Superclusters and Voids - same curvature?

[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

 

[Jorrie]

Hi Jon.

Beyond that [the central observer], 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.

Nope, I don't think so. For the quasi-homogeneous and isotropic scenario with static initial conditions that you described, Newton says that the collapse will [edit] appear to be isotropic in the frame [/edit] of any locally comoving observer inside the 'cloud' (ignoring a possible observable edge and keeping it non-relativistic). No other effects are needed, [edit] provided that one has given enough time for light to have traveled through the whole cloud since t0.[/edit]

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.

Newton dynamics does not hold all the way to the observable universe size, because the FRW metric and Newton are not quite compatible at that size. Also, the static initial conditions that you chose mean that it has a closed geometry (over critical density) for any size.

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.

If you take away all but a spherical collection of stars (anywhere inside the cloud, still many of them, initially static and uniformly spaced), things will remain homogeneous until it becomes relativistic. The only inhomogeneity will be inside the stars. If you include the (now empty space around the cloud), then the total is obviously not homogeneous, but that was not part of the original scenario.

The possibilities 1 to 3 that you listed are largely based on your views that I discussed above. Without agreeing on the correctness of those views, the discussion cannot continue fruitfully, I'm afraid.

Jon, you are again using a 'funny' term (to me at least): "scale expansion factor". What's that? If you meant 'scale factor' or 'expansion factor' (a), it does not make sense in the context you used it.

Jorrie

 

[jonmtkisco]

Hi Jorrie,

Sorry if the term "scale expansion factor" sounds funny to you. Due to Wallace's repeated admonition I feel constrained to minimize use of terms like "Hubble flow" and "expansion of space." I used the term "scale expansion factor" to have the same meaning as a Hubble constant: dot a / a , with the expansion rate being linear with distance from the observer.

For the quasi-homogeneous and isotropic scenario with static initial conditions that you described, Newton says that the collapse will [edit] appear to be isotropic in the frame [/edit] of any locally comoving observer inside the 'cloud' (ignoring a possible observable edge and keeping it non-relativistic).

OK, I didn't realize that a straight Newtonian collapse will appear "Hubble flow-like" (approach rate linear with distance) to any non-central observer (except for the visible edge). So why isn't it correct to interpret this as constituting a de facto (or pseudo-)Hubble scale contraction of a spherical subset of the observable universe? Why would that interpretation be necessarily wrong?

If you include the (now empty space around the cloud), then the total is obviously not homogeneous, but that was not part of the original scenario.

Yes, including the (almost) empty region outside the cloud (as I described it in my last post) is now part of my revised scenario. That's the question I'm asking now: Based on physics as we currently understand it, would we predict that the outside region would behave more like possibility 1, 2, or 3? Or if you think all three are incorrect, then please describe what you think is the most likely behavior for the region outside the cloud.

Jon

 

[Jorrie]

Hi Jon.

I used the term "scale expansion factor" to have the same meaning as a Hubble constant: dot a / a , with the expansion rate being linear with distance from the observer.

I suggest you rather use dot a / a, except that in your hypothetical scenario, there is no well defined a... I guess recession speed/distance ratio is a better option, which will not confuse anyone.

So why isn't it correct to interpret this as constituting a de facto (or pseudo-)Hubble scale contraction of a spherical subset of the observable universe? Why would that interpretation be necessarily wrong?

I don't think it is wrong, provided you pick a large enough subset so that it can be taken as approximately homogeneous and not so large that recession (or in-fall) velocities become relativistic. I think some structure formation studies are done more or less like this, but I'm uncertain of that.

Yes, including the (almost) empty region outside the cloud (as I described it in my last post) is now part of my revised scenario.

Your hypothetical scenario is now the same as if your original 'cloud of stars' had one very dense clump of stars somewhere inside it. You can now still approximate it by Newtonian gravity (within limits), but you can no longer use the homogeneous density approximation, but need to integrate the non-homogeneous http://en.wikipedia.org/wiki/Shell_theory" for a sphere. It is obvious that the FRL metric does not hold and in order to understand this cosmologically, I think you must look at the studies that Wallace referred you to (through the Wiltshire paper). To speculate about it without doing the computations would not be very useful.

