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Superclusters and Voids - same curvature?

  1. Nov 30, 2007 #1
    Superclusters and Voids -- same curvature?

    According to the mainstream 'standard model', is the geometric curvature of space believed to be exactly the same within superclusters as it is in within voids?

    In other words, does the much higher gravitational density within a supercluster manifest itself in the form of holistic curvature of the supercluster's geometry? Is the curvature of a supercluster's internal space considered to be "closed" if the supercluster is gravitationally contracting (as opposed to expanding with the Hubble flow)? Superclusters are believed to be gravitational bound structures (e.g., their gravitation resists expansion at the Hubble rate).

    I note that a single supercluster can comprise a sizeable subset of the observable universe's radius. The radius of a typical supercluster is around 5E+23 meters. The radius of the observable universe is 4.35E+26. There are estimated to be around 20 million superclusters in the observable universe. Number of voids is probably within an order of magnitude of that number.

    Jon

    p.s. Please don't mention anything about alternative cosmology theories. I received 4 demerit points for my last post, and if I receive 5 more I will be banned from the forum. Santa is keeping a list, and checking it twice; he knows when I am naughty or nice.
     
    Last edited: Nov 30, 2007
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  3. Nov 30, 2007 #2

    marcus

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    Reality bumpy. The mainstream standard LCDM is just averaged out. Everybody knows it's bumpy and curvature is a little different everywhere you go.
    And the expansion rate is different everywhere you go. But you have to make a simple model with averaged rates and curvature so that you can calculate stuff.

    Maybe Wallace will answer. I don't know how to answer. The model they use to calculate is simplified, so the answer to your question is YES. the simple model ignores the detailed distribution of matter, so voids and clusters are the same. But on the other hand, when they do computer modeling and work at detailed level they take into account the bumpiness. So in another sense the answer is NO----astronomers don't think the curvature is uniform. they treat it as uniform only when appropriate as an approx.

    How the dickens did that happen. The last post of yours i know was about the Hubble parameter in the early universe. it was a very sensible post, and about 10 minutes ago. how did you have time to get into mischief in the meantime
     
    Last edited: Nov 30, 2007
  4. Nov 30, 2007 #3
    Hi Marcus,

    If, as you say, spatial curvature can be "closed" within a supercluster, why wouldn't a photon beam emitted from a source within the supercluster find its path curved in a complete circle, such that it travels 'round and 'round and can't escape the bounds of the supercluster?

    Jon
     
  5. Nov 30, 2007 #4
    Hi Marcus,

    Don't mean to confuse you, but I got the 4 demerits for my prior post several days ago. I don't think I'm allowed to mention which one.

    Jon
     
  6. Nov 30, 2007 #5

    marcus

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    that sounds wacky. I don't recall ever saying anything of the sort!

    The universe as a whole can be spatially closed if for example Omega = 1.01
    and cosmologists take that possibility seriously
    but that is the whole thing, not just the region occupied by a supercluster

    light can go in circular paths around a black hole
    like at the radius 3Gm/c^2 the photosphere radius of a vanilla BH

    so I guess you could DESIGN a supercluster that was snuggled close in around a supersupermassive black hole and light went in circles----but it is very artificial example

    You might think that light go around in circles is if space is topologically S3
    which it very well could be---we dont know. that is the spatial closed case.
    But that doesn't allow for space expanding. So even if space as a whole is closed that doesnt mean light could ever make a full circuit. Expansion would most likely defeat such a circumnavigation project.

    I have to go, Jon. don't ask me any questions now or I might be tempted to stop and reply:smile:
     
  7. Nov 30, 2007 #6
    Hi Marcus,

    I didn't mean to put words in your mouth. A "closed" universe is a universe that is slightly over critical density and therefore will collapse someday, even if it's at a very long time in the future.

    Since an isolated, gravitationally bound supercluster also seems doomed to collapse over time (at least with respect to most of its matter content), isn't it accurate to refer to it as a "closed" geometry as well?

    My understanding is that in a "closed" universe, which resembles a 4-sphere, if there is enough time before final collapse to a singularity (whatever that means), a photon travelling in any direction will circle 'round the sphere and eventually return to approximately its origin, from the "backside". Is that wrong?

    I thought the point of geometric curvature is that it restrains the freedom of action of particles in freefall. At least in the case of positive curvature, they can travel only so far in one direction before returning to their starting point.

