Superclusters and Voids - same curvature?

[jonmtkisco]

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.

 

[marcus]

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.

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.

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

 

[jonmtkisco]

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

 

[jonmtkisco]

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

 

[marcus]

Hi Marcus,

If, as you say, spatial curvature can be "closed" within a supercluster,

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

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?

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 don't 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 doesn't 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

 

[jonmtkisco]

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 traveling 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

 

[marcus]

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.
...

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

 

[zankaon]

Modeling with manifolds

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 traveling 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

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.

 

[Wallace]

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.

As marcus suggests, closed universes need not collapse.

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?

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" , 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.

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.

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

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.

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.

 

[jonmtkisco]

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

 

[cesiumfrog]

Reality bumpy. The mainstream standard LCDM is just averaged out. [..] But [..]

Isn't this the area http://arxiv.org/abs/gr-qc/0702082" works in?

 

[marcus]

Isn't this the area http://arxiv.org/abs/gr-qc/0702082" works in?

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

 

[jonmtkisco]

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

 

[cesiumfrog]

Actually, I only know Wiltshire by a paper that I read (and my personal area is neither cosmology nor Sydney ), 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.

 

[cesiumfrog]

But with my correction, I think it's very possible

Let us know how he responds to your email.

 

[jonmtkisco]

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

 

[marcus]

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.

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.

 

[George Jones]

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.

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

 

[smallphi]

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.

 

[Jorrie]

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.

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

 

[jonmtkisco]

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.

 

[cristo]

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!)

 

[Jorrie]

Back-reaction

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

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):

Finite infinity represents a boundary to the region within which space would ultimately stop expanding if its entire future evolution were determined from the local dynamics of the FI region alone; a local, rather than a global statement.

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

 

[jonmtkisco]

Hi Jorrie,

Thanks for defining "back-reaction".

How would you measure the radius R at which the surface expansion rate (dR/dt) equals the escape velocity?

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 occurring 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

 

[Jorrie]

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?

Brave indeed, one needs to be... But what the heck. 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.

[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.]

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.]

 

[SpaceTiger]

The term "Hubble flow" is being greatly abused here and seems to be leading to some confusion. It should only be used to refer to the large-scale expansion of the universe, not infall onto localized overdensities. It is true that spherical overdensities can sometimes evolve gravitationally like a closed, matter-dominated universe, but the resulting motions are said to be peculiar motions (as Jorrie already mentioned) to distinguish them from the large-scale Hubble flow. The spherical approximation isn't a very good one anyhow, as the clusters are generally quite different from spheres.

I would ultimately defer to the GR experts on the "expansion" or "contraction" of space in the vicinity of clusters, but I don't think that those concepts were intended to be so liberally applied to such complex distributions of matter and energy. As smallphi mentioned, the split of spacetime into 3-space plus 1-time is not unique and it should be remembered that these perturbations are embedded in a global Hubble flow.

 

[jonmtkisco]

SpaceTiger,

I would ultimately defer to the GR experts on the "expansion" or "contraction" of space in the vicinity of clusters, but I don't think that those concepts were intended to be so liberally applied to such complex distributions of matter and energy.

Do you have a suggestion on how I can get one or more GR experts to answer the following question:

"Is a hypothetical isolated superdense object (such as a neutron star which is not gravitationally bound to any other nearby object and has no peculiar motion) "detached from the universal Hubble flow" in the sense that the object's gravity causes 'local' space to contract; and if so, what is the mathematical equation for calculating the contraction rate of space at a given small distance from the object?"

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.

...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.]

Jorrie,

Figure 1 of Wiltshire's paper "Cosmic clocks, cosmic variance and cosmic averages" shows a gravitationally bound "virialized region' with zero expansion rate, surrounded by a non-virialized, gravitationally 'collapsing region' of space with a negative expansion rate, which in turn is embedded in the general Hubble flow in which space is expanding. A copy of Wiltshire's Figure 1 is attached.

Surely the contraction of space in the 'collapsing region' is caused solely by the combined gravity of the 'virialized' and 'collapsing' regions. Wiltshire's notion clearly embraces the idea that quasilocal gravity causes contraction of space.

Moreover, surely the zero expansion rate within the 'virialized region' is caused by the virial effect which singlehandedly prevents gravitational collapse in that region. I agree with you completely that the virial effect constitutes nothing other than the summed effect of the individual peculiar motions of the very large number of local matter objects (including gas, dust, dark matter, etc). So logic seems to preclude any explanation for the quasilocal zero expansion rate, other than that peculiar motions of massive objects negate the local gravitational contraction of space.

The region-wide effect must be the summation of the effects of the many individual objects. Therefore, the peculiar motion of an individual object must create a positive expansionary vector in its local space. By deduction, the density of an individual body must contribute to the magnitude of the 'very locally' observable effect.

I'm happy to be convinced this interpretation is wrong, but I'm beginning to wonder whether GR has any accepted conclusion one way or the other.

Jon

 

[SpaceTiger]

Do you have a suggestion on how I can get one or more GR experts to answer the following question:

As marcus said, you might want to try using standard terminology rather than inventing your own. You'll also want to be less argumentative, given your lack of experience in the field and obvious unfamiliarity with the subject matter. Connecting concepts to one another is a good way to understand new material, but if you insist on making these crude analogies a permanent fixture of the dialog, you won't get far talking to trained experts.

"Is a hypothetical isolated superdense object (such as a neutron star which is not gravitationally bound to any other nearby object and has no peculiar motion) "detached from the universal Hubble flow" in the sense that the object's gravity causes 'local' space to contract; and if so, what is the mathematical equation for calculating the contraction rate of space at a given small distance from the object?"

