Is the expansion of the Universe limited to voids?

[Rolando]

In standard cosmology, the Hubble redshift in the light from distant galaxies is interpreted as due to an expansion of space. However, it is also said that within "gravitationally bound systems" up to the size of clusters and superclusters of galaxies, there is no such expansion. This means that the expansion occurs only within the voids between these.

 

Now, I have two questions:

 

First, how this is meant to be understood within the standard Big Bang cosmology. If we assume that only 0.1% of the volume of the Universe is filled with gravitationally bound systems, while the remaining 99.9% are voids, there was no space for voids when the age of the Universe was less than a tenth of what it is now. Thus, the rules must have been different then, in order to allow also gravitationally bound systems to expand.

 

Second, are there any astronomical studies that have shown voids to expand (distant voids being smaller)?

 

I would be grateful for explanations and for refernces to relevant papers.

Edited July 31, 2011 by Rolando

[Widdekind]

According to the book A Journey into Gravity & Spacetime, by J.A.Wheeler, "mass tells space-time how to curve; and, space-time tells mass how to move". Therefore, if masses are not moving apart -- i.e., they are 'gravitationally bound' -- then space-time is not "telling" them to expand apart. Er go, the "rubber sheet", of the space-time fabric, between gravity-bound objects, is non-expanding. Only the low-density, inter-galactic voids of deep space represent expanding, or stretching, space-time fabric.

Edited July 31, 2011 by Widdekind

[Rolando]

Er go, the "rubber sheet", of the space-time fabric, between gravity-bound objects, is non-expanding. Only the low-density, inter-galactic voids of deep space represent expanding, or stretching, space-time fabric.

 

Probalby you mean that the "rubber sheet" of the space-time fabric within gravity-bound objects is non-expanding.

Then we agree, but this was just the preamble to the questions.

 

There is a paper by Cooperstock, Faraoni and Vollick ”The influence of the cosmological expansion on local systems” (http://arxiv.org/PS_cache/astro-ph/pdf/9803/9803097v1.pdf). On p.4 they say: ”In this paper, we assume that homogeneous isotropic expansion is actually universal and we analyze the consequences of this assumption.” This means that they assume gravitational binding not to be the decisive factor. However, it seems to me that they do not actually live up to this assumption. They tacitly assume that at least the instruments of measurement (i.e., the standards of comparison) do not expand. If even these expanded, the expansion would not be observable.

 

 

Edited July 31, 2011 by Rolando

[Iggy]

First, how this is meant to be understood within the standard Big Bang cosmology. If we assume that only 0.1% of the volume of the Universe is filled with gravitationally bound systems, while the remaining 99.9% are voids, there was no space for voids when the age of the Universe was less than a tenth of what it is now. Thus, the rules must have been different then, in order to allow also gravitationally bound systems to expand.

I think "void" is a relative term. Some areas of the universe, the majority to be sure, have a current density below the critical density,

 

[math]\rho_c = \frac{3 H^2}{8 \pi G} [/math] ^(#1)

 

of their local area, and they have a tendency to expand. Other areas have a density above the critical density and they will want to collapse. In the past the critical density was no doubt different and the actual density was different, but I'm sure there still would have been a density inhomogeneity where some areas were above the critical density of the time and others below.

 

 

#1: ...where lambda is zero and H is the recession velocity in the area under consideration

[Widdekind]

Probalby you mean that the "rubber sheet" of the space-time fabric within gravity-bound objects is non-expanding.

Then we agree...

 

To clarify, yes, the space-time fabric, interior to a gravity-bound system of "objects" (e.g., stars, galaxies) is non-expanding.

 

Some of those "objects", e.g. measuring devices, are electro-chemically-bound, by direct atomic & molecular bonds. Evidently, directly "linking" atoms & molecules together, into macroscopic "objects", also imparts a "viscous drag", of that matter, into space-time, that also stops the latter from stretching.

[Rolando]

When the Hubble redshift still was interpreted as a Doppler shift (galaxies rushing away from each other within a pre-existing space), there was nothing that would suggest any local expansion. Neither measurement devices nor galaxies were assumed to expand, and for galaxy clusters it came as a surprise that they do not contain enough mass to account for their cohesion.