    Why would a photon circle around an entire closed universe, but not around a closed subset of a universe? Is the problem that there isn't enough curvature available in a subset such as a supercluster? Presumably the radius of curvature needs to be equal to or smaller than the actual physical radius of the supercluster. What is the minimum radius of curvature that a typical supercluster could reasonable be expected to possess? Is it derived from the gravitational binding energy? I note that a typical "homogeneous" gravitational binding energy of a supercluster is around 4E+42 joules.

    Jon
     
    Last edited: Nov 30, 2007
  8. Nov 30, 2007 #7

    marcus

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    Jon, I like you but it's hard to talk with you because of using words differently. I've said this before many time---a universe that is over critical density is said to be spatially closed but since 1998 it has not been assumed that this implies eventual collapse. So you are using language in a different way from what I'm used to.
    Try to fine-tune your use of words to agree with, say, Wallace. Otherwise just the semantic conflict tires me out and makes it no fun. Sorry:frown:
     
  9. Nov 30, 2007 #8
    Modeling with manifolds

    Perhaps one could think of an expanding manifold (i.e. continuum), but with also a concomitant contracting circle (or 3-volume). Of course a manifold could be fleshed out with additional elaboration such as geodesics with different local curvature; hence building up a model from a general abstraction perspective.
     
  10. Dec 1, 2007 #9

    Wallace

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    As marcus suggests, closed universes need not collapse.

    Clusters in a sense have already collapsed, and do not contract further. They are though to be 'virialised' since they have convert the gravitational potential released in the collapse phase into kinetic energy of internal dispersion velocities. To collapse any further would violate the http://en.wikipedia.org/wiki/Virial_theorem" [Broken], so they are in fact stable objects (although they do continue to cannibalise smaller collapse object that fall onto them, so things are somewhat chaotic).

    All mass and energy causes curvature as far as GR is concerned, but the open, close, flat dichotomy of the FRW solution only applies to the FRW solution, so you can't sensibly apply it to an object (such as a cluster) embedded within some other space-time.

    The mass of a cluster causes light rays to deviate, such as in gravitational lensing.


    Again, that only applies to positive overall curvature in a FRW universe, not to curvature more generally.

    I think marcus mentioned photon orbits around Black Holes. Try googling that to see what it takes to get photons to do circles. For the cluster example, a massive cluster will deflect the path of light rays by fractions of a degree, enough to cause gravitational lensing, but that is obviously no where near enough to induce photon orbits.
     
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  11. Dec 1, 2007 #10
    Hi Wallace & Marcus,

    First, Marcus I appologize for not qualifying my description of a closed universe to include the effect of lambda (cosmological constant). I certainly agree that an over-dense universe with lambda need not collapse. Somebody should coin a new term to replace the word "closed".

    Second, Wallace I'll go with your statement that superclusters are already fully collapsed due to their virial resistance to further collapse, although I understand that it's all supposed to collapse to black holes at some far distant time.

    Third, I understand the concept of gravitational lensing, but that isn't what I was trying to get at.

    The real question I'm trying to get at is whether current theory deems space to be contracting within very dense regions. Consider for example the region of space immediately adjacent to a neutron star. Is space contracting in this region? If space is contracting there, then the movement of a freefalling particle there should be affected not only by the direct gravitational force (spacetime curvature) of the neutron star, but also by a reverse Hubble-flow of local space towards the neutron star. Meaning that even after the direct effect of gravity is subtracted out, the particle still observes the distance between itself and the neutron star decreasing over time due simply to the contraction of the intervening space. (This decrease in distance may not occur if the particle has a lot of transverse velocity relative to the neutron star).

    Extremely dense regions of the observable universe (such as the local space of neutron stars) comprise an infintesimal fraction of the physical volume of the universe. As such, they seemingly must experience local negative expansion rates (contraction) which are many times larger than the average expansion rate of space in the observable universe. Otherwise they couldn't couldn't collectively significantly affect the average expansion rate. I understand that the combined mass of all stars in the universe makes up only about .4% of the of the total mass/energy and around 1% of the matter in the universe, which isn't insignificant. On the other hand, they make up only about E-1/33 of the volume of the universe.

    Isn't the math to calculate such a local contraction rate fairly straightforward?

    Jon
     
    Last edited: Dec 1, 2007
  12. Dec 1, 2007 #11
    Isn't this the area http://arxiv.org/abs/gr-qc/0702082" [Broken] works in?
     