The metric in the vicinity of a neutron star is the Schwarzschild metric, which is static. I've never seen a general relativistic treatment of an evolving spherical overdensity embedded in the large-scale Hubble flow (though it may exist). In the Newtonian limit it behaves much like a closed universe (in the absence of a cosmological constant). This is derived in Gunn & Gott 1972, see the "Classic Papers" sticky in the General Astronomy forum.

 

[Jorrie]

Surely the contraction of space in the 'collapsing region' is caused solely by the combined gravity of the 'virialized' and 'collapsing' regions. Wiltshire's notion clearly embraces the idea that quasilocal gravity causes contraction of space.

There was a long thread on "Is space expanding?" earlier this year, started by Wallace:

The classic test case is this. Imagine you are in an expanding universe and hold a galaxy at rest with respect to you but at a cosmological distance. According to Hubbles law a galaxy at that distance should be receding but you prevent this by using a chain or rockets or something to hold it in place. If you let go of the galaxy, what does it do?

This thread and the link to a Peacock paper point out some misconceptions that may arise out of the notion of expanding space. Without wanting to resurrect that whole debate, it has some bearing on what you asked, so I suggest you read all of that, if you have not done so already.

 

[Wallace]

Yes, and at the risk of being accused of self-promotion, have a read of http://arxiv.org/abs/0707.0380" . If you are still confused about the meaning and mismeanings of expanding space then read the thread Jorrie suggests.

 

[Wallace]

Do you have a suggestion on how I can get one or more GR experts to answer the following question:

"Is a hypothetical isolated superdense object (such as a neutron star which is not gravitationally bound to any other nearby object and has no peculiar motion) "detached from the universal Hubble flow" in the sense that the object's gravity causes 'local' space to contract; and if so, what is the mathematical equation for calculating the contraction rate of space at a given small distance from the object?"

Your use of the concept of expanding or contracting space makes no sense in the context of the question you are asking here, so I don't think your question has a meaningful answer.

'The Hubble Flow' describes how observers in a homogeneous and isotropic expanding Universe see test objects emitting radiation (i.e. galaxies). This process can, if you are careful, be described as the expansion of space, but you need to be careful about what this does and doesn't mean. In particular, if you are dealing with anything that happens inside a galaxy, the intellectual shorthand of expanding (or contracting) space simply doesn't apply.

Again, all of this is explained in the link provided in the previous post.

 

[jonmtkisco]

I've never seen a general relativistic treatment of an evolving spherical overdensity embedded in the large-scale Hubble flow (though it may exist). In the Newtonian limit it behaves much like a closed universe (in the absence of a cosmological constant). This is derived in Gunn & Gott 1972, see the "Classic Papers" sticky in the General Astronomy forum.

OK, I read Gunn & Gott. While it was generally informative about cluster formation (although quite out of date since it precedes LCDM), it says nothing at all about GR effects that might cause space to stop expanding, or contract, within a bound structure. No help there...

Yes, and at the risk of being accused of self-promotion, have a read of http://arxiv.org/abs/0707.0380" . If you are still confused about the meaning and mismeanings of expanding space then read the thread Jorrie suggests.

I'm missing the meaning to your self-promotion reference to the paper "Expanding Space: the Root of all Evil?" Are you one of the authors?

Anyway, I read that paper as well as the "Does Space Expand" thread that Jorrie referenced. Turns out I had already read the paper.

I like the paper because it takes a common sense approach to defining expanding space. Exactly the approach I had understood already, so it's good to confirm that I wasn't confused.

The paper is excellent in explaining why Peacock's "tethered galaxy paradox" is more slight-of-hand than a bona fide flaw in the idea that space expands:

"The motion of the particle must be analysed with respect to its local rest frame of the test particles, provided by the Hubble flow. In this frame, we see the original observer moving at v(rec,0) and the particle shot out of the local Hubble frame at v(pec,0), so that the scenario resembles a race. Since their velocities are initially equal, the winner of the race is decided by how these velocities change with time. In a decelerating universe, the recession velocity of the original observer decreases, handing victory to the test particle, which catches up with the observer." (p.4)

Peacock says that as time approaches infinity, "the peculiar velocity tends to zero, leaving the particle moving with the Hubble flow..." And he says, "... a particle initially at rest with respect to the origin falls towards the origin, passes through it, and asymptotically regains its initial comoving radius on the opposite side of the sky." I note that his use of the term "initially at rest with respect to the origin" is correct but misleading; the particle of course has been given an initial peculiar velocity towards the origin, and that relative velocity will continue after the test clock starts running. One thing that confuses me: I would have thought that as long as the particle's peculiar motion is towards the origin, its peculiar velocity would decelerate -- as above, "peculiar velocity tends to zero..." After the particle passes the origin, its recession velocity (ie., the sum of its residual peculiar motion and its Hubble flow motion) should start increasing again, in order to re-coalesce with the general Hubble flow. But the "Root of all Evil" paper does not describe such an effect; maybe that's because the paper is focused solely on the particle's own rest frame.

In any event, this interesting discussion does not help me understand how the local effects of gravity sum up to the global Friedmann flow. Statements like "FRW simply doesn't apply at local scales" are not very helpful; the fact that the specific FRW solution to the Einstein equations may provide an inaccurate or incomplete local description doesn't mean that the underlying logic of FRW is invalid locally. In GR, any global effect surely must be a summation of local effects, so it has to be possible to describe some kind of mechanics for transitioning from local to global equations. ("Root of all Evil" refers delicately to such a metric as "some kind of chimera of both [Scwharzchildian and FRW like] metrics.)

