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You don't hear it because it would be grossly misleading, implying as it does the existence to a center. I suggest you read the full explanation of the balloon analogy and its flaws on the link in my signature

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A 3D balloon expands with a center, so I don't understand you at all. I don't see how you think you are not implying a center.

EDIT: I think you are looking for what is called the "raisin bread analogy"

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while the balloon expands and stretches the material it is made of gets thinner and contracts.

Expansion wins when the balloon inflates faster than the material contacts. Gravity wins where the material contracts faster then the overall expansion.

This is not a good way of interpreting the balloon analogy. The thickness of the balloon does not have any counterpart in the model of the universe that it is supposed to be an analogy for.

It looks to me like the balloon analogy is causing more problems for you than it solves. (You are correct, btw, when you say in your OP that the analogy does not explain how gravity comes into play; but your reworking of it does not solve that problem.) My advice would be to abandon it and look for a better way of understanding how the FRW model of the universe works.

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ChrisVer

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However even this is not flawless because it needs the exact coordinate system , that you see the FRW metric written into, to work...

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your distances (rulers) expand

Putting that "rulers" in is not correct. Rulers don't expand. Distances between galaxies, as measured by rulers which remain at a constant length, expand. Don't misinterpret the scale factor in the metric as describing "expansion of rulers". Coordinates are just coordinates. All the scale factor is telling you is how much proper length (as measured by rulers whose length remains the same) corresponds to a given increment of coordinates.

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ChrisVer

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Putting that "rulers" in is not correct. Rulers don't expand. Distances between galaxies, as measured by rulers which remain at a constant length, expand. Don't misinterpret the scale factor in the metric as describing "expansion of rulers". Coordinates are just coordinates. All the scale factor is telling you is how much proper length (as measured by rulers whose length remains the same) corresponds to a given increment of coordinates.

Maybe you are right. But this also has helped me in understanding the redshift because of expansion, since a ruler that measured at emission time a wavelength [itex] \lambda_{em}[/itex], got "expanded" and gave the observed redshifted [itex] \lambda_{o}[/itex], which are connected by the scaling of the two same "rulers"... I don't know, I feel like we are rephrasing the same thing (you could as well think that the rulers' lengths did not expand, but there was a mismatch between the wavelength at the time of emission and the wavelength at the time of observation as measured by the same length ruler).

"The ball hit the wall or the wall the ball?"

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a ruler that measured at emission time a wavelength ##\lambda_{em}##, got "expanded" and gave the observed redshifted ##\lambda_{o}##,

No, the ruler did not expand, the wavelength of the light expanded. The ruler stayed the same; if it had also expanded, then when it measured the wavelength, it would have gotten the same answer as before, ##\lambda_{em}##, because it would have expanded to the same extent as the light it was measuring. Or, if the ruler expanded but the light stayed the same, then the ruler would measure a

I realize that the above is English, not math, and the math is unequivocal regardless of how you try to describe it in English. But if we are going to use English at all to communicate about this stuff, I think it behooves us to try to use English that at least invites the same sort of reasoning that you would do if you were using the math directly, or at least does not invite reasoning that would clearly be incorrect if you were using the math directly. That's why I tried to illustrate above how different ways of describing the math lead to different kinds of reasoning, and some of those kinds of reasoning lead to wrong answers.

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A better representation of our time in the universe today would be the part before the balloon has it's balloon shape. Not smooth, but full of creases (maybe folds?). These creases are expanding slower than other parts of the balloon. Slower expanding creases are what we perceive as gravity.

No. What you are calling "gravity" here is really "gravity within isolated bound objects like galaxies, stars, planets, etc.". These objects are not expanding at all, so thinking of them as "creases that are expanding slower" is not correct.

When I said that the balloon analogy doesn't capture the effects of gravity, what I meant was that it doesn't capture the effects of the gravity of all the matter in the universe, when it's averaged out to a continuous "cosmological fluid" with a certain average density and pressure, on the dynamics of the universe as a whole. The balloon analogy doesn't capture that at all. To understand that, you need to look at the Friedmann equations. The internal gravitational behavior of isolated systems like galaxies, stars, and planets is completely negligible on this scale; they all just average out to the cosmological fluid.

