it is built on a strong foundation of observational data, and second because the local model is neatly integrated into the global Friedmann model and General Relativity. It's exactly what I was hoping to find, except I want to read a lot more explanation on this subject!

    I would like to find some more observational analysis of whether superclusters such as Virgo are actually contracting gravitationally overall. I assume they must be because their contents tend to be moving radially towards a rich cluster near the center, and there is little indication of strong virial motion that would support the supercluster structure against collapse.

    My sense from these papers is that individual rich clusters are probably the largest stable structures in the universe. Each with its own unitary zero gravity surface.

  5. Jan 4, 2008 #4


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    Interesting stuff. Isn't the Virgo cluster as a whole also moving towards the Great Attractor?
    If so, it's status is not very different from our Local Group, or is it?

    I suppose it depends on what you mean by a 'stable structure'.
  6. Jan 9, 2008 #5
    Jorrie, when I said that rich clusters are probably the largest 'stable structures', I meant stable in the sense that they are fully collapsed gravitationally and virialized. Thus they will not experience significant contraction. As compared to (probably all) superclusters, which are not virialized and are still fairly early in the stage of gravitational collapse. By the way, the Virgo Cluster contains over 1000 galaxies in a volume only slightly larger than our Local Group (which contains 2 major and 3 minor galaxies.)

    Not only is the Virgo cluster moving towards the Great Attractor, it is also being pulled and pushed by other sources. Two informative recent papers on this subject, are http://http://arxiv.org/PS_cache/arxiv/pdf/0705/0705.4139v2.pdf" [Broken].

    Kocevski says 44% of the Local Group's peculiar velocity is due to infall into the Virgo - Great Attractor region, and 56% is induced by more distant overdensities between 130-180 Mpc. The latter flow would apply essentially to our entire Local Supercluster as well. Slightly over half of the distant contribution comes from the Shapely Supercluster region, (which is roughly behind the Great Attractor) and another significant contributor is the Horologium-Reticulum Supercluster. Kocevski also calculates that the Perseus-Pisces supercluster (which is in roughly the opposite direction as the Great Attractor) counteracts much of the Great Attractor's effect beyond 60 Mpc.

    The Tully paper seems to agree generally with Kocevski (who is a co-author on the Tully paper), but draws special attention to the influence of the Local Void. It assigns flow amplitudes of 259 km/s away from the Local Void, 185 km/s flow towards Virgo, and 455 km/s flow towards the Great Attractor (Centaur-Hydra-Norma), Shapely, and other distant sources. These 3 influences are roughly orthogonal to each other, each aligning with one of the 3 Supergalactic cardinal axes. It is difficult to observe exactly how large the Local Void is and how much matter it contains, but the paper estimates that its radius must be at least 23 Mpc to exert the necessary "push" on us. Our Local Group forms one part of the Local Void's immediate boundary wall.

    Tully seems to strongly believe that the underdensity of voids will expand at greater than the Hubble rate which literally "pushes" the wall structures (like us) away from its center. He applies the Friedmann formula to calculate that a truly empty void would experience 16 km/s per Mpc of extra expansion above the normal Hubble flow rate. To the extent the void isn't entirely empty, the extra expansion will be less. The extra flow rate gets higher the further a test particle is away from the void center. (The surrounding wall shells don't influence the interior expansion rate, of course.) Over time, the extra expansion rate causes voids to evacuate their matter content, making them increasingly empty, and causing overdensity to increase at the boundary walls. Tully notes that one dwarf galaxy has been observed in the Local Void with a peculiar velocity of at least 230 km/s away from the void center, which is consistent with the accelerated expansion model.

    It's quite interesting to contemplate that the expansion of the empty vacuum in voids literally "pushes" superclusters and filaments away, but I don't see any clearer way to describe the phenomenon. Of course to a large degree this is simply the influence of dark energy, or alternatively, Wiltshire's model of clocks running faster in voids.

    As the local frame of reference, Tully prefers what he calls the Local Sheet instead of Local Void. He defines the Local sheet as the galaxies within 7 Mpc of us. He notes that this region contains 5 times as many galaxies as the Local Group (providing more accurate measurement opportunity), and that the bulk flow of the Local Sheet is sharply discontinuous from the flows of other nearby structures such as the slightly more distant Leo Spur. The Local Sheet is only about 3 Mpc thick in its narrowest dimension, which is aligned with the Supergalactic Plane. Tully says the Local Sheet is participating in the cosmic expansion "though probably somewhat retarded."