Jorrie

 

[jonmtkisco]

Hi Jon.

Your hypothetical scenario is now the same as if your original 'cloud of stars' had one very dense clump of stars somewhere inside it. You can now still approximate it by Newtonian gravity (within limits), but you can no longer use the homogeneous density approximation, but need to integrate the non-homogeneous http://en.wikipedia.org/wiki/Shell_theory" for a sphere. It is obvious that the FRL metric does not hold and in order to understand this cosmologically, I think you must look at the studies that Wallace referred you to (through the Wiltshire paper). To speculate about it without doing the computations would not be very useful.
Jorrie

Hi Jorrie,

The Shell Theory equations seem straightforward enough for regions outside of the sphere; the sphere is treated as a gravitational point source. That is what I had understood.

As far as I can tell, my "possibility #3" is consistent with the mainstream expectation of how an isolated mass is supposed to behave. For example, in their paper "Fractal Approach to Large-Scale Galaxy Distribution" (5/05), Baryshev and Teerikorpi cite the Lemaitre-Toman-Bondi (LTB) model, which is an exact solution of Einstein's dequations and a generalization of the FRW models with a non-zero density gradient. They say:

"The LTB model has been used for understanding the kinematics and dynamics of galaxies around individual mass concentrations. For example, Teerikorpi et al. (1992), and Ekholm et al. (1999) could put in evidence the expected behaviour in the Virgo supercluster: 1) Hubble law at large distances, 2) retardation at smaller distances, 3) zero-velocity surface, and 4) collapsing galaxies at still smaller distances." (p.71)

Of course, observations of our Local Group find results that seem inconsistent with the LTB model. That is the Sandage-de Vaucouleurs (S-V) paradox which Wiltshire refers to. Observations show that the Hubble scale expansion of local galaxies is quite close to the overall Hubble value, seemingly with little or no influence from the gravitation of the obviously significant local clumpiness.

Wiltshire claims that his model gives an "implicit" solution of the S-V paradox. But on further consideration his "solution" is not what I would have expected. The point of the S-V paradox is that less variation from the Hubble rate is observed locally than what is expected to be produced by local clumpiness. Wiltshire seems to be saying that even though "wall observers" like us observe significant quasilocal variations in expansion rates, that the underlying expansion rates are actually identical in voids and clusters, and it is the differences in clocks which distorts our observations. But I would think that doesn't solve the S-V paradox, on the contrary it makes it worse. Wilthire says that the "real" variance in expansion rates is smaller than we observe; but S-V says that the observed variance is already too small. Making the variance smaller only exacerbates the paradox. If anyone understands what Wiltshire really means on this point, I'd appreciate an explanation.

There is another point where I think Wiltshire is trying to duck a possible contradiction. He says that the universe is void-dominated, which seems right. A void-dominated universe should be below critical density and therefore have negative overall curvature. But negative overall curvature would conflict with the WMAP CMB observations. So instead, he proposes that the universe is flat overall, but that our entire observable horizon is inside of a single underdense perturbation which has negative curvature. So we have to go to scales larger than our observable horizon to verify that the universe is indeed flat. While his logic seems sound, I can't help being skeptical about how neatly such a duex ex machina solves an otherwise intractible conflict for him. Essentially he's putting all of his eggs in a single basket which may prove impossible to verify.

It also seems to me that it is just a matter of time before any region of the full universe becomes void-dominated. Even if a region the size of our observable universe starts out somewhat overdense, the voids will expand faster than the bound clusters, and eventually it will be void-dominated and underdense on average. I don't see how the current (supposed) underdensity of our observible universe can be tracked back in any definitive way to prove that our observable universe was initially overdense, underdense, or pretty much exactly at critical density.

Jon

 

[Jorrie]

Hi Jon.

Hi Jorrie,
The Shell Theory equations seem straightforward enough for regions outside of the sphere; the sphere is treated as a gravitational point source. That is what I had understood.

