# Universal expansion

## Main Question or Discussion Point

Space expands. So we are told.

But why only intergalactic space? I asked Stephen Hawking once (I happen to live in the same town), and he replied 'gravitationally bound systems (such as the Local Group of galaxies) do not expand'.

Why not? Does gravity have a limited range?

An expansion rate of 1 part in 13.7 billion per year would surely show up on the solar-system scale. It doesn't. How can Space expand, but only if the distances involved are vast? There would seem to be a discontinuity. Not happy.

Janus
Staff Emeritus
Gold Member
Gravity doesn't have a limited range, but it does get weaker with distance (Gravitational attraction falls by the square of the distance). When objects are close enough to each other, like the galaxies of our local group are, their mutual gravitational attraction is strong enough to hold them together against expansion. If they are further apart, like groups of galaxies are, the gravitational attraction is much smaller and expansion predominates.

Fair enough, but at what distance does universal expansion outride gravity? Universal expansion should have SOME effect even at intragalactic distances, producing an apparent weakening of gravity so that it no longer follows the 1/r^2 rule. In fact inside galaxies and galaxy clusters the opposite is observed, to explain which we hypothesise Dark Matter.

If no effects of universal expansion are observed at less than inter-galaxy-cluster distances, there must be a discontinuity - a distance beyond which expansion suddenly takes over.

Wallace
The expansion of the Universe it not universal, in the sense that there is no force present in general that 'causes' expansion to occur. The Universe expands because it did so in the past, just as a ball thrown in the air continues upwards not because there is a force constantly making it do so but simply because it has momentum. Now, objects such as galaxies have already pulled material into them due to their excess of matter and hence gravitational attraction. However, there is no residual universal expansion that the gravity has to continually overcome, since the material no longer has any momentum to expand.

It is a common error and misconception that the expansion of the Universe is caused by a universal 'expansion of space' that is perpetuated freely and often. In reality 'the expansion of space' is at best a description of the result of the fact that the Universe is expanding, by which I mean that things are moving apart from everything else, but it is not a cause.

Note that in the case of the cosmological constant or dark energy existing, then they do operate universally, adding an acceleration to the expansion and this complicates things as little, however long before dark energy played a significant role in the dynamics of the Universe expansion occurred without any force driving it, it simply expanded due to the initial momentum provided by inflation.

Now, objects such as galaxies have already pulled material into them due to their excess of matter and hence gravitational attraction. However, there is no residual universal expansion that the gravity has to continually overcome, since the material no longer has any momentum to expand.
Hi Wallace,
I agree with the general sense of what you're saying, but I have an issue with the quoted statement that gravitationally bound objects have lost their expansion momentum. I think that statement needs to be very carefully qualified.

Example: Milky Way and Andromeda galaxies are believed to be gravitationally bound to each other, and therefore are moving towards each other with a certain peculiar velocity relative to the CMB rest frame. (I will ignore any peculiar velocities caused by other massive objects.) Observers in MW or Andromeda might interpret that each other's galaxies have lost expansionary momentum.

However, an observer in a very distant galaxy (which is not gravitationally bound to us) will observe that both MW and Andromeda are moving away from the observer galaxy at a normal hubble rate, but net of any radial element of their respective peculiar velocities. At very great distances, the peculiar velocities become insignificant compared to the hubble expansion rate. Therefore the distant observer would say that MW and Andromeda have NOT lost any significant amount of expansionary momentum.

I think it's best to say that no object (and no region of empty space, for that matter) ever "loses its expansionary momentum". The gravity of nearby masses merely imposes a peculiar velocity overlay onto the background hubble flow. But the background Hubble flow still makes the same mathematical contribution towards increasing the distance between two points in space that it would make if those points were occupied by massless test particles rather than massive objects.

Expansionary "momentum" is a strange beast compared to the normal momentum of peculiar velocity. The expansionary momentum can't be described by a vector because it is directionless (or rather, equal in all directions). Thus, technically the net velocity of expansion is zero, because the equal expansion vectors in all directions cancel each other out. Finally, a distant observer will describe a distant galaxy as having a relatively "high" expansionary momentum compared to a nearby galaxy, yet no local observer will describe its own galaxy as having an expansionary momentum which is any different than a local observer on any other galaxy.