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  7. Jan 9, 2008 #6


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    Very interesting read jonmtkisco , the part about local voids (cleaning house) is particularly so.
  8. Jan 11, 2008 #7
    Thanks Wolram, I'm glad you share my interest.

    A couple of random thoughts occur to me about this topic.

    First, if the outer edge of the Local Void is pushing radially outward against the walls of the void, at around 260 km/s, then those walls (including our Local Sheet) are also experiencing average transverse stretching (perpendicular to the void center) at that rate, per every radius-length subsection of the circumferance. It's no wonder that matter structures are being stretched into elongated filaments and thin walls... I would think that the transverse stretching should also show up in the bulk flow calculations as a contribution to observed peculiar motion of clusters which are perpendicular to the void center (with respect to our Local Sheet). I Haven't seen anything written specifically on that point.

    Second, I want to clarify a statement in my first post: "In any event, my interpretation is that this adjustment is the standard treatment: gravitational peculiar flows and Hubble flows are both simply subtractions from the “real” net CMB dipole flow."

    The Hubble flow would not be subtracted from the CMB dipole, because we are comoving with the CMB [edit: deleted "dipole"] and therefore would not perceive any angular peculiar motion arising from the Hubble flow. But the standard approach is to subtract the normal Hubble constant (e.g., 74 km/s per Mpc) from the observed bulk motion, to calculate the actual peculiar motion. This demonstrates confidence that a Hubble Flow vector exists everywhere in the universe, including inside bound structures. However, Tully emphasizes that if the "consensus" normal Hubble constant changes, then the peculiar motions will need to be recalculated.

    Last edited: Jan 12, 2008
  9. Jan 12, 2008 #8
    I need to correct this statement. Kocevski's 44%/56% split was calculated after the inflow velocity of the Local Group towards the Virgo cluster (the figure he adopts from the literature is 170 km/s) is subtracted from the CMB dipole. So the total percentage influence of "local" structure (Virgo & GA combined) on our peculiar motion would be around half again as large as the 44%/56% split suggests.

    Last edited: Jan 12, 2008
  10. Jan 13, 2008 #9
    Hey Jon

    I have a similar question in mind but as I am not working in this field I would like just to ask it and may be this will give some idea.

    If Hubble law consequence is the expansion of the Universe, all galaxies are receding from us at increasing speeds proportional to their distances. Consequently, we are at the centre of this expansion. But we know that we aren’t because the Universe has no centre (anthropocentric model is not valid) and the centre is everywhere. Question : are the recession speeds cumulative and how ? In other words, let’s assume three galaxies aligned (our Milky Way (named A) and two other aligned as the closest (name B) receding at z1 and the second (named C) at z2). Then what append if the 3 galaxies are not aligned but at the top of a "rectangular triangle" (even I don't know what should be such a triangle in the local inertial frame) and how to calculate the zi of each one with respect to one (A for example, then B then C)
    Consequently, this conduct to the following question: Based on the fact that the recession is mainly considered as a radial speed, what would be the model if we consider the redshift Doppler effect due to the tangential speed perpendicular to the line of sight? Are we able to distinguish the contribution of each speed direction ?

  11. Jan 13, 2008 #10
    Hi Alain, you ask some good questions although I'm not sure I grasp everything you are saying.

    If we are talking only about the normal Hubble cosmic expansion flow, without considering bulk flows or other peculiar motions, then yes, recession speed is cumulative along any given line of sight pointing directly (radially) away from us. Recession speed simply is directly proportional to line of sight distance.

    As far as I know, for distant objects there currently is no technique available to directly measure velocity vectors which are transverse (e.g., perpendicular) to our line of sight. For example, transverse motion does not produce either expansionary or doppler redshift which is observable to us. We can use our various measurement techniques only to estimate the one-dimensional distance directly along our line of sight, and combine that with measurements of angular position (not angular motion per se).

    For example, it is not currently known whether the nearby (.7 Mpc) Andromeda galaxy (M31) has significant tranverse motion with respect to our Milky Way. Therefore, although we know that the two galaxies have a substantial velocity vector along the line of sight towards each other, we cannot calculate for certain when or if they will eventually collide.