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  13. Dec 1, 2007 #12

    marcus

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    I shouldn't talk. you are the GR grad student at Canberra* and Wiltshire is a prominent cosmologist in New Zealand. It is a cinch that you know a lot more about his work than I do. But since you ask me the question, I have to say I think you are spot on. however I didn't have him or anyone definite in mind.

    BTW I see that Wiltshire got the February 2007 paper you link to (a long one!) accepted for publication by New Journal of Physics.
    http://www.iop.org/EJ/abstract/1367-2630/8/12/E07
    Personally I am skeptical of Wiltshire's efforts to obviate Lambda by explaining the appearance of accelerated expansion in other ways. I haven't read his papers consistently or thoroughly so can't judge, but from what I've sampled they seem so contrived. He arranges things just right so that Lambda goes away, isn't needed, and we still see the same supernova data.
    Kea used to post here at PF and was often propounding his ideas and acquainting us with his papers. Now she has her own blog and comes here less.

    If you find some of Wiltshire's arguments convincing, please give us a paraphrase and point us at specifics. Don't be put off by my lukewarm reception---he could be on the right track.

    ==EDIT TO CORRECT FAUX PAS==
    I forgot that the Australian National University was at Canberra, and got the research field of General Relativity confused with Cosmology. So I had to correct the part in red:redface:
     
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  14. Dec 1, 2007 #13
    Hi cesiumfrog and marcus,

    I just read Wiltshire's paper for the first time and I find it to be encouraging and stimulating. While it would be a home run if his calculations entirely obviated the need for lambda, that's not the central point. His key thesis is that time clocks and spatial curvature, and therefore expansion/contraction rates, vary significantly depending on whether one is in a void or a supercluster (finite infinite region). This should have significant impacts on observations of high-redshift phenomena. He is right to call upon cosmologists to declare one way or the other on the validity of this principle, and to incorporate it specifically into calculations, such as the WMAP CMB analysis.

    I disagree with him on one technical point. He assumes that spatial geometry is flat within gravitationally bound regions which experience zero average expansion rates. But having exhaustively considered the "escape velocity" principle, all of us on this forum know that if density is positive, a region cannot be flat unless it is expanding at escape velocity. Therefore, according to standard GR, a region with zero expansion rate must have positive curvature. Wiltshire seems to conclude, at least implicitly, that since voids have negative curvature and bound regions are flat, the average large scale curvature must be somewhat negative. (He attributes this potentially to a large scale perturbation in density which may subsequently be offset by an even larger scale perturbation which is over-dense). But with my correction, I think it's very possible that the average large scale curvature is flat, without resorting to large scale perturbation theories.

    Jon
     
    Last edited: Dec 1, 2007
  15. Dec 1, 2007 #14
    Actually, I only know Wiltshire by a paper that I read (and my personal area is neither cosmology nor Sydney :wink:), but I mentioned him here because I think his work is interesting.

    In general, GR people have been very sceptical of astronomers claims (based on Newtonian models) about dark matter and dark energy. It's a basic matter of us having a theory that is almost too elegant, and has been thoroughly verified in particular regimes, so when we look to other regimes where we just aren't sure yet how to apply our elegant theory (due only to a shortcoming of our computers and not the theory itself) we're loath to propose (wart-like) additional physics. Wiltshire is aiming to figure out what GR predicts in these other regimes, and so far he claims the result to be that we can explain observations without quite as much dark stuff as the Newtonian models would say.

    His work seems relevant to discussion of curvature on this scale, but unfortunately also seems unfinished. Personally I think it's unlikely that all forms of evidence for dark stuff will turn out to just be relativistic artefacts, much like GR shouldn't be the final theory of physics.
     
  16. Dec 1, 2007 #15
    Let us know how he responds to your email. :smile:
     
  17. Dec 1, 2007 #16
    Hi cesiumfrog,

    I agree with you.

    By the way, if I were writing him an email, I think I would also opine that one who theorizes about local deviations in expansion rate bears the responsibility of articulating as to whether local effects are detectable. In particular, should we anticipate observing a non-trivial Hubble flow in the direction of an extremely dense object such as a neutron star, or even towards a regular star?

    Jon
     
  18. Dec 1, 2007 #17

    marcus

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    At one point I think you mentioned your advisor was Susan M. Scott and I carelessly forgot that ANU is at Canberra. Her field would be General Relativity, not cosmology! I corrected my post. Pardon my combination of haste and confused geography.
    But the main point I wanted to make is all the stronger. You can give us a valuable informed perspective on what Wiltshire is doing. I like what you say about warts.