When opposing "forces" or "effects" (I prefer the latter term) are in play, a motion vector can be described as either (a) two discrete opposing vectors which must be summed, or (b) the single net vector resulting from that sum. I see no reason why (b) should be the preferred description rather than (a). Each description is valid if viewed from its own perspective. As an uninformed, unintentionally obnoxious "newby", I humbly submit that any preference for (b) over (a) must be empirically demonstrated, not merely asserted (even if the preference is virtuously intended to prevent students "more trouble than the explanation is worth...")

Jon

[EDIT 1: The Schwartzchild and FRW metrics actually are quite closely related to each other mathematically, as Pervect pointed out in a thread a while back. I don't see why they should be irreconcilable.]

[EDIT 2: The following excerpt is from the Scientific American article "Misconceptions about the big bang" dated March 2005. I realize that SA is a popular publication, but this article was written by Davis & Lineweaver, who are acknowledged experts on the subject of spatial expansion:

"Is Brooklyn Expanding?
In Annie Hall, the movie character played by the young Woody Allen explains to his doctor and mother why he can't do his homework. "The universe is expanding.� The universe is everything, and if it's expanding, someday it will break apart and that would be the end of everything!" But his mother knows better: "You're here in Brooklyn. Brooklyn is not expanding!"

His mother is right. Brooklyn is not expanding. People often assume that as space expands, everything in it expands as well. But this is not true. Expansion by itself--that is, a coasting expansion neither accelerating nor decelerating--produces no force. Photon wavelengths expand with the universe because, unlike atoms and cities, photons are not coherent objects whose size has been set by a compromise among forces. A changing rate of expansion does add a new force to the mix, but even this new force does not make objects expand or contract.

For example, if gravity got stronger, your spinal cord would compress until the electrons in your vertebrae reached a new equilibrium slightly closer together. You would be a shorter person, but you would not continue to shrink. In the same way, if we lived in a universe dominated by the attractive force of gravity, as most cosmologists thought until a few years ago, the expansion would decelerate, putting a gentle squeeze on bodies in the universe, making them reach a smaller equilibrium size. Having done so, they would not keep shrinking.

In fact, in our universe the expansion is accelerating, and that exerts a gentle outward force on bodies. Consequently, bound objects are slightly larger than they would be in a nonaccelerating universe, because the equilibrium among forces is reached at a slightly larger size. At Earth's surface, the outward acceleration away from the planet's center equals a tiny fraction (10E30) of the normal inward gravitational acceleration. If this acceleration is constant, it does not make Earth expand; rather the planet simply settles into a static equilibrium size slightly larger than the size it would have attained." (p.5)]

 

[Wallace]

One thing that confuses me: I would have thought that as long as the particle's peculiar motion is towards the origin, its peculiar velocity would decelerate -- as above, "peculiar velocity tends to zero..." After the particle passes the origin, its recession velocity (ie., the sum of its residual peculiar motion and its Hubble flow motion) should start increasing again, in order to re-coalesce with the general Hubble flow. But the "Root of all Evil" paper does not describe such an effect; maybe that's because the paper is focused solely on the particle's own rest frame.

Careful, what is meant by 'peculiar velocity tends to zero' is that the magnitude of the velocity goes to zero. You can set the origin to be anywhere, so it doesn't make sense to say anything depends on whether 'the particle's peculiar motion is towards the origin'. If a test particle goes through the chosen origin it will indeed begin to move in the 'opposite' direction from where it started, however to whole time the peculiar velocity will decrease. You've gotten something confused there I think.

In any event, this interesting discussion does not help me understand how the local effects of gravity sum up to the global Friedmann flow. Statements like "FRW simply
doesn't apply at local scales" are not very helpful;

If we couldn't see past the outer reaches of our galaxy, we would never have come up with the FRW solution as being a reasonable way to describe our Universe. The internal dynamics of a galaxy are not governed by anything like an FRW metric.

the fact that the specific FRW solution to the Einstein equations may provide an inaccurate or incomplete local description doesn't mean that the underlying logic of FRW is invalid locally.

What do you mean by 'the underlying logic of FRW'? The FRW metric describes a completely homogeneous and isotropic infinite Universe. For any scale that this is a poor approximation (such as a galaxy) the results obtained using these assumptions are not valid. There is nothing controversial about that statement.

In GR, any global effect surely must be a summation of local effects

GR is a non-linear theory, so the effect of multiple parts is not the sum of the individual components.

so it has to be possible to describe some kind of mechanics for transitioning from local to global equations. ("Root of all Evil" refers delicately to such a metric as "some kind of chimera of both [Scwharzchildian and FRW like] metrics.)

There are various approximations for this. The earliest and simplest is the 'swiss cheese model'. I can't remember if that is mentioned in Root of all Evil, but you could probably find something using google.

When opposing "forces" or "effects" (I prefer the latter term) are in play, a motion vector can be described as either (a) two discrete opposing vectors which must be summed, or (b) the single net vector resulting from that sum. I see no reason why (b) should be the preferred description rather than (a). Each description is valid if viewed from its own perspective. As an uninformed, unintentionally obnoxious "newby", I humbly submit that any preference for (b) over (a) must be empirically demonstrated, not merely asserted (even if the preference is virtuously intended to prevent students "more trouble than the explanation is worth...")