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bapowell

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The balloon analogy is only an analogy, and no analogy is perfect (or else it wouldn't be analogy). I'll take the illusory extra dimension if it means being able to use a common household object to explain something as abstract and important as the expanding universe.

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The fact that the surface of the balloon is a 2D analog for our 3D universe forces us to imagine our universe as a 3-sphere with a topology analogous to the 2-sphere.

But one drawback of this (other than the temptation to ask where the "center" is) is that our current best-fit model has the universe being spatially flat, not closed, and it's really hard to imagine a spatially flat universe as an expanding balloon.

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bapowell

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The models pertain to the *observable universe*, don't forget! So that gives us a great opportunity to teach the distinction between the "whole" universe and just our observable part of it -- that we see just a small patch on this huge inflating balloon. This segues into the analogy with the surface of the earth appearing flat even though it's actually spheroidal.But one drawback of this (other than the temptation to ask where the "center" is) is that our current best-fit model has the universe being spatially flat, not closed, and it's really hard to imagine a spatially flat universe as an expanding balloon.

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ChrisVer

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The models pertain to the *observable universe*, don't forget! So that gives us a great opportunity to teach the distinction between the "whole" universe and just our observable part of it -- that we see just a small patch on this huge inflating balloon. This segues into the analogy with the surface of the earth appearing flat even though it's actually spheroidal.

Do you mean that the Universe as a whole cannot be flat?

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bapowell

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No, it can be, just that the observations are mum on this. I don't mean to imply that the universe is necessarily spherical just because the balloon analogy suggests this. If it is, then what I wrote above stands. If it is instead some other topology, then the balloon analogy is still useful for illustrating Hubble expansion and the cosmological principle, as well as the distinction between local and global geometry.Do you mean that the Universe as a whole cannot be flat?

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it can be, just that the observations are mum on this

More precisely, observations are mum given the assumption that inflation happened, and expanded the universe to such an extent that the observable part we see is too small a patch of the whole for our observations of flatness within the observable part to tell us anything useful about the spatial geometry of the whole. That's not to say that the assumption is wrong, just that the "observations are mum" conclusion does depend on that assumption, so there is a sense in which it is model-dependent.

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So this analogy will never be able to show expansion and gravity? No matter how much we change it?

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ChrisVer

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More precisely, observations are mum given the assumption that inflation happened, and expanded the universe to such an extent that the observable part we see is too small a patch of the whole for our observations of flatness within the observable part to tell us anything useful about the spatial geometry of the whole. That's not to say that the assumption is wrong, just that the "observations are mum" conclusion does depend on that assumption, so there is a sense in which it is model-dependent.

But inflation made the whole universe flat... even if we are just in a patch of the whole, if the "whole" began from inflation, then it should have been fine-tuned to flat as well..

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So this analogy will never be able to show expansion and gravity? No matter how much we change it?

I don't think it will be able to show the effect of gravity on the expansion as a whole, no.

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inflation made the whole universe flat

Inflation makes the universe expand by a very large factor, but that doesn't mean it changes the spatial topology. If the universe had the spatial topology of a 3-sphere before inflation, it has the spatial topology of a 3-sphere after inflation--it's just a much, much bigger 3-sphere, so big that our observable universe is just a small patch and we can't tell it's a 3-sphere. When people talk about inflation solving the "flatness problem", they are referring to our observable universe, as bapowell said, not to the whole universe.

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bapowell

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I think they are mum given the easier assumption that the particle horizon doesn't mark the edge of the whole universe. Inflation is just one reason this might be the case.More precisely, observations are mum given the assumption that inflation happened, and expanded the universe to such an extent that the observable part we see is too small a patch of the whole for our observations of flatness within the observable part to tell us anything useful about the spatial geometry of the whole. That's not to say that the assumption is wrong, just that the "observations are mum" conclusion does depend on that assumption, so there is a sense in which it is model-dependent.

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