 

The Doppler interpretation was abandoned when the CMBR had been discovered. The FLRW-models predict a monopole anisotropy in this radiation. Such an anisotropy was not seen. Subsequently (I am not aware of any other reason), the expansion came to be attributed to space as such. This leads to the delimitation problem that bothers me, but which often goes unnoticed.

 

If the problem is noticed, the limit is often drawn at the scale of galaxy clusters (gravitationally bound systems). There is no expansion at any smaller scale. However, this would be incompatible with the Big Bang paradigm at early times, when the size of the Universe was not yet large enough for housing any voids.

 

Iggy mentioned the possibility of drawing the limit between regions below and above the critical density. This appears to me more reasonable, but the critical density does not have this function in the standard paradigm. It is also not immediately clear how a place-specific matter density should be defined. The "critical gravitational potential" is well-defined and could do the same job, but it also lacks this function in the standard paradigm.

 

It has also been assumed that the expansion is universal, but in these cases, the effects on the measuring devices and standards have been overlooked. Truly universal expansion of space would not be observable. A redshift could be explained as due to a universal contraction of space, if it is assumed that light (moving along null-geodesics) is not affected, but I do not wish to argue for such a model.

[michel123456]

Rolando, I like your questions very much. Where were you all this time?

 

(...)It has also been assumed that the expansion is universal, but in these cases, the effects on the measuring devices and standards have been overlooked.

I suppose so.

Truly universal expansion of space would not be observable.

I am not sure. Since the Speed of Light is constant, over large distance a linear delay is produced that may authorize to observe it, especially if expansion is not linear.

[Iggy]

When the Hubble redshift still was interpreted as a Doppler shift (galaxies rushing away from each other within a pre-existing space), there was nothing that would suggest any local expansion. Neither measurement devices nor galaxies were assumed to expand, and for galaxy clusters it came as a surprise that they do not contain enough mass to account for their cohesion.

 

The Doppler interpretation was abandoned when the CMBR had been discovered. The FLRW-models predict a monopole anisotropy in this radiation. Such an anisotropy was not seen. Subsequently (I am not aware of any other reason), the expansion came to be attributed to space as such. This leads to the delimitation problem that bothers me, but which often goes unnoticed.

Your description of the history does not sound very familiar to me.

 

A doppler shift interpretation and a metric expansion interpretation should be different coordinate choices for the same situation. Whichever way you look at it you should get the same physical outcome. Both interpretations are valid. A couple of articles saying this...

 

Are galaxies really moving away from us or is space just expanding?

 

This depends on how you measure things, or your choice of coordinates. In one view, the spatial positions of galaxies are changing, and this causes the redshift. In another view, the galaxies are at fixed coordinates, but the distance between fixed points increases with time, and this causes the redshift. General relativity explains how to transform from one view to the other, and the observable effects like the redshift are the same in both views.

 

http://www.astro.ucla.edu/~wright/cosmology_faq.html#MX

 

A common belief about big-bang cosmology is that the cosmological redshift cannot be properly viewed as a Doppler shift (that is, as evidence for a recession velocity), but must be viewed in terms of the stretching of space. We argue that, contrary to this view, the most natural interpretation of the redshift is as a Doppler shift, or rather as the accumulation of many infinitesimal Doppler shifts. The stretching-of-space interpretation obscures a central idea of relativity, namely that it is always valid to choose a coordinate system that is locally Minkowskian. We show that an observed frequency shift in any spacetime can be interpreted either as a kinematic (Doppler) shift or a gravitational shift by imagining a suitable family of observers along the photon's path. In the context of the expanding universe the kinematic interpretation corresponds to a family of comoving observers and hence is more natural.

 

http://arxiv.org/PS_cache/arxiv/pdf/0808/0808.1081v2.pdf

The view presented by many cosmologists and astrophysicists, particularly when talking to nonspecialists, is that distant galaxies are “really” at rest, and that the observed redshift is a consequence of some sort of “stretching of space,” which is distinct from the usual kinematic Doppler shift. In these descriptions, statements that are artifacts of a particular coordinate system are presented as if they were statements about the universe, resulting in misunderstandings about the nature of spacetime in relativity.