Again, in GR (even in SR) you can't just sum vectors naively. In any case it's not clear what the two 'vectors' you refer to above are?

The whole point of the Root of all Evil paper is that you shouldn't try and combine a local and global view, for instance saying "the self gravity of a galaxy overcomes the expansion of space" treats gravity globally as a geometric effect and locally as a force and introduces the notion that there are two competing effects. Instead that paper argues that there is no expansion to overcome, we simply have gravity and mass and the metric in the region of a galaxy has no major component that looks like an 'expansion'.

 

[jonmtkisco]

If a test particle goes through the chosen origin it will indeed begin to move in the 'opposite' direction from where it started, however to whole time the peculiar velocity will decrease.

Thanks Wallace, I agree.

What do you mean by 'the underlying logic of FRW'? The FRW metric describes a completely homogeneous and isotropic infinite Universe. For any scale that this is a poor approximation (such as a galaxy) the results obtained using these assumptions are not valid.

By 'the underlying logic' I mean that local expansion will slow, stop, or go negative, depending on the local density. Whether the tendency to do so follows the normal FRW equation is another matter.

In any case it's not clear what the two 'vectors' you refer to above are?

The same things you describe as "the two competing effects": gravity and the expansion of space.

The whole point of the Root of all Evil paper is that you shouldn't try and combine a local and global view, for instance saying "the self gravity of a galaxy overcomes the expansion of space" treats gravity globally as a geometric effect and locally as a force and introduces the notion that there are two competing effects. Instead that paper argues that there is no expansion to overcome, we simply have gravity and mass and the metric in the region of a galaxy has no major component that looks like an 'expansion'.

Well yes, I know the paper says that. That's the one section of the paper that I have trouble accepting. Pretty much the rest of the paper seems right to me.

Wallace, here are two more examples of why I think that the "all or nothing" view of expansion doesn't reflect reality:

1. Consider a galactic cluster today. Let's start with the surface which defines the outer boundary within which matter infall will occur (Wiltshire's "finite infinity"). Now run time backwards for that cluster until shortly after inflation, when the outer boundary of the overdense perturbation which coincides with the cluster outer surface was, say, the size of a grapefruit. The grapefruit contains essentially all of the matter that will be part of the future of the cluster. Obviously, density is extremely high within the grapefruit -- many orders of magnitude higher than in the present cluster.

What do we observe? While the matter within the perturbation grapefruit is vigorously collapsing gravitationally, the cluster matter in its entirety is expanding at a dramatic rate. Within a period of, say, 5GY, the grapefruit will expand to a volume of around E+71 cubic meters. By that time, evidence of gravitational collapse will also have appeared in the form of galaxies, stars, etc. What mathematical metric describes a gravitationally bound collection of matter which is collapsing gravitationally but expanding rapidly at the same time? I submit that the only reasonable explanation is that gravity is acting in direct opposition to the expansion of space itself. In the early universe, the expansion rate outruns the rate of gravitational collapse. Eventually the volume within the cluster outer surface roughly stabilizes, at a time when the density has dropped precipitously and the Hubble expansion rate has fallen even more. By that time, peculiar virial motion probably has superseded the Hubble expansion of space as the dominant anti-collapse vector.

2. Consider Wiltshire's Figure 1 portraying a cluster's outer boundary surface (finite infinity). As shown in his figure, the region near finite infinity experiences positive expansion, while somewhat closer to the center is a surface where expansion velocity is zero. I submit that when an observer moves outwards past the surface of zero expansion, there will be a gradual increase in the expansion rate, starting at zero and increasing (towards some more outward surface) to the average Hubble flow expansion rate. Clearly, the "all or nothing" proposition does not apply within this region. The gradual increase in expansion rate as one moves outward must be the result, again, of a contention between opposing effects. As the effect of the cluster's gravity grows weaker with distance, the expansion effect of the underlying Hubble flow becomes more prominent and eventually dominates. There's really nothing surprising about that.

If these examples aren't clear to you, I can explain further. I think these examples demonstrate that contention between gravity and expansion is an expected condition throughout the universe. If there is no mathematical model for how to calculate the local result of this contention, then we'd better get to work.

Jon

 

[Wallace]

By 'the underlying logic' I mean that local expansion will slow, stop, or go negative, depending on the local density. Whether the tendency to do so follows the normal FRW equation is another matter.

I can think of no sensible definition for the term 'local expansion of space'? 'Local' in GR is a somewhat slippery term (Chris Hillman can give a more precise description if needed), but in rough terms means a region around a point that is small enough to be described by a Minkowski metric, this is a fundamental property of the equivalence principle. It therefore makes no sense to use the phrase 'local expansion of space'. If you disagree you will have to very carefully define what you mean.

The same things you describe as "the two competing effects": gravity and the expansion of space.

Eeek! The 'expansion of space' is nothing more than an intellectual shorthand, or metaphor, for thinking about how the way the FRW solution behaves. It is NOT a force, or anything else that CAUSES things to happen. It is the RESULT of the way in which gravity works on material in a homogeneous, isotropic, expanding Universe. To consider that gravity 'competes' with the expansion of space is akin to asking how the acceleration of a body competes with it's velocity, or some other ill-posed statement.

I assure you I've never suggested that gravity and 'the expansion of space' compete!

Your point 1. is a strawman argument, I've no idea what you are arguing against? You describe my view as an 'all or nothing' approach? I have not idea what you mean by that or how any of what you described argues against what I've been explaining?