The Shell Theorem works perfectly well inside any spherically symmetrical mass concentration, provided that the conditions are within the weak-field, low-speed (Newtonian) limit. I'm not sure what a relativistic Shell Theorem entails.

I'll leave the rest of your post for Wallace to consider...

Jorrie

 

[jonmtkisco]

Hi Jon.

Your hypothetical scenario is now the same as if your original 'cloud of stars' had one very dense clump of stars somewhere inside it. You can now still approximate it by Newtonian gravity (within limits), but you can no longer use the homogeneous density approximation, but need to integrate the non-homogeneous http://en.wikipedia.org/wiki/Shell_theory" for a sphere. It is obvious that the FRL metric does not hold and in order to understand this cosmologically, I think you must look at the studies that Wallace referred you to (through the Wiltshire paper). To speculate about it without doing the computations would not be very useful.
Jorrie

Hi Jorrie,

The Shell Theory equations seem straightforward enough for a point outside of the sphere; the sphere is treated as a gravitational point source. That is what I had understood.

As far as I can tell, my "possibility #3" is consistent with the mainstream expectation of how an isolated mass is supposed to behave. For example, in their paper "Fractal Approach to Large-Scale Galaxy Distribution" (5/05), Baryshev and Teerikorpi cite the Lemaitre-Tolman-Bondi (LTB) model, which is an exact solution of Einstein's equations and a generalization of the FRW models with a non-zero density gradient. They say:

"The LTB model has been used for understanding the kinematics and dynamics of galaxies around individual mass concentrations. For example, Teerikorpi et al. (1992), and Ekholm et al. (1999) could put in evidence the expected behaviour in the Virgo supercluster: 1) Hubble law at large distances, 2) retardation at smaller distances, 3) zero-velocity surface, and 4) collapsing galaxies at still smaller distances." (p.71)

Of course, observations of our Local Group find results that seem inconsistent with the LTB model. That is the Sandage-de Vaucouleurs (S-V) paradox which Wiltshire refers to. Observations show that the Hubble scale expansion of local galaxies is quite close to the overall Hubble value, seemingly with little or no influence from the gravitation of the obviously significant local clumpiness.

Wiltshire claims that his model gives an "implicit" solution of the S-V paradox. But on further consideration his "solution" is not what I would have expected. The point of the S-V paradox is that less variation from the Hubble rate is observed locally than what is expected to be produced by local clumpiness. Wiltshire seems to be saying that even though "wall observers" like us observe significant quasilocal variations in expansion rates, the underlying expansion rates are actually identical in voids and clusters, and it is the differences in clocks which distorts our observations. But I would think that doesn't solve the S-V paradox, on the contrary it makes it worse. Wilthire says that the "real" variance in expansion rates is smaller than we observe; but S-V says that the observed variance is already too small. Making the variance smaller only exacerbates the paradox. If anyone understands what Wiltshire really means on this point, I'd appreciate an explanation.

There is another point where I think Wiltshire is trying to duck a possible contradiction. He says that the universe is void-dominated, which seems right. A void-dominated universe should be below critical density and therefore have negative overall curvature. But negative overall curvature would conflict with the WMAP CMB observations. So instead, he proposes that the universe is flat overall, but that our entire observable horizon is inside of a single underdense perturbation which has negative curvature. So we have to go to scales larger than our observable horizon to verify that the universe is indeed flat. While his logic seems sound, I can't help being skeptical about how neatly such a duex ex machina solves an otherwise intractible conflict for him. Essentially he's putting all of his eggs in a single basket which may prove impossible to verify.

It also seems to me that it is just a matter of time before any region of the full universe becomes void-dominated. Even if a region the size of our observable universe starts out somewhat overdense, the voids will expand faster than the bound clusters, and eventually it will be void-dominated and underdense on average. I don't see how the current (supposedly) underdensity of our observible universe can be tracked back in any definitive way to prove that our observable universe is overdense, underdense, or pretty much exactly at critical density.