    What I find hopeful at this point is not Wiltshire's line of research but what Pereira and Aldrovandi are doing---a deSitter form of the Strong Equivalence Principle and a deSitter form of the Field Equation: the theory stays elegant in my view, and then Lambda is no longer a free parameter but can be derived from the matter density. They even get roughly the right value for it!
    http://arxiv.org/abs/0711.2274
    I'm looking for someone who can show me the weak points of this paper.
     
    Last edited: Dec 1, 2007
  19. Dec 2, 2007 #18

    George Jones

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    I don't know anything about Wiltshire's arguments, but Wiltshire has a long post today on CosmoCoffee,

    http://cosmocoffee.info/viewtopic.php?p=3084&sid=ae35bb823047f9f71248ac4c27766172#3084

    and he gave a link to slides for a talk that he has given at various places:

    http://www2.phys.canterbury.ac.nz/~dlw24/universe/colloquium.pdf [Broken]
     
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  20. Dec 2, 2007 #19
    According to GR, the 4-curvature of spacetime, the Ricci scalar is proportional to the energy momentum tensor trace. If we neglect CMB and intergalactic gas, there is nothing in the void so the 4-curvature must be zero. That doesn't mean that the whole Riemann tensor is zero though.

    The split of spacetime in 3-space and 1-time is not unique. In the homogeneous cosmology we do the split using coordinates comoving with the matter. If you have voids, that reference system of coordinates is not available so terms like 'expansion in the void' are ill defined, you have to specify expansion in what chosen coordinate system.
     
  21. Dec 2, 2007 #20

    Jorrie

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    Hi Jon, my 2c's worth: Do you think the orbits of planets and stars would be stable if there was another 'force' like the one you postulate? Would a radially in-falling object from infinity fall faster than escape velocity?

    Jorrie
     
  22. Dec 2, 2007 #21
    Hi George Jones, thanks for finding the additional Wiltshire material. Are non-university affiliated people allowed to post questions on Cosmic Coffee?

    Hi Marcus, I agree that Pereira & Aldrovandi's work is interesting, but not to the exclusion of Wiltshire's ideas. You already have a separate thread on that topic. Personally, I struggle to meaningfully understand P&A's math, so it's very difficult for me to comment about it.

    Hi Jorrie, no fair answering a question with a question! I asked whether standard GR theory admits to non-trivial Hubble flows towards highly dense objects. By implication, I assume your answer is "no". But isn't that answer entirely inconsistent with Marcus' and Wallace's statement that of course curvature is "lumpy" at the quasi-local level? The denser an object is, the more dramatically lumpy the quasi-local curvature is. I have not heard an explanation of how purely local effects of gravitation can in aggregate cause an enormous impact the overall expansion rate of a universe that is mostly not gravitationally bound together, without the divergence in local expansion rate being detectible. It's as if standard GR assumes some sort of cosmological "smoothing agent" which allows gravity to aggregate to large scale effects that exceed the summation of observable local effects. (Even if dark energy acts a smoothing agent in a sense, the theoretical problem existed just as much before the effects of dark energy became significant.) I'm not trying to argue one way or the other, but if the answer is simple, could someone please just explain it to me!!! And by the way, Wiltshire and others clearly postulated this concept before I asked about it, so I don't understand why they don't grapple more explicitly with it.

    Since you asked, my guess is that orbits could be stable even in the presence of some amount of locally inward Hubble flow. As the flow carries a body inwards, its transverse momentum would drive it tangentially outwards again, and an equilibrium would be reached. Perhaps that equilibrium point would be at a somewhat smaller orbital radius than it would in the absence of the local Hubble flow. Also, I don't consider the local Hubble flow to be a "force" per se, anymore than the expansion of space is a force.

    Would a radially infalling object fall faster than escape velocity? In the absence of significant transverse velocity, it seems that logically it would. In the same way that spatial expansion delays the arrival of in-falling photons. I'm not claiming that such a result is consistent with observations. I'm just pointing out that GR is a locally-driven theory, and therefore I don't understand how it could cause a certain effect on large scales without causing an appropriately scaled version of the same effect quasi-locally. Surely this isn't a new question in GR, there must be books and papers on the subject.

    If GR did admit to a non-trivial Hubble flow towards a dense object, it seems to me that flow would have a fixed velocity depending only on radial distance from the object. As a particle moves closer, the flow velocity increases. Thus it would model quite differently from direct gravity, which of course imparts only acceleration over time, not velocity per se.

