# An expanding universe, part of a bigger leading edge?

1. Mar 30, 2007

### Corkie2003

The mathematics passes me by, so please be patient.

I have an idea that may have been posited before, but I've not seen it.

Could it be that the expansion of the universe as we see it is only a relatively minescule fraction of the whole expansion?

I have a mental image of the gaseous expansion of an explosion, which viewed from the outside would appear to be an expanding ball of gases. However, if viewed from within one of the expanding edges from a minute or atomic perspective, one might draw the conclusion that the area around oneself was expanding in ALL directions.

The truth would be that this was only the case in that particular region of the expanding gases, but that there was actually a point at which the expansion began; another geographic location. From one's atomic viewpoint, one could not see the start point for the expansion, much beyond the immediate vicinity and certainly not the expansion going on on the other side of the originating point.

The expansion might still be accelerating, just as during the acceleration phase of an explosion, even though from the leading edge, the force for expansion might not be visible.

The question I'm asking is whether an expanding 'ball' theory has been proven not to be the case.

Can anyone help?

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2. Mar 30, 2007

### Staff: Mentor

The universe would need to be extrordinarily large for us to not notice that it wasn't homogenous. And afaik, there is no good way to explain how a boundary would work (what would it look like if you were there?).

This is why it isn't a good idea to try to visualize it as an explosion...

3. Mar 30, 2007

### MeJennifer

I don't see the problem in explaining it.
Hypersurfaces of space-time are hyperbolic spaces, in hyperbolic spaces boundaries can never be reached and each point looks like it is in the center.

Last edited: Mar 30, 2007
4. Mar 30, 2007

### Corkie2003

Well, as far as I can gather, the universe is only as big as we can see, and the rest (that we can't) is moving away from us faster than light, but the supposition is that the none-observable part must be the same as our observable universe. This being the case, we would/could not actually know how large the universe actually is, or what shape, only the visible bit of it.

This goes back to my question of whether our visible portion could actually be an inordinately large boundary that is expanding in one direction and carrying us within it, even though from our perspective, it seems to be doing so in all directions.

If we were on a macroscopic scale and on the expanding edge of say a nuclear explosion, then all around us would appear to be expanding in all directions, even though we were merely a within a tiny part of a leading edge.

I can't think of a better way to explain myself.

5. Mar 30, 2007

### marcus

You have to be careful with the words and be definite about the meaning, but no, an "expanding ball" picture has not been ruled out.

We are not talking about any kind of real explosion. That is a metaphor. I think you realize this. The mental picture of the leading surface of a nuclear explosion is just a way of picturing the expanding ball idea.

It has not been ruled out that space is an expanding THREE-SPHERE.

A two-sphere is like the surface of a balloon, perhaps inhabited by very flat animals that don't require more than 2D to live in.

A three-sphere is the analogous thing but 3D instead of 2D, and it can expand just like the more familiar two-sphere.

I'm not saying that space is a kind of material, like rubber I am just using a verbal shorthand to say something about the geometry of space. That it could be geometrically equivalent to a sort of bumpy puckered threesphere (almost perfect but locally puckered by the gravity of galaxies and black holes and stuff---the imperfections invisible on large scale)

this hasnt been ruled out. One of the world's top cosmologists is Ned Wright and he put out a paper recently which allowed for it. he gave a "best fit" to several kinds of current data. The best fit was a three-sphere with
Omega = 1.011
I think if you translate that it means the threesphere curvature has radius 130 billion lightyears. That is what the more scientific usual statement Omega = 1.011 would turn out to mean.

In these kind of pictures, the sphere is all there is. There is nothing inside or outside because that would be in a different dimension we have no evidence of. useless to think about. There is just the sphere. But if you want to describe the degree of curvature or flatness of it, you can say that the radius of curvature is 130 billion LY.

And he said not to PREFER this picture, because even tho it is the best fit it is still not much better than simply saying FLAT. That is, Omega exactly equal to 1.0000. No curvature. he said that for practical purposes flat fits the data too and is hardly different from the three-sphere picture.

So we dont know for sure about this. We just havent ruled stuff out yet.

Anybody who wants to read the pure unadulterated ned wright paper can find it discussed here
https://www.physicsforums.com/showthread.php?p=1220828#post1220828
and online here
http://arxiv.org/abs/astro-ph/0701584
Constraints on Dark Energy from Supernovae, Gamma Ray Bursts, Acoustic Oscillations, Nucleosynthesis and Large Scale Structure and the Hubble constant
Edward L. Wright (UCLA)
16 pages, 8 figure

See discussion section page 14:

"Using all the data together
gives the plot shown in Figure 5. The best fit model is slightly closed with
Omega_tot = 1.011 and M = 0.315. "

When he says "SLIGHTLY CLOSED" that is code for the very large 3-sphere! that is the picture he is conveying, and the radius of curvature 130 billion LY is calculated from his Omega figure of 1.011. Exciting times in cosmology these days

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6. Mar 30, 2007

### MeJennifer

When I see comments like this I can't help thinking what ever happened to 100 years of relativity.
In relativity you need four dimensions not three.

And you cannot have a space-time in GR where only the spatial dimensions are closed.

Last edited: Mar 30, 2007
7. Mar 30, 2007

### marcus

this comment is based on a Jennifer's misunderstanding, the picture I'm talking about is compatible with a 4D spacetime continuum, the S3 x R case is one that is often studied
I would not normally reply to total incomprehension but don't want the O.P. to be confused.
That is a false statement. Please give your source. People used to say that sort of thing in popular writing before 1998 but it is simply wrong and I havent seen it claimed for halfadozen years by anyone qualified as a General Relativist.