Have a read of the structure formation section of any cosmology textbook. If you have access to Peacock 'Cosmological Physics' that would be particularly good. There are three phases of collapse of an object, turnaround, collapse and virialisation, so look for those concepts. For the most part you've grasped the basics of this, based on your point 1., but it is important in trying to communicate with others that you use the correct terminology. None of this is in opposition to anything I've been trying to explain.

2. Consider Wiltshire's Figure 1 portraying a cluster's outer boundary surface (finite infinity). As shown in his figure, the region near finite infinity experiences positive expansion, while somewhat closer to the center is a surface where expansion velocity is zero. I submit that when an observer moves outwards past the surface of zero expansion, there will be a gradual increase in the expansion rate, starting at zero and increasing (towards some more outward surface) to the average Hubble flow expansion rate. Clearly, the "all or nothing" proposition does not apply within this region. The gradual increase in expansion rate as one moves outward must be the result, again, of a contention between opposing effects. As the effect of the cluster's gravity grows weaker with distance, the expansion effect of the underlying Hubble flow becomes more prominent and eventually dominates. There's really nothing surprising about that.

Again, you're on the right track here but you've missed the point about expansion of space. It is the RESULT of how gravity acts on that over density. To state things simply, we don't have an equation with a 'gravity' term and an 'expansion of space' term. What we have is an equation that describes how matter and gravity interact. Once we've solved this equation we can find it convenient to point to some behavior of the solution and say 'that is the expansion of space', but it makes no sense to add an extra term into the equations to describe this, since it is already there!

Gravity (and the initial conditions) CAUSE the expansion of space, they don't fight against it.

 

[jonmtkisco]

I can think of no sensible definition for the term 'local expansion of space'?

...but it is important in trying to communicate with others that you use the correct terminology.

To state things simply, we don't have an equation with a 'gravity' term and an 'expansion of space' term. What we have is an equation that describes how matter and gravity interact.

Hi Wallace,

The verbal arm-waving you use in your notes conveys little substance, just vague generalities. Telling me that I'm wrong or confused doesn't add to the substance. I can't tell whether you are drawing distinctions that matter, or just philosophical preferences for how you like to visualize these theories.

The point of my examples was simply to demonstrate that the effects of gravity and expansion directly interact and contend with each other at a quasi-local level. My terminology "quasi-local" has the same meaning Wiltshire ascribes to it. My point is that there are real-life examples where the expansion rate in or near a gravitationally bound object takes on an "intermediate rate", between the net-zero expansion of a bound galaxy and the normal, average Hubble flow of the universe. If you agree with that point, can't you just say "I agree" rather than making contentious comments like "I have no idea what you're arguing against?"

I made my point in response to the conclusory statements in the "Root of all Evil" paper:

"One response to the question of galaxies and expansion is that their self gravity is sufficient to 'overcome' the global expansion... However, this suggests that on the one hand we have the global expansion of space acting as the cause, driving matter apart, and on the other hand we have gravity fighting this expansion... There is no expansion for the galaxy to overcome, since since the metric of the local universe has already been altered by the presence of the mass of the galaxy."

As my examples demonstrate, quasilocal space clearly is affected by the contending effects of expansion and gravity. Expansion is the RESULT of initial conditions; gravity is the RESULT of local curvature of space caused by mass-energy. The fact that both constitute RESULTS does not make their contention imaginary. At best, one can argue (as that paper seems to), that quasi-local effects are the result of a "netting" of expansionary and contractive effects. Insisting loudly that the result must be considered only in "net" form and not as an interaction of two contending effects strikes me as a silly distinction without a difference. It may win relativity "Inquisition" quasireligious debating points, but it doesn't help us understand or measure the underlying sources of the contending effects.

Let's assume for the purposes of discussion that there are not two "contending" equations, instead there is only one "net" equation. OK, so what is different as a result? Does that one equation provide for the possibility of a quasilocal net contraction of space towards superdense objects, or not? That was my original question. I have already agreed that there is no net contraction of space within quasilocal regions which are at equilibrium due to virial effects (peculiar motion). So at most, any quasilocal net contraction of space must be very close to the superdense object, where gravitational influence would have its best opportunity to outweigh the virial influence (due to the inverse square law).

I read both the Peacock and Peebles chapters on expansion and collapse of galaxies and clusters. I think it's all consistent with what I already said. I didn't find any "correct terminology" there that would make my statements clearer than they already are.

Jon

 

[Wallace]

Hi Wallace,

The verbal arm-waving you use in your notes conveys little substance, just vague generalities. Telling me that I'm wrong or confused doesn't add to the substance. I can't tell whether you are drawing distinctions that matter, or just philosophical preferences for how you like to visualize these theories.

The point of my examples was simply to demonstrate that the effects of gravity and expansion directly interact and contend with each other at a quasi-local level. My terminology "quasi-local" has the same meaning Wiltshire ascribes to it. My point is that there are real-life examples where the expansion rate in or near a gravitationally bound object takes on an "intermediate rate", between the net-zero expansion of a bound galaxy and the normal, average Hubble flow of the universe. If you agree with that point, can't you just say "I agree" rather than making contentious comments like "I have no idea what you're arguing against?"

Hmmm, if I don't understand what you've written, surely it is better to say so than to blindly agree to a statement I don't understand the meaning of! As to your other accusations, I assure you that it is crucially important to use the same meaning of words as everybody else does in physics and it is not mere pedantry to point that out. It is impossible to communicate if we all invent our own meaning for words.