 

http://arxiv.org/PS_cache/arxiv/pdf/0808/0808.1081v2.pdf

 

Iggy mentioned the possibility of drawing the limit between regions below and above the critical density. This appears to me more reasonable, but the critical density does not have this function in the standard paradigm.

I agree FLRW doesn't have that function because it assumes as an approximation that the universe is homogeneous.

 

It is also not immediately clear how a place-specific matter density should be defined. The "critical gravitational potential" is well-defined and could do the same job, but it also lacks this function in the standard paradigm. It is also not immediately clear how a place-specific matter density should be defined.

The formula, [math]\rho_c = \frac{3 H^2}{8 \pi G} [/math], works not only for finding the critical density of the visible universe as a whole, but any particular part of it as well. If you draw a sphere around an area of interest and you want to know if that area will collapse or expand in the future then mark a point in the center of the sphere. The velocity between the point and the edge is [math]H[/math]. Using that to find [math]\rho_c[/math] and comparing it to the real measured density, [math]\rho[/math], will say if the area will eventually collapse or expand.

 

The important point, i think, is that inhomogeneities existed in the past. Some areas were above their local [math]\rho_c[/math] and some areas below. The areas of segregated mass that we see now are a result of that.

[Rolando]

Since the Speed of Light is constant, over large distance a linear delay is produced that may authorize to observe it, especially if expansion is not linear.

You are right. Universal expansion of space would not be observable if light that is on its way is affected in the same way as matter that is at rest (co-moving with the Hubble flow). If this is not the case, a frequency shift may be observable, but not necessarily a redshift. If it should be the case that light conserves its original features (since it moves along null geodesics and does not age), a blueshift will be observed.

 

As long as light and matter are affected in the same way, I think it does not matter whether expansion is linear or not.

 

Your description of the history does not sound very familiar to me.

I admit that it was a bit impressionistic.

 

A doppler shift interpretation and a metric expansion interpretation should be different coordinate choices for the same situation. Whichever way you look at it you should get the same physical outcome. Both interpretations are valid. A couple of articles saying this...

 

I think there is a difference between the two views in how the observer is affected, but I may change my opinion after having red the references. Thank you very much for these!

 

I agree FLRW doesn't have that function because it assumes as an approximation that the universe is homogeneous.

 

The formula, [math]\rho_c = \frac{3 H^2}{8 \pi G} [/math], works not only for finding the critical density of the visible universe as a whole, but any particular part of it as well. If you draw a sphere around an area of interest and you want to know if that area will collapse or expand in the future then mark a point in the center of the sphere. The velocity between the point and the edge is [math]H[/math]. Using that to find [math]\rho_c[/math] and comparing it to the real measured density, [math]\rho[/math], will say if the area will eventually collapse or expand.

 

The important point, i think, is that inhomogeneities existed in the past. Some areas were above their local [math]\rho_c[/math] and some areas below. The areas of segregated mass that we see now are a result of that.

In order to calculate the local density [math]\rho[/math], it is necessary to decide about the radius of the sphere, and this seems to involve an arbitrary decision. If you consider the gravitational potential [math]\Phi[/math], you do not have this problem (perhaps others).

 

I have to read more carefully. The method you propose does work.

Edited August 1, 2011 by Rolando

[Iggy]

In order to calculate the local density [math]\rho[/math], it is necessary to decide about the radius of the sphere, and this seems to involve an arbitrary decision.

I agree it is arbitrary, but I think it is appropriately arbitrary. If we want to know if a galaxy will expand then r would be rather small. To find out if a supercluster is going to expand indefinitely then the sphere under consideration, and its r, would be quite a bit bigger. It is good that we can examine any size sphere we want, so good I think to have r be an open variable.

 

If you consider the gravitational potential [math]\Phi[/math], you do not have this problem (perhaps others).

I agree you could find the gravitational potential and kinetic energy of the mass in an area of space to see if that area will eventually collapse, but it is really the same thing as the previous equation. The equation is derived by comparing the gravitational potential of an area to the kinetic energy of the mass constituents. It is a simplified form of that equation. The only variables needed are density and velocity (assuming the area is homogeneous, velocity increases with distance, and omitting the cosmological constant).

[michel123456]

A doppler shift interpretation and a metric expansion interpretation should be different coordinate choices for the same situation. Whichever way you look at it you should get the same physical outcome. Both interpretations are valid. A couple of articles saying this...