    The bulk flow models, such as the ones described in the papers I referenced, calculate the transverse vectors of these bulk flows only as models or simulations ("n-body simulations"). These models and simulations assign gravitational overdensities and underdensities at discrete locations and gravitational amplitudes, both of which are estimated based on the most recent observations (including many excellent observations by the Hubble Space Telescope). That data is used to calculate hypothetical transverse velocity vectors which "best fit" the data model's expectations of infall and outfall forces. Some of the recent simulations involve thousands of data points which are crunched in sophisticated supercomputer algorithms.

    If others are knowledgeable on this subject, please feel free to contribute to the discussion.


    p.s., In an earlier post I mentioned stretching of void-boundary filaments and walls which is transverse to the center of the void. However, that stretching is not necessarily transverse to our own line of sight as we observe galaxies embedded in the same void boundary we are embedded in. It depends on how far around the spherical rim of the void the observed galaxies are.
    Last edited: Jan 13, 2008
  12. Jan 23, 2008 #11
    Hi Jorrie,

    This post is to respond to your recent statement in the "Dark Energy is Furphy" thread, to the effect that the expansion of space in voids does not 'push' the void contents outwards:

    Jorrie, although I agree that in some cases void wall galaxies can 'pull' nearby void interior galaxies towards them, I disagree that void interior galaxies are not being 'pushed' outwards by an "anti-gravity-like" acceleration force. I think the weight of recent scholarship is on my side on this point. Here are some thoughts:

    1. The Earth-Moon system you describe is not a good example for disproving the 'push' theory. Clearly that system comprises a single gravitationally bound structure. In addition, there is no reason to believe that space at the L1 point is underdense compared to the cosmic average. At the scale of this system, the Hubble expansion flow is insignificantly tiny and is completely swamped by the peculiar motion imparted by the gravity of the Earth or Moon. So the only relevant force is the 'pull' of gravity.

    2. In general, observations suggest that large voids are expanding at faster than the average Hubble rate, due to their internal underdensity. This radial expansion in turn causes transverse stretching of the bubble wall structure. Clearly then, a void together with all of its integrated wall galaxies cannot be considered a single gravitationally bound structure. In that context, it makes no sense that a wall galaxy could pull a galaxy deep in the interior of the void towards itself with peculiar motion, while at the same time it is unable to prevent nearer wall galaxies from moving away from it in the local Hubble flow.

    3. Both the Newtonian Shell Theorem and the GR Swiss-Cheese (Einstein-Straus) model based on Birkhoff's theorem say that to the extent a void is roughly spherical and its bubble-wall structure is roughly uniform, the wall galaxies will exert no net gravitational 'pull' on the void contents. Structural anisotropies may result in some net peculiar pull on some contents (particularly near the wall), but in general the gravitational pull of the wall on the void contents will be supressed.

    4. In the LCDM 'concordance' model with [tex] \Omega_{\Lambda} = 0.76[/tex], dark energy is believed to accelerate the expansion of voids, and over a 13.7 Gy expansion period, Tully (see reference in post 01.09.08 23:38 above) says this has accumulated to an extra ~ 16 km/s per Mpc of expansion rate within a completely empty void. Tully says:

    "These values are in good agreement with results from simulations reported by van de Weygaert & Schaap (2007). Those simulations show that in models with [tex]\Lambda = 0[/tex] the voids are not fully evacuated at the present epoch and motions out of voids are consequently lower than if the voids were empty. However in the simulations with [tex]\Omega_{}\Lambda ~ 0.7[/tex], the voids are quite empty at z = 0, suggesting that we can give serious consideration to this possibility in the case of the Local Void." (Tully is trying to get comfortable that large voids really are quite empty).

    Tully concludes that our Local Sheet is experiencing a bulk flow away from the Local Void at ~ 260 km/s. As I said in the earlier post, he notes that this movement is orthogonal to the direction of our bulk flows towards Virgo, the Great Attractor and Shapely. In other words, there is no observable gravitational 'pull' explanation for this flow component. The reasonable explanation is outflow 'push' from the local Void. In another shorter http://http://arxiv.org/abs/0708.0864" [Broken] Tully says:

    "There is ongoing discussion about whether places where nothing is seen are truly empty. The Local Void generates a 'push' of 260 km/s. Perhaps we are seeing here the best evidence available that voids in the distribution of galaxies are really empty."