I made my point in response to the conclusory statements in the "Root of all Evil" paper:

As my examples demonstrate, quasilocal space clearly is affected by the contending effects of expansion and gravity. Expansion is the RESULT of initial conditions; gravity is the RESULT of local curvature of space caused by mass-energy. The fact that both constitute RESULTS does not make their contention imaginary. At best, one can argue (as that paper seems to), that quasi-local effects are the result of a "netting" of expansionary and contractive effects. Insisting loudly that the result must be considered only in "net" form and not as an interaction of two contending effects strikes me as a silly distinction without a difference. It may win relativity "Inquisition" quasireligious debating points, but it doesn't help us understand or measure the underlying sources of the contending effects.

Once again you are being unnecessarily unpleasant, how on Earth could my posts be construed as being a "quasireligious (sic) Inquisition"!? Surely making this statement is unhelpful to the discussion!

The root of the problem here is the you are interchangeably using the terms 'expansion' in a general sense and 'the expansion of space'. It may seem like a pedantic difference to you, however the entire problem with previous debates about the expansion of space was that people each had their own sense of what that meant that was different to others and were therefore unable to properly discuss the issue. That is the intent of 'Root of all Evil', to formulate a precise framework for the meaning of expanding space. If you re-define that meaning, but keep the terms the same, then of course we will disagree!

Let's assume for the purposes of discussion that there are not two "contending" equations, instead there is only one "net" equation. OK, so what is different as a result? Does that one equation provide for the possibility of a quasilocal net contraction of space towards superdense objects, or not? That was my original question. I have already agreed that there is no net contraction of space within quasilocal regions which are at equilibrium due to virial effects (peculiar motion). So at most, any quasilocal net contraction of space must be very close to the superdense object, where gravitational influence would have its best opportunity to outweigh the virial influence (due to the inverse square law).

Of course the equations of GR allow for an over density to collapse to a virilised object, they would be pretty useless if they didn't! The equations tell you everything you need to know. The problem conceptually comes about when AFTER solving the equations that determine what happens to a collapsing over dense lump, you add ad hoc concepts about competing effects of gravity and 'expansion of space'. Once again, I re-iterate that the expansion of space does nothing but is nothing more than an intellectual shorthand to understand the results. Of course the GR equations determining the collapse of an overdensity will be influenced by the 'local' (in a very loose sense) conditions, such as the size of the overdensity and how overdense it is, as well as 'global' (in a loose sense) conditions such as the net expansion rate, mean density, etc etc.

The point is that everything has already been considered by gravity, so it is confusing and misconceive to put the self gravity of an overdensity and 'the expansion of space' in opposition.

I read both the Peacock and Peebles chapters on expansion and collapse of galaxies and clusters. I think it's all consistent with what I already said. I didn't find any "correct terminology" there that would make my statements clearer than they already are.

Jon

You need to understand that just because your statements are clear to YOU they are not neccessarily clear to everyone else! It's good to hear that you've read Peacock and Peebles.

 

[jonmtkisco]

The equations tell you everything you need to know... Of course the GR equations determining the collapse of an overdensity will be influenced by the 'local' (in a very loose sense) conditions, such as the size of the overdensity and how overdense it is, as well as 'global' (in a loose sense) conditions such as the net expansion rate, mean density, etc etc.

Hi Wallace,

I'll skip the nonsubstantive stuff and get back to the question.

Since the GR equations tell us everything we need to know... Do they tell us that space can contract quasilocally very close to a superdense body?

Jon

 

[Wallace]

Hi Wallace,

I'll skip the nonsubstantive stuff and get back to the question.

Since the GR equations tell us everything we need to know... Do they tell us that space can contract quasilocally very close to a superdense body?

Jon

The GR equations do not contain the concept of expanding or contracting space. This I think is the key point. This concept is an intellectual shorthand that is useful if it is properly defined, but you won't find this phrase used much (if at all) in textbooks or formal descriptions of GR. The only context in which the phrase 'expanding space' is commonly used is the FRW solution, rather than solutions that deal with locally collapsing spherically symmetric bodies.

So the best answer I can give to your question is that it is, unfortunately, not a well posed question. I don't mean that as a criticism, but you are asking a question that doesn't have a meaningful answer.

We can of course talk meaningfully about what GR does predict will happen to a collapsing body, but there is no sensibly defined 'contraction of space' in this situation.

I think it is important for me to point out that Wiltshires use of expanding and contracting space is not standard. I think this is probably a root cause of the miscommunication here, in that you've been taking Wiltshire's definitions, which he is pretty much alone in using. One of the problems I have with Wiltshire's paper (I've discussed this paper with him in the past) is precisely his use of the term. Again it is not a pedantic point, his whole proposal revolves around imbuing 'space' with energy and the capacity to do work in a way that is not generally accepted. I think I need to make the distinction between the standard use of GR and Wiltshire's use. Of course Wiltshire may well be right, but that remains to be seen. By his own admission he hasn't demonstrated that the effect he suggests inhomogeneities have on observed parameters is any where near big enough to explain dark energy.

In principle I guess my view of GR is more Machian than Wiltshire's. Space is only as 'real' as magnetic fields, the curvature of space, like the density of field lines, explains how mass, in the case of gravity, and charges, in the case of magnetism, interact. What I think Wiltshire does, to some extent, is take the solution, notice the curvature of space, and then suggest additional effects due to this. This is akin to working out the way two charges are interacting, then taking the field lines that could be determined to exist and then suggesting that those field lines do something additional. This is a mistake since the effects of magnetism have already been taken into account in the original solution.