 

Quote

 

Are galaxies really moving away from us or is space just expanding?

 

This depends on how you measure things, or your choice of coordinates. In one view, the spatial positions of galaxies are changing, and this causes the redshift. In another view, the galaxies are at fixed coordinates, but the distance between fixed points increases with time, and this causes the redshift. General relativity explains how to transform from one view to the other, and the observable effects like the redshift are the same in both views.

 

http://www.astro.ucl...ogy_faq.html#MX

 

 

Really? I thought the difference was that expansion of space was an explanation for FTL recession. That leaves no room for the first view where galaxies are changing position.

 

I agree it is arbitrary, but I think it is appropriately arbitrary. If we want to know if a galaxy will expand then r would be rather small. To find out if a supercluster is going to expand indefinitely then the sphere under consideration, and its r, would be quite a bit bigger. It is good that we can examine any size sphere we want, so good I think to have r be an open variable.

(...)

 

If you take arbitrarily r inside the Earth, you will conclude that our planet is collapsing.

[Rolando]

A doppler shift interpretation and a metric expansion interpretation should be different coordinate choices for the same situation. Whichever way you look at it you should get the same physical outcome. Both interpretations are valid. A couple of articles saying this...

 

Iggy, the first reference you gave us is to a FAQ by Ned Wright.

Question: Are galaxies really moving away from us or is space just expanding?

Answer: This depends on how you measure things, or your choice of coordinates. In one view, the spatial positions of galaxies are changing, and this causes the redshift. In another view, the galaxies are at fixed coordinates, but the distance between fixed points increases with time, and this causes the redshift. General relativity explains how to transform from one view to the other, and the observable effects like the redshift are the same in both views. ...

 

This does not seem to be (or to have been) the majoity opinion, considering that the "expanding space" view dominates in text books, encyclopedias and popularizations, where the Doppler shift interpretation is often condemned. However, in the second reference you gave us (the third one was to the same paper by Bunn and Hogg "The kinematic origin of the cosmological redshift"), the expanding space view is condemned instead. This is an informative paper. I found the arguments in favour of the kinematic view convincing, but the arguments against the "expanding space" view less so. I also had a look at papers in which the Bunn & Hogg paper was quoted. Those who refer to it are mostly critical.

 

The subsequent entry in the FAQ:

Question: Why doesn't the Solar System expand if the whole Universe is expanding?

Answer: This question is best answered in the coordinate system where the galaxies change their positions. ...

 

This is a cheep way out, since the question becomes tricky only in the other coordinate system. Why don't the distances between the orbits of the planets increase with time if space expands? The same passage in the FAQ also contains a reference to Cooperstock et al. about which I mentioned earlier that they showed no awareness of the effects on their measuring devices.

 

I also found a paper, "Expanding Space: the Root of all Evil?", http://arxiv.org/abs/0707.0380, in which it is attempted to put the "expanding space" view on a tenable foundation. Unfortunately, even in this paper, the question that bothers me is not touched. The authors behave like Ned Wright and Cooperstock et al. and so fail to notice the problem.

 

I have not changed my opinion. The "expanding universe" view is not equivalent to the "expanding space" view. It is, on the contrary, equivalent to a "contracting space" view!

 

"Expanding Universe": Galaxies move away from each other. Nothing special happens to light and to us and our devices. We see a Doppler shift.

"Contracting space": Space contracts universally, including us and our devices. Nothing special happens to light. We see a redshift that looks like a Doppler shift.

"Expanding space": Galaxies remain in place. Light waves are stretched on their way due to expansion of space. Although space expands, we and our devices do not expand. Where is the limit of this exception?

[Rolando]

Now, I have two questions:

 

Second, are there any astronomical studies that have shown voids to expand (distant voids being smaller)?

Meanwhile, I have found relevant papers, such as Charlie Conroy et al. (2005) "The DEEP2 Galaxy Redshift Survey: The Evolution of Void Statistics from z ~ 1 to z ~ 0" http://arxiv.org/PS_...8/0508250v2.pdf

In the abstract, they say among other things that "We also clearly detect evolution in the VPF with cosmic time, with voids being larger in comoving units at z ∼ 0.", where VPF = "void probability function".