    Side question: What exactly does the term "back-reaction" mean in the sense Wiltshire uses it? I can't find it in any dictionary.

    Jon

    p.s., The more I think about Wiltshire's paper, the more I think he should define "infinite infinity" to be the surface at which the average expansion rate is below escape velocity inside the surface, and above escape velocity outside the surface. That seems more meaningful to me than his somewhat arbitrarily defined surface where average expansion is zero inside. The Friedmann equations indicate that zero is not a very meaningful rate when the average density everywhere is positive.
     
  23. Dec 2, 2007 #22

    cristo

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    Here is a short paper by Wiltshire on, what I presume is, the same topic as the long one linked to above (it mentions that paper in the abstract, anyway!)
     
  24. Dec 2, 2007 #23

    Jorrie

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    Back-reaction

    Hi Jon. I'll leave the bulk of your questions to the competent advisors, just my view on the above: I think it is the fact that the (local) gravitational field itself has energy and hence reacts on itself, causing additional curvature. The Friedmann solution largely ignores this, since it is a smoothed solution. This effect alone can probably not account for the perceived cosmic acceleration, I understand.

    Jorrie

    [Edit]

    PS: Escape velocity of an expanding region (a notion both of us picked up from Prof. Peebles' books, it seems) is quite a slippery concept in cosmology and can lead to all sorts of confusion. As an example, suppose a large spherical region of space (radius R) has a gravitationally bound central region, with empty space around it. How would you measure the radius R at which the surface expansion rate (dR/dt) equals the escape velocity?

    [Edit2]

    Despite the above said, your 'expansion rate equal to escape velocity' radius for FI may be exactly the same as Wiltshire's (in the case of zero Lambda):
    This is essentially what expansion rate at escape speed for a matter-only case means, but let's rather stick to the published definition!

    -J
     
    Last edited: Dec 3, 2007
  25. Dec 3, 2007 #24
    Hi Jorrie,

    Thanks for defining "back-reaction".

    Yes, that's a good question. Maybe Wiltshire is right, that zero velocity is the best surface to measure "finite infinity". It probably represents the "continental divide", where everything on the inside flows into the supercluster eventually, and everything outside doesn't.

    On my question about the possibility of a Hubble flow towards very dense objects -- the only explanation that occurs to me is that maybe the same virial effect which prevents clusters from contracting is the phenomenon which negates most of the "lumpy" expansion rate inside the cluster. Each galaxy's own peculiar motion kinetic energy would virially reduce the amount of spatial contraction it causes. If this is so, however, shouldn't the Friedmann equations need to be modified to take account of virial resistance to deceleration?

    In any event, it still seems that there might be some residual, non-trivial spatial contraction occuring very, very close to superdense objects. Perhaps much closer than any stable planetary orbits around them. That might explain why such an effect has not been directly observed.

    I still think my question demands an answer. For example, if GR admits of no gravitational contraction of space anywhere within gravitationally-bound clusters, then an explanation is required as to how the densest objects within that cluster can possibly contribute their "fair share" towards the average deceleration of universal expansion. Is anyone brave enough to venture an answer?

    Another point that strikes me about Wiltshire's proposition: When we observe a galaxy on the far side of a void, we are observing the past through a future lens... awesome, dude...

    [edit: Further explanation to my "virial smoothing" point: If a particular superdense object has very small peculiar motion, it should experience non-trivial inward Hubble flow. If it has high peculiar motion, it may experience zero local Hubble flow, or even outward flow, depending on its peculiar speed.]
    Jon
     
    Last edited: Dec 3, 2007
  26. Dec 4, 2007 #25

    Jorrie

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    Brave indeed, one needs to be... But what the heck.:wink: GR does not proclaim no contraction of space (whatever that may mean) inside gravitationally bound clusters. If an object is not virially stabilized (say it starts as stationary relative to the center), it will fall in. Whether that means contraction of space, I'm not sure. However, the mass of any object in a gravitationally bound structure adds to the density of the region, which adds to the density of the whole.

    Sorry Jon, this makes no sense to me. Peculiar motions may add to or subtract from[*] the normal Hubble flow, depending on the direction. AFAIK, it has nothing to do with how dense the object under consideration is.

    [*Edit: not meaning influencing the Hubble flow; just influencing the observed cosmological redshift of the object.]
     
    Last edited: Dec 4, 2007
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