This is an overly simplistic argument against Wiltshire and is somewhat unfair, but in a loose sense I think that's what my problems with his paper boil down to.

 

[jonmtkisco]

We can of course talk meaningfully about what GR does predict will happen to a collapsing body, but there is no sensibly defined 'contraction of space' in this situation.

Hi Wallace,

OK, in the interest of getting past semantics, I will rephrase my question to try to get at the same point.

Imagine a hypothetical isolated spherical cluster made up of one trillion neutron stars which are gravitationally bound together. Each neutron star is equidistant from its nearest neighbors. They start out with no peculiar motion.

This cluster will begin to collapse on itself gravitationally. Which of the following answers best describes the initial collapse of the cluster, as observed from the single neutron star which is at the exact center of the cluster:

1. All of the stars accelerate with peculiar motion toward the center star, and observed velocities at each point in time are roughly equal for all of the stars, without regard to distance of any observed star from the center. (or in any event, the most distant stars do not attain higher velocities than the nearer stars, at each point of elapsed time.)

2. All of the stars become less distant from each other as time elapses; the approach velocity tends to be proportional to distance from the center (i.e., the stars furthest from the center appear to approach much faster than stars near the center).

3. A combination of (1) and (2).

The experiment ends before any of the stars collide with each other or attain substantial transverse or rotational velocities. Of course, the central observer will need to wait until the light arrives from the most distant stars before evaluating the results.

Jon

 

[Wallace]

1. All of the stars accelerate with peculiar motion toward the center star, and observed velocities at each point in time are roughly equal for all of the stars, without regard to distance of any observed star from the center. (or in any event, the most distant stars do not attain higher velocities than the nearer stars, at each point of elapsed time.)

As much as you would like to dismiss things at will as 'semantics' your use of 'peculiar velocity' makes no sense here. You can't use terms at will and expect that communication will be clear. Peculiar velocity is a term that is used to define the variation in the recession velocity of a distant galaxy from the expected recession velocity from the Hubble Law. In your thought experiment there is no Hubble flow and hence no sensibly defined peculiar velocity.

In any case the case 1. does not describe the situation. There is clear spherical symmetry here and a true centre of the cloud. Observers on different start would see the distant and velocity law differently, and for all but the central observer the law would be anisotropic. In principle an observer on one of the start could work out what their radius from the centre is.

2. All of the stars become less distant from each other as time elapses; the approach velocity tends to be proportional to distance from the center (i.e., the stars furthest from the center appear to approach much faster than stars near the center).

Remember that each observer can only measure the relative velocity between them and another body along the line of site to that object, so each observer couldn't directly observer how quickly another star was moving towards the centre. Of the top of my head I'm not sure if the stars closer to the centre or the edge will accelerate at a greater rate (my intuition and back of the envelope calculation disagree!) but there will be a difference.

3. A combination of (1) and (2).

definitely (2) and not a combination.

Again I'd like to state that you can't simply dismiss whatever you like as 'semantics'. It's clear we've made progress here, largely by aligning the language used to describe the underlying concepts.

 

[Jorrie]

Of the top of my head I'm not sure if the stars closer to the centre or the edge will accelerate at a greater rate (my intuition and back of the envelope calculation disagree!) but there will be a difference.

If the 'star cloud' started statically, the stars closest to the edge will have greater radially inward acceleration, as measured by a central observer, hence they will always move faster radially, I think.

 

[Wallace]

Yes you and Jon are right, the stars at the edge will have a greater velocity (in the rest frame of the centre of the cloud) than the ones nearer the centre. Don't know why I raised the possibility of the opposite, fuzzy thinking late at night I think!

 

[Jorrie]

I predict Jon's next question may be: "this is the same as the time-reversed Friedmann (contracting space), so why does the Friedmann cosmology not hold in this collapsing cloud case?" As I understand it, it may be the case if the 'cloud' is larger than the observable universe and is collapsing, but I'm not sure.

 

[jonmtkisco]

Good guess Jorrie,

That's close to what my next question is.

However, I'm going to start from the assumption that the Friedmann equation isn't accurate if applied to a nonhomogeneous, quasilocal region which is much smaller than the observable universe.

I am trying to understand whether the unadulterated quasilocal gravitational collapse of a set of massive objects will mimic one of the key attributes of a (reverse) Hubble contraction: that, as a factor of elapsed time, the approach velocity varies (precisely or roughly or somewhat) in proportion to distance from the observer.

Now, it seems to me that if ONLY a centrally located observer will observe this phenomenon isotropically, then it is best to consider this to be a form of peculiar motion. Conversely, if non-central observers (excluding perhaps observers on the outer edge of the collapsing sphere) observe SOME DEGREE of this phenomenon (i.e., they observe other stars approaching them somewhat isotropically at velocities somewhat proportional to distance from them) then this might also include an element of (reverse) Hubble contraction. It seems possible to me that observations by a non-central observer might indicate a combination of peculiar motion towards the center, and (reverse) Hubble contraction.

If the set of stars I described tends to shrink in scale while the distances between each neighboring star tend to remain equal (but declining as a function of time), then I would consider it to be a (reverse) Hubble scale contraction.

If, on the contrary, the outermost stars tend to "crowd in" on their inward neighbors due to higher local acceleration rate in the outer "shells" of the cluster, then I would view this as "normal" gravitational peculiar motion.

I think it's OK to use the term "peculiar motion" to distinguish it from Hubble-like scale expansion/contraction effects. For the purposes of discussion, we can just assume that the Hubble expansion outside the cluster is zero.