Unfortunately, they do not show this in their paper in an easily verified and convincing way.

[Iggy]

If you take arbitrarily r inside the Earth, you will conclude that our planet is collapsing.

Correct, gravitationally it wants to collapse.

 

Why don't the distances between the orbits of the planets increase with time if space expands?

FLRW assumes that the universe is homogeneous. There are no variations in density. Because of this, it is only accurate at very large scales. It does not predict, and no one would expect, small dense areas like a solar system to expand.

 

The choice between a kinematic coordinate system and an expanding coordinate system has nothing to do with whether or not dense areas of space are gravitationally bound. The critical density inside a galaxy is different than the critical density of the universe as a whole.

[michel123456]

"Contracting space": Space contracts universally, including us and our devices. Nothing special happens to light. We see a redshift that looks like a Doppler shift.

 

It is not evident that one would observe a redshift.

In a contraction state, you will observe objects that travel in the same direction with you differently than objects coming from perpendicular or opposite directions. The objects moving in roughly the same direction will look like getting away from each other only if contraction happens under accelerated motion: that would be the redshift. The objects coming from the other side of the contraction point will look like coming closer: that would be a blueshift.

 

In order to observe only redshift, one must consider that all observed objects are moving in the same direction (IOW the contracting point is infinitely far away) and that the contraction is accelerating (that's the easy point).

[Widdekind]

Question: Why doesn't the Solar System expand if the whole Universe is expanding?

Answer: This question is best answered in the coordinate system where the galaxies change their positions. ...

 

 

...Why don't the distances between the orbits of the planets increase with time if space expands?

 

"Expanding space": Galaxies remain in place. Light waves are stretched on their way due to expansion of space. Although space expands, we and our devices do not expand. Where is the limit of this exception?

 

Please pay particular attention, to the vast difference in size scale. On the scale of billions of light-years, our cosmos is (quasi-)uniform. Therefore, on such size scales, space-time-and-gravity behaves one way. But, on the scale of light-minutes, our solar-system-within-our-cosmos is varying, in its various properties. Therefore, on those size scales, space-time-and-gravity behaves a totally other way.

 

You have asked an interesting question -- if, within gravity-bound (i.e., galactic scale) systems, space is not stretching; then, how far out-into-deep-space, must one venture, before space just-barely-begins-to-stretch ? Logically, there must, indeed, be such a "Hubble Lagrange Point", on the peripheral marches, of galactic-scale, gravity-bound structures. To give a guess, when the local over-density decreases down to ~0, so that the ambient density decreases down to the cosmic average, then space-time might begin to behave as it does on average, i.e., stretch.

[BJC]

Please pay particular attention, to the vast difference in size scale. On the scale of billions of light-years, our cosmos is (quasi-)uniform. Therefore, on such size scales, space-time-and-gravity behaves one way. But, on the scale of light-minutes, our solar-system-within-our-cosmos is varying, in its various properties. Therefore, on those size scales, space-time-and-gravity behaves a totally other way.

 

You have asked an interesting question -- if, within gravity-bound (i.e., galactic scale) systems, space is not stretching; then, how far out-into-deep-space, must one venture, before space just-barely-begins-to-stretch ? Logically, there must, indeed, be such a "Hubble Lagrange Point", on the peripheral marches, of galactic-scale, gravity-bound structures. To give a guess, when the local over-density decreases down to ~0, so that the ambient density decreases down to the cosmic average, then space-time might begin to behave as it does on average, i.e., stretch.

 

Interesting study:

The influence of the cosmological expansion on local systems

F. I. Cooperstock, V. Faraoni, D. N. Vollick (University of Victoria)

(Submitted on 9 Mar 1998)

 

Following renewed interest, the problem of whether the cosmological expansion affects the dynamics of local systems is reconsidered. The cosmological correction to the equations of motion in the locally inertial Fermi normal frame (the relevant frame for astronomical observations) is computed. The evolution equations for the cosmological perturbation of the two--body problem are solved in this frame. The effect on the orbit is insignificant as are the effects on the galactic and galactic--cluster scales.