Jon

I have lost count of the number of times I have raised this matter at Astronomy bashes and before eminent astronomers and cosmologists (living in Cambridge, England, helps.) Not only can I not usually make sense of their answers (which can be put down to insufficient intellect on my own part) but they disagree with each other, as seen in these postings. This is perhaps more significant.

Is something rotten in the State of Cosmology? Or, Michael Faraday's Sandemanian faith notwithstanding, are there really matters of importance which cannot be explained to the simple?

Hi Shelanachium,

On the subject of the expansion of space, I think you'll find that there is agreement on the important underlying facts, but the analogies people use to convey a simplified understanding of those facts may differ because of differences in emphasis and context.

If you think there is a difference of opinion on a specific fact, let's discuss it.

Jon

Wallace
Hi Wallace,
I agree with the general sense of what you're saying, but I have an issue with the quoted statement that gravitationally bound objects have lost their expansion momentum. I think that statement needs to be very carefully qualified.
I think it is obvious that my statement was in regards to the momentum that particles within the same bound object have with respect to each other. Once this is removed particles do not feel any residual universal expansion with respect to each other. Was this really not clear in my explanation?

Shelanachium, I'm sorry this is all so confusing, there is so much written and discussed on this topic and much of it is not very good unfortunately. At the professional level though, there isn't any real problem, it's just that an unfortunate series of analogies have been consistently misrepresented leading to confusion.

Hi Wallace,

It wasn't clear to me and I didn't think it would be clear to many amateur readers.

In general, I think the concept of object A losing expansionary momentum with respect to object B" is more confusing than helpful. It makes it sound like the hubble momentum has been permanently lost or altered, when it hasn't. For example, if a third object C strikes object A, causing object A move far enough away from object B that it is no longer gravitationally bound to object B, this causes object A to almost instantly "regain its expansionary momentum" with respect to object B. I find that description to be unhelpful. It's much more explanatory to treat this as an overlay of peculiar motion vectors on top of an invariant background expansion.

I also think the analogy can cause confusion between momentum and velocity. Imagine a tiny grain of sand in a stable orbit around the sun. You would say that the sand grain and the sun have lost their expansionary momentum with respect to each other. But how can a nearly massless sand grain cause the massive sun to lose substantial expansionary momentum with respect to anything? The confusion here seems to arise from purporting to subtract a velocity vector from a momentum vector.

Maybe it would help if you describe what specific problem your terminology is trying to avoid.

Jon

Hi Wallace,

I think an explanation in the 11 Sept 06 Barnes & Frances paper you linked in the other thread provides helpful description:

We can divide the proper velocity $$\left( \dot{r}_{p} \right)$$ of a test particle into a recession component and a peculiar component as follows:

$$\dot{r}_{p} = \dot{R} \left( t \right) \chi \left( t \right) + R \left( t \right) \dot{\chi} \left( t \right) = v _{rec} \left( t \right) + v_{pec} \left( t \right)$$

If we move our coordinate origin so that $$\chi \left( t \right) = 0$$ at time t, then we see that the proper velocity of the test particle is solely its peculiar velocity. Thus peculiar velocity is simply proper velocity relative to the local Hubble flow.
Jon

Wallace
The question in the OP was simple, why don't bound objects expand with the Universal expansion? This is the question that needs a simple answer.

Take your computer monitor. It is not receding from you. Is this because it has a peculiar velocity finely tuned to exactly match the universal expansion of space attempting to drive it away from you? In one sense this is true, but it is certainly a complex question to determine how and why this match is so perfect.

A simpler answer is simply that the material that makes up you and your monitor have ceased receding from each other. Since the only reason things recede in general is that they did so in the past there is clearly no reason to suspect that your monitor is being pushed away from you and the resultant motion finely balanced by a velocity towards you.

The problem is that there is a prevailing misconception that the expansion of space causes things to move apart. This is a bizarre almost Aristotelean idea, i.e. that things in motion need a force continually applied to keep them in motion. As dark ages as this sounds, that is the implication of attributing the recession of galaxies to the expansion of space. In fact, basic physics says that if everything was moving apart a moment ago of course it will be doing so now. As soon as this relative motion between any two bodies ceases, where the two bodies are two pieces of material in a bound object, there is no longer any propensity to move apart, and hence they do not recede from each other.