Jon

 

[Wallace]

The outer stars would 'crowd in' in the way you suggest. This process you describe wouldn't look like a collapsing Universe that is homogeneous and isotropic to any of the observers in the cloud (including the central observer). Clearly the flow is isotropic to the central observer but it wouldn't follow a Hubble law as the infall velocity is not a linear function of radius from the centre.

 

[jonmtkisco]

Hi Wallace,

Well that's a definitive answer.

In your opinion, then is there no circumstance in which a (reverse) Hubble-like contraction can occur in a quasilocal region of space (assuming that the overall Hubble flow of the universe is zero)?

Is there any circumstance in which a Hubble-like expansion can occur in a quasilocal region of space if the overall Hubble flow of the universe is zero?

Jon

 

[Wallace]

I could think of some very contrived situations, but nothing in which the self gravity of the over-dense lump is important, so say for test particles in deSitter space peculiar velocities are very quickly damped. This is not in the spirit of your question though, since this effect is due to the global properties of the space, not properties of the local region of the over-density.

It's hard to completely rule something out in the way you request (i.e. 'no circumstances') but certainly this doesn't occur in our Universe, at least in the way we understand it.

It's hardly surprising, the Hubble flow is a result of the Friedman equations which are derived and applicable only for a isotropic and homogeneous Universe. Of course the results of this won't apply if these assumptions don't hold. It's like asking if an object traveling on a ballistic trajectory subject to Newtonian gravity obeys the same result as a ball on a spring. Both these situations in Newtonian physics obeys the same laws, but have different conditions and therefore different solutions.

I'm not quite sure what this line of questioning is getting at? What would it mean either way if a collapsing or expanding cloud did or didn't look like a Hubble flow? What is the significance of this question in relation to any broader questions? Again, I'm not critising, I just don't understand the motivation behind your question. Perhaps if you make that clear it would help.

You may be interested in work that people do looking at the very local Hubble flow (where by very local they generally mean less than about 3 Mpc or so from us). There is a thought that the local flow is 'colder' than expected, in that the expectation is that in this local region we shouldn't really see a Hubble flow due to it being swamped by local motions, however we do see a Hubble flow, with less deviations than expected, with the slope of the Hubble law the same as the global one. It's likely that this problem is more to do with intuition failing (i.e. this should have been expected in the first place) rather than something wrong with the standard model, but it's difficult to calculate structure formation and velocities at these scales so the situation isn't clear.

This issue is mentioned in Wiltshires paper, under the name Hubble-Sandage-deVacoulers paradox. If you follow the references he gives you should find some papers on this issue.

 

[Jorrie]

...This process you describe wouldn't look like a collapsing Universe that is homogeneous and isotropic to any of the observers in the cloud (including the central observer). ... but it wouldn't follow a Hubble law as the infall velocity is not a linear function of radius from the centre.

Are you sure about this? After all, the acceleration is linear with distance from the center, for as far as a Newtonian approximation holds. Hence the instantaneous infall speeds will be linear with distance in the central observer's frame.

One can actually say that in the frame of any internal observer that is falling with the stars, the instantaneous (negative) recession speeds will be linear with distance. What is observed at any time by such observers will probably not be 'Hubble-like' because of the speed of light time delay. [Edit] On a 2nd thought, the time delay does not matter; the Doppler shift should look 'Hubble-like' at all times, because it is a function of the difference in relative speed at emission and reception times only. I understand that it is not the same as the expanding universe in reverse, but there are intriguing similarities![/edit]

Or am I missing something crucial here?

 

[jonmtkisco]

Hi Jorrie,

I think you are correct that from a central observer's vantage point, the "peculiar acceleration of gravity" will cause instantaneous infall speeds to remain linear with distance as time passes.

Beyond that, logic still seems to me to require that in addition to the gravitational collapse you described, there must be a second "overlay" effect of a quasilocal (Hubble) scale contraction factor within the hypothetical cluster.

Hypothetically, if the same cluster were enlarged (adding more stars) to a size equal to our observable horizon, the observable universe would be above critical density and FRW would calculate a global scale contraction factor.

If hypothetically, the size of the cluster were then reduced repeatedly by eliminating successive outer shells (layers) of stars, at some point the observable universe would no longer qualify as "homogeneous", and we would no longer trust in the FRW equations.

At that point, we should observe one of three possibilities:

1. The observable universe at all quasilocal regions outside of the cluster will have the same scale expansion factor, equal to the average scale expansion factor calculated by the FRW equation; notwithstanding that the universe no longer qualifies as "homogeneous".

2. The observable universe at all points outside outside the cluster will have the same scale expansion factor (which might be positive, zero or negative), which bears no known relationship to the FRW equation; we have no theoretical solution currently for calculating that expansion factor.

3. The observable universe outside the cluster has a scale expansion factor which will vary in different quasilocal regions, based on distance from the center of the cluster. The scale expansion factor is negative close to the outer surface of the cluster; it approaches zero asymptotically at greater distances from the cluster. The rationale for this possibility is that gravity imparts the negative acceleration to the scale expansion factor, and since the strength of gravity diminishes with distance, so does the quasilocal negative acceleration of the scale expansion factor.

For the purposes of this hypothetical, assume that all space outside the cluster is essentially empty, except for a relatively small number of separate isolated galaxies which enable us to measure redshift and luminosity at various distances. And lambda = 0.

Anyone want to pick one of the above three choices and defend the logic? Or construct an additional possibility that I haven't captured? No change to, or critisism of, the factual scenario I hypothesized is allowed.

Jon