    In a http://http://arxiv.org/PS_cache/astro-ph/pdf/0404/0404397v1.pdf" [Broken] van de Weygaert says:

    "Primordial underdensities are the progenitors of voids. Because underdensities are regions of suppressed gravitational attraction, representing an effective repulsive gravity, matter flows out of their interior and moves outward to the edges of these expanding voids. Voids expand, become increasingly empty and develop an increasingly spherical shape (Icke 1984). Matter from the void’s interior piles up near the edge: usually a ridge forms around the void’s rim and at a characteristic moment the void’s interior shells take over the outer ones. At this shell-crossing epoch the void reaches maturity and becomes a non-linear object expanding self-similarly, the implication being that the majority of observed voids is at or near this stage (Blumenthal et al. 1992)."

    In a longer http://http://arxiv.org/PS_cache/arxiv/pdf/0708/0708.1441v1.pdf" [Broken] van de Weygaert & Schaap describes the velocity flows calculated in a large-scale simulation:

    "The flow in and around the void is dominated by the outflow of matter from the void, culminating into the void’s own expansion near the outer edge. ... Not only is [the interior flow] slightly elongated along the direction of the void’s shape, but it is also sensitive to some prominent internal features of the void. ...

    "The general characteristics of the void expansion are most evident by following the density and velocity profile along a one-dimensional section through the void. ... The first impression is that of the bucket-like shape of the void, be it interspersed by a rather pronounced density enhancement near its centre. This profile shape does confirm to the general trend of low-density regions to develop a near uniform interior density surrounded by sharply defined boundaries. Because initially emptier inner regions expand faster than the denser outer layers the matter distribution gets evened out while the inner layers catch up with the outer ones. ...

    "The velocity profile strongly follows the density structure of the void. The linear velocity increase is a manifestation of its general expansion. The near constant velocity divergence within the void conforms to the super-Hubble flow expected for the near uniform interior density distribution. Because voids are emptier than the rest of the universe they will expand faster than the rest of the universe with a net velocity divergence equal to

    θ = 3(α − 1) , α = Hvoid/H ,

    where α is defined to be the ratio of the super-Hubble expansion rate of the void and the Hubble expansion of the universe.

    "Evidently, the highest expansion ratio is that for voids which are completely empty.... The expansion ratio α for such voids may be inferred from Birkhoff’s theorem, treating these voids as empty FRW universes whose expansion time is equal to the cosmic time. For a matter-dominated Universe with zero cosmological constant, the maximum expansion rate that a void may achieve is given by

    θmax = 1.5 [tex]\Omega [0.6,m][/tex],

    with m the cosmological mass density parameter. For empty voids in a Universe with a cosmological constant a similar expression holds, be it that the value of α will have to be numerically calculated from the corresponding equation. In general the dependence on Λ is only weak. Generic voids will not be entirely empty, their density deficit ≈ 0.8 − 0.9."

    5. Van de Weygaert also mentions that large voids are created by merging of smaller voids, something that seems inconsistent with a history of formation through gravitational 'pull' collapse into overdense regions.

    "In the interior of the void several smaller subvoids can be distinguished, with boundaries consisting of low density filamentary or planar structures. Such a hierarchy of voids, with large voids containing the traces of the smaller ones from which it formed earlier through merging, has been described by theories of void evolution. (Regos & Geller, 1991; Dubinski et al., 1993; van de Weygaert & van Kampen, 1993; Sheth & van de Weygaert, 2004)."

    In conclusion, I think the 'push' theory is logical and reasonably well-established.

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  13. Jan 24, 2008 #12


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    I agree that the under-density in a void plays a role in the 'cleaning' of the void, but I still find it hard to view anything but dark energy as providing "anti-gravity-like" or "pushed" movement. Dark energy provides that equally well in the voids and in the void walls, so it should not be the discriminating factor. What's left is kinematics – void galaxy separation rates must have slowed down less than the separation rates in the void walls, causing wall density to decrease slower than void density.

    I agree for spheres, but there is little evidence of spherical voids, making me think that some peculiar movement will be present, but I do agree that it is probably not the dominant effect here.

    Hmm, I suppose one can call it a 'push theory', but without a mechanism (force or whatever, except dark energy), it's not a clear-cut 'push', is it?