We can debate this on analogies but it's helpful to see how the pro's do this. What you see is that when the internal dynamics of galaxies or galaxy cluster is considered, we use plain units, not co-moving co-ordinates, to describe the motion. You could describe the motion of the Milky Way in co-moving co-ordinates, the result would be that it would be constantly shrinking in these co-ordinates, but it is an unnecessary complication to do so. Clearly co-moving co-ordinates, and the expanding space analogy, do not do a good job of intuitively explaining bound objects, you can do it, that's for sure, but it's an complication that is not needed. In the same way, it is possible, but clearly absurd, to explain why you do not recede from your computer by using concepts such as peculiar velocities.

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The question in the OP was simple, why don't bound objects expand with the Universal expansion? This is the question that needs a simple answer.
Wallace, I think you are oversimplifying the question, which Shelanachium clarified in the second post: "Fair enough, but at what distance does universal expansion outride gravity?" Calculating how gravity's affect on peculiar velocity compares to Hubble recession velocity as distance increases requires an explanation of the peculiar velocity vector overlaid on a background expansion.

For example, one can calculate a surface at a proper distance from the MW galaxy at which a massive object's gravity exactly offsets the expansionary force of the cosmological constant away from the object. Some pros call this a "zero-gravity sphere." It is calculated as:

$$R_{V} = \left( \frac{3}{8\pi} M / \rho_{V} \right) ^{1/3}$$

In your preferred terminology, I believe you would say that a test particle released with zero peculiar velocity just inside the zero-gravity sphere has no expansionary momentum relative to the massive object, while a particle released just outside the zero-gravity sphere does have expansionary momentum relative to the massive object. I don't think that answer is very enlightening.

Take your computer monitor. It is not receding from you. Is this because it has a peculiar velocity finely tuned to exactly match the universal expansion of space attempting to drive it away from you? In one sense this is true, but it is certainly a complex question to determine how and why this match is so perfect.

A simpler answer is simply that the material that makes up you and your monitor have ceased receding from each other. Since the only reason things recede in general is that they did so in the past there is clearly no reason to suspect that your monitor is being pushed away from you and the resultant motion finely balanced by a velocity towards you.
Not to be picky, but your computer monitor example doesn't make your point very well. The distance between you and your monitor is so small that the Hubble recession over a human lifetime is insignificantly tiny. For that matter, the gravitational attraction between you and your monitor also is insignificantly tiny. So it is utterly insignificant whether the tiny gravity is in or out of balance with the tiny recession velocity. The significant force keeping them equally distant in this example is surface friction. (Although I feel myself being tugged away from my own monitor shortly.)

Recession velocity is simply too small to be significant at sub-galactic scales. That's why the pros simplify it out of the equations at those scales. But at larger scales such as the MW-Andromeda distance or larger, recession velocity becomes mathematically significant and cannot be ignored; at those scales motion must be analyzed as the net sum of gravitationally-caused motion and background recession motion. That's why the pros use different coordinate systems at different scales.

The problem is that their is a prevailing misconception that the expansion of space causes things to move apart. This is a bizarre almost Aristotelean idea, i.e. that things in motion need a force continually applied to keep them in motion.
I agree with you that we don't want people to think that force must be continually added to keep bodies in motion. The concept of momentum is at least somewhat helpful in avoiding that confusion.

However, in order to accomplish that objective, I don't think we need to extrapolate all the way to a theory that says expanding space is the result of the movement of massive objects rather than the cause of the objects' movement. To me that is a separate theory entirely, one which I think is controversial and far from universally accepted by the pros. In fact, as you've pointed out there is a flourishing technical literature currently debating whether or not the expansion of space is "real".

When there are widely held differences of opinion between the pros, I think this Forum should explain both points of view rather than adopting one as the only correct solution.

Jon

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Wallace
Wallace, I think you are oversimplifying the question, which Shelanachium clarified in the second post: "Fair enough, but at what distance does universal expansion outride gravity?"
This very question is ill posed (not to critisise the questioner) and doesn't have a sensible answer since there is no universal expansion that gravity attempts to counter. It is perfectly acceptable to answer a question by pointing out that the question is in error.

Not to be picky, but your computer monitor example doesn't make your point very well. The distance between you and your monitor is so small that the Hubble recession over a human lifetime is insignificantly tiny. For that matter, the gravitational attraction between you and your monitor also is insignificantly tiny. So it is utterly insignificant whether the tiny gravity is in or out of balance with the tiny recession velocity. The significant force keeping them equally distant in this example is surface friction. (Although I feel myself being tugged away from my own monitor shortly.)