 

( http://arxiv.org/abs/astro-ph/9803097 )

 

On page 6: "Order of Magnitude Estimates" the authors give an estimate of gravitational attraction to expansion. Inside Solar system 10⁴⁰ higher; inside a galaxy is 10¹¹ times stronger, between galaxy clusters is still 10⁷ times stronger than expansion.

 

Could mean one of two things: (1)expansion occurs even in galaxy clusters but is far too small to detect (likely) or (2)expansion occurs in space quanta (unlikely - but more interesting).

[Iggy]

You have asked an interesting question -- if, within gravity-bound (i.e., galactic scale) systems, space is not stretching; then, how far out-into-deep-space, must one venture, before space just-barely-begins-to-stretch ? Logically, there must, indeed, be such a "Hubble Lagrange Point", on the peripheral marches, of galactic-scale, gravity-bound structures. To give a guess, when the local over-density decreases down to ~0, so that the ambient density decreases down to the cosmic average, then space-time might begin to behave as it does on average, i.e., stretch.

 

Ignoring the cosmological constant (just as an approximation) if the distance you are talking about is [math]D[/math], the measured density of the area you are talking about is [math]\rho[/math], the measured velocity of the "far out-into-deep-space" point as compared to the starting point is [math]V[/math], and the gravitational constant is [math]G[/math] then the area will expand if,

 

[math] \rho < \frac{3 \left( \frac{V}{D} \right)^2}{8 \pi G} [/math]

 

and will contract if,

 

[math] \rho > \frac{3 \left( \frac{V}{D} \right)^2}{8 \pi G} [/math]

 

You can get this by solving the escape velocity of an expanding sphere.

Edited August 6, 2011 by Iggy

[Rolando]

It is not evident that one would observe a redshift.

In a contraction state, you will observe objects that travel in the same direction with you differently than objects coming from perpendicular or opposite directions. The objects moving in roughly the same direction will look like getting away from each other only if contraction happens under accelerated motion: that would be the redshift. The objects coming from the other side of the contraction point will look like coming closer: that would be a blueshift.

 

In order to observe only redshift, one must consider that all observed objects are moving in the same direction (IOW the contracting point is infinitely far away) and that the contraction is accelerating (that's the easy point).

I thought of a "contraction of space" that affects only gravitationally bound systems, so that the Universe as a whole would not contract. This would be observationally equivalent to the familiar idea of an "expanding Universe".

 

You have asked an interesting question -- if, within gravity-bound (i.e., galactic scale) systems, space is not stretching; then, how far out-into-deep-space, must one venture, before space just-barely-begins-to-stretch ? Logically, there must, indeed, be such a "Hubble Lagrange Point", on the peripheral marches, of galactic-scale, gravity-bound structures. To give a guess, when the local over-density decreases down to ~0, so that the ambient density decreases down to the cosmic average, then space-time might begin to behave as it does on average, i.e., stretch.

Extrapolating the calculations by F. I. Cooperstock et al., one would conclude that this "Hubble Lagrange point" must be very far out.

 

On page 6: "Order of Magnitude Estimates" the authors give an estimate of gravitational attraction to expansion. Inside Solar system 10⁴⁰ higher; inside a galaxy is 10¹¹ times stronger, between galaxy clusters is still 10⁷ times stronger than expansion.

 

Could mean one of two things: (1)expansion occurs even in galaxy clusters but is far too small to detect (likely) or (2)expansion occurs in space quanta (unlikely - but more interesting).

It seems to me that the calculations by Cooperstock et al. are far from being realistic. If gravity between the galaxies within large clusters is still 10⁷ times stronger than expansion, everything smaller than a Hubble sphere or so would be gravitationally bound. There could not be any voids smaller than this.

 

Iggy, your comments suggest that you have a preconceived model in mind. Is there any more comprehensive description accessible?

Edited August 8, 2011 by Rolando

[michel123456]

I thought of a "contraction of space" that affects only gravitationally bound systems, so that the Universe as a whole would not contract. This would be observationally equivalent to the familiar idea of an "expanding Universe".

 

So you are proposing that gravitationally bound systems are collapsing. Indeed our local cluster is characterized by the blueshift of its galaxies.