    I think one should rather stick to the observations that there appears to be a higher expansion rate across voids than across walls. If I understand this correctly, it means that from our perspective, the difference between the recession speeds of the far and the near sides of a void is higher than what the cosmic average for that separation should be. Am I right on this?

    Last edited: Jan 24, 2008
  14. Jan 24, 2008 #13


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    Gravity acting as an entirely attractive force (no dark energy or cosmological constant) leads to under dense regions voids 'pushing' material outwards in co-moving co-ordinates. This is what is meant in the references given by Jon when the researchers mentioned talk about a 'push' caused by voids. As usual in astro/cosmo, researchers talk in shorthand that assumes a level of understanding of the lingo that can easily be misinterpreted. Fundamentally, the apparent push in co-moving co-ordinates is clearly due to the 'pull' of gravity occurring in real physical space. Co-moving co-ordinates are much easier to work with however hence the void=push shorthand.

    This is very different to the ideas of Wiltshire*(see edit) and others in which the presence of the voids changes the background expansion (i.e. the overall averaged Hubble parameter of the Universe). In this case there is the implication that a 'real' push is produced by inhomogeneities in the Universe. It is important not to confuse these two ideas, if that is what is being done.

    Edit: on reflection Wiltshire is not a good example, since in his model there is still no 'real' push. In any case there is still an effect on the overall averaged cosmology due to inhomogeneities which is not the case in the standard model where voids do cause a push in co-moving co-ordinates. There are some other non-standard models that do claim voids effectively cause a 'real' push, but again this is not to be confused with the somewhat counter-intuitive terminology used to describe structure formation in the standard model.
    Last edited: Jan 24, 2008
  15. Jan 24, 2008 #14
    Hi Jorrie,

    I agree that it's accurate to describe this merely as voids decelerating less rapidly than walls. But I don't think that description is sufficient to get our arms around the phenomenon.

    Because voids are expanding faster, they really do create a 'bulk flow' of motion away from their center. Our Local Sheet has a velocity component of 260 km/s away from the Local Void, which represents a real displacement with respect to the rest frame of the CMB backround. Since this breeze is blowing up our tailpipe, I think 'push' is objectively the best term to describe it.

    Yes, the typical void has a dimensional ratio of 1:0.7:0.5 among its three axes. Also, voids tend to align themselves in parallel to their largest and smallest axis, but the distribution with respect to the middle axis tends to be random. See http://http://arxiv.org/abs/0711.2480v1" [Broken].

    Yes, definitely.

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  16. Jan 24, 2008 #15
    Hi Wallace, glad to hear from you again!

    I have to disagree with you on this one Wallace. There is no gravitational 'pull' causing our Local Sheet's 260 km/s bulk flow away from the Local Void. So I don't understand what 'pull' you may be referring to.

    Assuming that comoving coordinates are specified with respect to the cosmic average Hubble Flow, a comoving observer would indeed observe our Local Sheet moving with a 260 km/s peculiar motion away from the Local Void (which is underdense as compared to the cosmic average density).

    We can readily discern that the Local Void is expanding at a super-Hubble rate, because it is causing our Local Sheet to be displaced with respect to the rest frame of the CMB. It actually changes the angular vector of our CMB dipole. That would not be the case if we were merely comoving with the cosmic-average expansion.


    [edit: I suppose one could claim that any above average expansion of all voids is equivalent to an under-expansion of the rest of the universe, and so attribute the differential deceleration rates as being caused by 'pull' rather than 'push'. That would be true for example if one took the density and expansion rate in voids to be the baseline against which everything else is measured (such as comoving coordinates). But that would clearly be a non-standard approach, since standard cosmology starts with the FRW average density and expansion rate. It also suggests that somehow cosmic expansion (even without dark energy) is somehow less "real" than gravity. I see no objective basis for such a perspective.]
    Last edited: Jan 24, 2008
  17. Jan 25, 2008 #16


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    Hi Jon. I guess this "push-pull" cosmology 'controversy' can easily go into circles!

    I suppose one can say the same for any expansion - it always creates an apparent "bulk flow of motion" away from every point, but nobody describes non-Lambda expansion after inflation as a "push". The fact that voids expand faster than filaments creates something observationally similar to peculiar motion relative to the average Hubble flow. I suppose from that point of view one can call it a push...