Recession velocity is simply too small to be significant at sub-galactic scales. That's why the pros simplify it out of the equations at those scales. But at larger scales where recession velocity is significant, such as the MW-Andromeda distance or larger, recession velocity becomes mathematically significant and cannot be ignored; at those scales motion must be analyzed as the net sum of gravitational pull and background recession velocities. That's why the pros use different coordinate systems at different scales.
Sorry Jon, but this is simply incorrect. Hubble expansion in bound objects isn't just small, it really is zero. If it were small we would be able to measure it on the scales of solar systems, and this is simply not observed. There has been a lot of literature on this. Hubble expansion on a galactic scale would certainly be measurable. For the Milky Way, Hubble expansion would indicate a recession of ~ 2 Km/s for the far edge of the Milky Way from us. Small yes, but not undetectable.

However, in order to accomplish that objective, I don't think we need to extrapolate all the way to a theory that says expanding space is the result of the movement of massive objects rather than the cause of the objects' movement. To me that is a separate theory entirely, one which I think is controversial and far from universally accepted by the pros. In fact, as you've pointed out there is a flourishing technical literature currently debating whether or not the expansion of space is "real".
Sorry Jon, but again this is simply wrong. There is zero technical literature that suggests that the expansion of space is the cause of the recession of galaxies. There is debate about the nature of expanding space, that's true, but not at this level. This idea is entirely a misconception at the pop-sci level.

Hubble expansion in bound objects isn't just small, it really is zero.
Wallace, you are misrepresenting what I said. I said that there is a background Hubble expansion factor in small regions such as the solar system, but in bound collections of matter it is entirely offset (at least to the level of mathematical significance) by the peculiar motion vector induced by gravity. I also pointed out that we don't have the faintest idea whether as a practical matter you and your monitor alone constitute a gravitationally bound system.

As even Francis & Barnes state in the one http://arxiv.org/abs/0707.0380v1" [Broken] that sets out what you describe as the universal technical view,

The metric of spacetime in the region of a galaxy (if it could be calculated would look much more Schwarzchildian than FRW like, though the true metric would be some kind of chimera of both.

Francis & Barnes don't explicitly claim that their preferred explanation is the only technically correct one; rather they worry that using a different explanation would cause students to come away with a picture which is "somewhat murky and incoherent, with the expansion of the universe having mystical properties." The same concern you expressed, and which I share.

Frankly I think the distinction of whether expanding space creates distance between objects or whether separating objects create space between them is substantively meaningless, a debate of semantics. It becomes a problem when people try to make unjustified extrapolations from the way the analogy is worded. There is no reason why the two different perspectives, if interpreted correctly, must lead to different substantive calculations.

Jon

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Space expands. So we are told.

But why only intergalactic space? I asked Stephen Hawking once (I happen to live in the same town), and he replied 'gravitationally bound systems (such as the Local Group of galaxies) do not expand'.
It is unfortunate that you did not get a real answer to you "why" question from professor Hawking. As far as I know there is no single paper that demonstrates that what you ask is demonstrably true in general relativity. Perhaps someone will prove my ignorance by providing a reference. And please not the kind of " 'tis so and we do not need to prove so" or we just define it as such kind of "explanations".

Fact of the matter is that spacetimes with a positive cosmological constant have a spacelike infinity for timelike and null lines. FRW solutions require that the energy-momentum tensor has the form of a perfect fluid whose density and pressure are functions of the time coordinate only. As Hawking wrote, this fluid can be thought of as a smoothed out approximation to the matter in the universe. To conclude that from such a model one can make definitive statements about local off density and pressure fluid concentrations is something I would characterize as being careless.

"Sorry Jon, but this is simply incorrect. Hubble expansion in bound objects isn't just small, it really is zero."

If that is in fact true then I am confused by Lineweaver's statement in his Scientific American article:

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 (10�30) 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.

In fact, in our universe the expansion is accelerating, and that exerts a gentle outward force on bodies.
Hi Dilletante,

The Davis & Lineweaver SA article is helpful in understanding this subject. As you can see from the quoted sentence above, they are not talking strictly about the "original" expansion rate, which is decelerating over time as a result of gravity. They are talking about the present acceleration of the expansion rate, which is believed to be caused by the domination of the expansion rate by dark energy (the cosmological constant). Dark energy acts sort of like an antigravity force. The "outward" acceleration force of dark energy is what counteracts the "inward" acceleration force of gravity in the quoted sentence.