 

From this link

Our Group of Galaxies

Edwin Hubble first used the term “Local Group” to describe the isolated group of about a dozen nebulae, or island universes that could be observed around our galaxy. These galaxies, as we know them today, showed a blueshift in their spectra as compared to the other galaxies that were further away and whose spectra exhibited a redshift.

 

Our group is defined by its two largest members, the Milky Way and Andromeda (M31) galaxies. The center of mass for the group lies between these two galaxies.

 

And it has been estimated that in a few billion years the Milky Way and Andromeda Galaxy will engage tango.

 

However I don't know if this blueshift alone can explain the observed redshift of other clusters.

[Iggy]

Iggy, [/size]your comments suggest that you have a preconceived model in mind. Is there any more comprehensive description accessible?

Besides disregarding the cosmological constant, it is model independent.

 

A somewhat comprehensive description can be found on Ned Wright's Cosmology Tutorial - Part 2 with the paragraph that begins "We can compute the dynamics of the Universe".

 

If you want to know if an area of space will eventually collapse or continue to expand indefinitely, mark the area as a sphere. Measure the radius of the sphere -- [math]r[/math], and the velocity of the edge of the sphere compared to the center -- [math]v[/math], and solve:

 

[math]\frac{3 \left( \frac{v}{r} \right)^2}{8 \pi G} [/math]

 

That will be the critical density. If it is greater than the measured average density of the sphere (mass / volume) then it will continue to expand.

Edited August 9, 2011 by Iggy

[Rolando]

So you are proposing that gravitationally bound systems are collapsing. Indeed our local cluster is characterized by the blueshift of its galaxies.

It does not look like a collapse when everything shrinks in proportion.

 

And it has been estimated that in a few billion years the Milky Way and Andromeda Galaxy will engage tango.

 

However I don't know if this blueshift alone can explain the observed redshift of other clusters.

Within stable gravitationally bound systems, blueshifts will be as common as redshifts. It does not tell anything about redshifts between clusters.

 

Besides disregarding the cosmological constant, it is model independent.

 

A somewhat comprehensive description can be found on Ned Wright's Cosmology Tutorial - Part 2 with the paragraph that begins "We can compute the dynamics of the Universe".

 

If you want to know if an area of space will eventually collapse or continue to expand indefinitely, mark the area as a sphere. Measure the radius of the sphere -- [math]r[/math], and the velocity of the edge of the sphere compared to the center -- [math]v[/math], and solve:

 

[math]\frac{3 \left( \frac{v}{r} \right)^2}{8 \pi G} [/math]

 

That will be the critical density. If it is greater than the measured average density of the sphere (mass / volume) then it will continue to expand.

Thank you for this reference. This kind of reasoning is usually applied to the Universe as a whole, and this is also what Ned Wright seems to have had in mind. Your applying it to regions with different density within the Universe is innovative.

[michel123456]

It does not look like a collapse when everything shrinks in proportion.

 

But there must be a geometrical centre for this "shrinking in proportion". Where do you put it?

[imatfaal]

Besides disregarding the cosmological constant, it is model independent.

 

A somewhat comprehensive description can be found on Ned Wright's Cosmology Tutorial - Part 2 with the paragraph that begins "We can compute the dynamics of the Universe".

 

If you want to know if an area of space will eventually collapse or continue to expand indefinitely, mark the area as a sphere. Measure the radius of the sphere -- [math]r[/math], and the velocity of the edge of the sphere compared to the center -- [math]v[/math], and solve:

 

[math]\frac{3 \left( \frac{v}{r} \right)^2}{8 \pi G} [/math]

 

That will be the critical density. If it is greater than the measured average density of the sphere (mass / volume) then it will continue to expand.

 

I like that Iggy - but surely that only works when you can assume isotropy and homogeneity. Of course on a small scale this is not a valid assumption and one cannot use shell theorem and others to simplify matters. The large sphere that fits between andromeda and the milky way may well have a calculated critical density far greater than the measured mass/volume - but it ain't gonna expand because of the milky way and andromeda

[Rolando]

But there must be a geometrical centre for this "shrinking in proportion". Where do you put it?

I do not think of a centre.

We can consider gravitationally bound systems as stable and the regions between them as expanding.

We can also consider gravitationally bound systems and everything within them as contracting and the regions between them as stable.

The Universe looks the same in these cases.