    [Edit: I've attempted a 2-d spacetime diagram for the void-filament situation and for what it's worth, it's attached. It shows what the recession spacetime vectors might look like (more or less) for a homogeneous case and a non-homogeneous case, centered on the void. Interestingly, one can obviously see Wiltshire's different clock rates. From this perspective, it looks like the filaments are being pushed...]

    Attached Files:

    Last edited: Jan 25, 2008
  18. Jan 25, 2008 #17
    Hi Jorrie,

    Yes, and I find Wallace's implicit point on this to be interesting. It's kind of a 'Machian' cosmology, starting with a zero-density expansion as the baseline for the comoving coordinates and non-Lambda expansion rate, and then describing every movement which departs from that rate as being caused by the combined effect of "all of the matter in the universe", (and by Lambda if it's part of the model).

    Unless the discussion is focused specifically on voids, a non-Lambda expansion is always slower than the cosmic average, so it isn't pushing. It's only in voids that it is accurate to refer to it as a push, because the non-Lambda expansion is actually faster than the cosmic average Hubble rate.

    Good diagram Jorrie. If it were extended further to the right, what would the arrows on the second void look like? Same as the first, or different?

  19. Jan 25, 2008 #18


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    Hang on, your are mixing first and second derivatives !? You can't talk of a 'flow' causing a push or a pull (unless the fluid is viscous). So you suggest that

    which is nonsense, since you are claiming that that velolcity of material (the rate of flow) is affecting the acceleration it causes nearby material to experience (a push or pull).

    Voids can be described as pushing material outwards because the local undensity changes the way the local expansion rate proceeds, i.e. by changing the second derivate of the flow. But you can't look at a single point in time, compare local first derivatives (expansion rates) and know what will happen at the next moment in time. To do this you need to know what the distribution of matter is.

    It is hardly 'Machian', non-standard or in anyway controversial to suggest that gravitational acceleration is caused by the gravitational pull of material.
  20. Jan 25, 2008 #19
    Hi Wallace, I appreciate discussing this interesting subject with you, but as a personal favor, could you please refrain from using inflammatory language like "nonsense", as well as extraneous exclamation points. Whether you are right or wrong, browbeating is not going to help your argument carry the day.

    I understand your point, that once a void wall galaxy has been accelerated to a given velocity, then even in the absence of any subsequent acceleration force, its peculiar momentum vector (with respect to the CMB rest frame) would continue (subject to other gravitational interactions and the general decay of peculiar velocities in expanding space.) So I should limit my use of the term 'push' to include only (1) the past acceleration which caused the galaxy to reach its current peculiar velocity, and (2) the present and future acceleration which will cause its peculiar velocity to increase further. Fair enough, but I don't think it changes the gist of what I was getting at.

    Of course, the internal super-Hubble expansion metric of a void without Lambda does not actually accelerate in an absolute sense, once the void has become fully evacuated. Rather, its Einstein-de Sitter deceleration factor is less than the cosmic average deceleration factor. Interestingly however, the peculiar velocity of a wall galaxy of such a void will continue to accelerate absolutely (i.e., with respect to the CMB frame) over time because as the void continues to expand, the same internal super-Hubble metric is applied over a larger and larger radius. I suppose one would describe that acceleration as resulting from the negative curvature of the void's interior geometry (?)

    I appologize if you perceived I was denigrating what you said. Maybe I misinterpreted what you said.

    Since there is no specific, localized gravitational overdensity (such as a supercluster) which is gravitationally 'pulling' the void wall outward to account for its super-Hubble expansion rate, I assumed that the gravitational 'pull' you were referring to was the gravitation of "all of the matter in the universe" located outside of the void. In the sense that, depending on one's perspective, one can say that the cosmic overdensity outside voids causes the expansion rate outside voids to decelerate faster, which in turn accounts for the identified bulk flow component of our Local Sheet with respect to the CMB frame.

    If that's not what you were referring to, please explain. Your comment was brief and it appeared a bit cryptic to me, so I was extrapolating. No harm intended!

    Last edited: Jan 25, 2008
  21. Jan 25, 2008 #20


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    Hi Jon.
    From the same (bubble) reference frame the Hubble flow will be more profound in farther regions and the word-lines will all tend towards the [itex]\pm 45[/itex] degrees as the particle horizon is approached.

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