Jon

Well now, from the avalanche of responses to my original posting, haven't I made my earlier point: NOBODY AGREES! Or are you all saying the same thing? - and this non-mathematical guy mostly into biology and chemistry, but who at 57 still asks questions like a ten-year-old, fails to understand. Is there someone out there of Asimovian lucidity can explain this stuff to the likes of me?

Amen, Shelanachium !!

Either Hubble expansion in bound systems is zero or it is not. Very curious as to whether this point can be conclusively resolved within current theory.

Is there someone out there of Asimovian lucidity can explain this stuff to the likes of me?
Hi Shelanchium, yes he had an understudy in Sri Lanka, we're tracking him down as we speak...

I don't think your expression of distress is justified. Nothing is rotten in the state of cosmology. As was explained earlier, the underlying facts of the expansion are fairly well accepted. It's the analogies we use to simplify the explanation that tend cause debate.

Here's what I suggest as your take-away package from this discussion (doggie bag):

1. Go with Wallace's description of what is probably the majority view, that expansion of the universe is caused simply by matter objects moving apart from each other because they were previously moving apart from each other. The increase in empty space being the result, not the cause of expansion. This description is straightforward because it analogizes to the concept of momentum.

2. Go with MeJennifer's admonition that there currently is no exact GR solution for local energy inhomogeneities, such as gravitationally bound collections of matter (e.g. galaxies) and underdense regions (e.g. voids). However there is a solution for spherical regions of cosmic-average density, where the matter is collected in spherically symmetrical clumps (such as a single central mass). This solution is called the "Swiss Cheese" solution, and it is based on Birkhoff's theorem.

3. I don't think you will find it intuitive to think of objects which are gravitationally bound together as having "lost their expansionary momentum only with respect to each other." It is too abstract to say that the Schwartzschild static-space metric applies as between two bound objects, while the FLRW expanding-space metric applies as between those same two objects and all other objects in the universe. It is more intuitive to say that so long as two objects are gravitationally bound, their local expansion away from each other is more or less suppressed, i.e. the "pause" button is pushed.

4. As Wallace said, your question, "at what distance the Hubble expansion exceeds the force of gravity" requires clarification. You must be clear whether you are referring to accelerated expansion resulting from dark energy (cosmological constant). If you are, then the "zero-gravity sphere" can be calculated as I set out in a prior post.

If you are referring to the "original" Einstein-de Sitter expansion, with the cosmological constant (Lambda) = 0 (not the current concordance model), then the Hubble expansion is merely a decelerating (due to gravity) velocity, not an accelerational force. A nonaccelerating expansion velocity can temporarily offset gravitational collapse, but cannot prevent it from occurring eventually.

If the terminology is not clear, please ask specific questions. But it won't be helpful to assert that cosmology is lost in some tractless desert.

Jon

Either Hubble expansion in bound systems is zero or it is not. Very curious as to whether this point can be conclusively resolved within current theory.
I would like an answer to the same question! My understanding is that any expansionary "offset" to gravity is insignificant within our solar system and even within the MW galaxy. However, cosmologists have recently observed what they interpret to be Hubble expansionary effects within our Local Group, and within our local supercluster, both of which appear to be gravitationally bound structures. See https://www.physicsforums.com/showthread.php?t=206803" thread for more on this topic.

Jon

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Just I think Cosmology is getting a bit like Ptolemy's epicycles. We got inflation, then dark matter, then a resurrected cosmological constant - and what next?

I know it is only an act of faith to believe like Dirac that the fundamental rules of the Universe are simple. (I prefer RULES to LAWS, for the universe works more like a game than a courtroom).

When simplicity fails to appear, it is usually because we have not gone deep enough. Ptolemy sought simplicity at the level of ORBITS, which therefore had to be compounded of combinations of perfect circles, to him the most elegantly simple paths. The true simplicity was unveiled by Newton as lying much deeper, in the forces controlling the orbits - and even a ten-year-old can grasp Newton's rules, even if their consequences have kept great mathematicians busy for centuries.

For the same reason I have no fear that if a simple Theory of Everything is discovered, science will cease to be fun. Chemists still have great fun, though the basic physical rules underlying chemistry have been known now for decades. When we get the TOE we shall be like bright kids who've just learnt the rules of Chess. Care to put up a bright 6-year-old against Kasparov?