Jon

 

[jonmtkisco]

Hey Wallace,

It's your turn to weigh in here...

 

[jonmtkisco]

Jorrie found the 2005 article http://arxiv.org/PS_cache/astro-ph/pdf/0507/0507364v1.pdf" by A.D. Chernin et al which provides a clear explanation for a model of very local scale expansion which resolves the Sandage-de Vaucouleurs paradox. Apparently this model of cluster formation is referred to as the "Little Bang", a term I had not heard. The model says that only the small core of the Local Group is gravitationally bound, out to a Zero Gravity Surface at 1.5-2 Mpc from the Milky Way - Andromeda barycenter. So pretty much only these two galaxies are gravitationally bound together. The remainder of the local group (including 86-some small galaxies) is not gravitationally bound together, and these outer galaxies are expanding away from us at the general Hubble rate.

This model predicts that the universe is dominated by low mass structures like our Local Group; each such structure contains only a handful of large galaxies. As a result, only these small core clusters are gravitationally bound; clusters and superclusters themselves are not. Other galaxies contained in a cluster probably originated within the Zero Gravity Surface core; the chaotic mix of high peculiar velocities inside the core caused most of the galaxies to exit the core radially. Later the cosmic expansion (including the cosmological constant at larger distances) cooled and normalized exited galaxies' peculiar velocities, and they asymptotically rejoined the cosmic Hubble flow. So today we see these cluster structures which appear to be bound but in fact are mostly expanding at the Hubble rate.

I think this model makes a lot of sense. I would think that it still works with the Wiltshire model, although as far as I can tell it says that the fraction of the volume of the observable universe which is gravitationally bound must be a tiny percentage of the 20-25% figure Wiltshire uses in his paper. I'm not sure if that affects the general outcome of Wiltshire's results...

Chernin defines the Zero Gravity Surface as the surface where "the gravity of the Local Group dark matter and baryons is balanced by the antigravity of the vacuum. Observations show that these are just the distances [1.5-2 Mpc] from which the observed Hubble flow takes start."

They say:

"These considerations suggest that cosmic vacuum may control the dynamics of the observed Universe at both global spatial scales approaching the observation horizon and local scales deep inside the cell of matter uniformity. Because of this, the cosmological expansion may be not only a global phenomenon, but also a local one..."

Very interesting.

Jon

 

[jonmtkisco]

Is anyone on this Forum aware of observational data or theoretical logic which challenges the 'Little Bang' model described in Chernin (et al)'s paper?

The paper says: "low mass groups, like the Local Group, dominate, and the Hubble flow is not significantly disturbed around them." I interpret this to mean that, in general, individual clusters and superclusters are not unitary, gravitationally bound structures. Instead, the largest gravitationally bound physical structures (in general) are individual galaxies and small local groups containing a handful of large galaxies. For example, the gravitational influence of our Local Group, comprised essentially of the Milky Way and Andromeda large galaxies, extends only about 1.5-2 Mpc from its barycenter.

Mainstream estimates of the mass of clusters are mostly based on the virial theorem, which assumes that clusters are in gravitational equilibrium with their virial kinetic energy. But if only multiple individual subsets of clusters are internally gravitationally bound, the virial theorem would not yield an accurate mass estimate for an entire cluster. The cluster's total mass should be somewhat smaller than if it were gravitationally bound. This in turn might indicate that the intra-cluster medium (ICM) contains less dark matter than normally supposed (and perhaps less dark matter than galactic halos contain). Which in turn could require adjusting the LCDM ratios of cold dark matter and baryonic matter for the observable universe as a whole.

[edit: Also requiring an explanation is why most clusters are observed to have a tightly bound core of very hot ICM gas at their physical center. If the physical center of a large cluster is but one of many galaxy group cores in the cluster, then why would the ICM gas be heavily skewed towards that single center, rather than distributed more evenly around each of the galaxy group cores?]

It seems to me that Chernin's model must be very controversial, but I'm not aware of any specific commentary.

And, I haven't seen any other logically compelling solution for the Sandage-de Vaucouleurs paradox.

Jon