You are implying that if spacetime is spatially closed that there also has to be some sort of time closure like a big crunch or other. You are saying an unbounded expansion is impossible (edit to clarify, in the spatially closed case). I thought all the regulars here at PF cosmology knew better. I'm surprised at you Jennifer, and disappointed. I think you should restrain yourself from interjecting comment in cases where you lack basic understanding.

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8. Mar 30, 2007

### MeJennifer

I am not saying that at all.

What I am saying is that if the spatial dimensions are closed the temporal dimension must be closed as well.

9. Mar 30, 2007

### marcus

That is what I thought you were saying.
That is false.
I asked you to find a source. I dont think any qualified writer on GR has said anything like that for over 5 years. It has to do with the positive cosmological constant.
I cant take time to respond further unless you can provide some link showing where you could have gotten that idea. If you can provide a link maybe I can help you out of the misunderstanding. Or someone else can. Just get a link that shows where your confusion starts---where you think some competent person is saying that.

If you were taking a GR course and you said this on the final
if the spatial dimensions are closed the temporal dimension must be closed as well.
you might very well get an F, or incomplete, or some such thing you wouldnt be happy with.

Last edited: Mar 30, 2007
10. Mar 30, 2007

### MeJennifer

Sorry but this is basic general relativity.

A closed universe in general relativity looks like a 4-sphere, not a 3-sphere with some open time dimension.

By the way Marcus, what's up with all these ad hominum remarks?

11. Mar 30, 2007

### marcus

HELP! They're denying the existence of de Sitter space!!!:surprised

I have to give up on you Jennifer, put you on ignore or something. Hopefully somebody else will straighten you out on this.

One of the best solutions to the Einstein equation is topologically the 3-sphere x R and called dS

A Dutchman named Willem de Sitter in 1917 (just two years after GR was first published!)

Anybody interested can see the definition here, all you need is highschool maths to see how it is defined
http://en.wikipedia.org/wiki/De_Sitter_space

as you can see from the wikipedia formulas it is the cartesian product of infinite time-axis R with a three-sphere S3
in mathematical shorthand R x S3

A nice lower dimensional analog to imagine is the 2D deSitter space which is topologically R x S1
a long tube but horned out at both ends---or a tube with a "waist". Some math teachers would call it a hyperboloid of revolution.

Anyway, Willem de Sitter realized that the 4D de Sitter space has a natural metric on it which gives a solution for the Einstein equation for a universe which is SPATIAL CLOSED (spatially finite, at any given moment space is like a sphere, in fact is a 3sphere) and TEMPORAL OPEN (time is infinite forwards and backwards, like R the infinite time axis)

Last edited: Mar 30, 2007
12. Mar 30, 2007

### marcus

It is too much of a nuisance to have to respond to flat contradictions of basic GR facts.

Maybe we should have a tutorial about de Sitter space. It is becoming very important as a model. On par with Minkowski space, and I think potentially more so. And it is kind of "thing one" in GR, basic basic.

In the meanwhile, I have to find out where the "ignore" button is so as to avoid being told that the number 4 doesnt exist and therefore 2+2 must equal 5

Great! I found it. You click on the person's name. and select "view profile" and on the profile page there's a place where it says "put so and so on buddy list" and "put so and so on ignore list"---and you just do the obvious clicks. It's great. What a relief!

and if anybody doesnt like to hear from me about spatial-closed-temporally-open solutions to GR, or my adverse opinion of the 1930 Milne picture then please they should reciprocate and put me on ignore! i'd be so happy

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13. Mar 30, 2007

### marcus

To put it simply and to wrap the discussion up. You CAN have a space-time in GR where only the spatial dimensions are closed---a metric giving a natural slicing with that property.

And in fact that type of spacetime is of growing importance in research these days. And could well be the way the world actually is.
That you don't believe such a solution to GR is possible is a problem you have to deal with on your own. Good luck with it.

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14. Mar 30, 2007

### MeJennifer

You can only have such kind of "solutions" if you add a fudge factor (e.g. the cosmological constant).

I don't consider the cosmological constant part of the theory of relativity, and so did Einstein by the way, he called it "the biggest blunder of my life", and he died with that opinion!

I think he was right in taking it out of his theory.

And even if there is some sort of dark kind of energy then it is simply wild guessing to assume that such energy can be expressed in the form of some sort of a constant. And it seems some are already trying to fudge it even more by making into some kind of semi-constant.

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15. Mar 30, 2007

### Wallace

Remember that things we take as basic physics now were once fudge factors. Gravity, electromagnetic fields, electricity etc etc.

Of course many other things such as spontaneous generation, the fluid theory of heat and Descartes little magnetic screws turned out to be complete phurphies.

Whether or not dark energy turns out to be the former or the latter, we do not know yet. However, a solution of the equations of general relativity containing dark energy in general or a specific case such as the cosmological constant is perfectly valid.

Don't confuse the question of whether something is a valid solution with the question of whether it is the correct physical theory.

To suggest that the addition of dark energy in the standard model of cosmology is nothing more than wild guessing disrespects your own ability to comprehend the reasons it was brought into the standard theory.

16. Mar 31, 2007

### hellfire

I agree with Wallace and marcus that the cosmological constant term is perfectly valid. However:

I think that this is basically correct. You can consider this from two different points of view. On the one hand the cosmological constant is a modification of the original Einstein-Hilbert action. In this sense it may be some kind of fudge factor although in the modern formulation of general relativity it is often considered. On the other hand a de-Sitter space may be also the result of a matter scalar field acting as a cosmological constant. In that case, the Einstein-Hilbert action remains untouched, however, we have a matter component that violates some of the usual energy conditions. Again a kind of fudge factor somehow.

17. Mar 31, 2007

### Corkie2003

Thanks very much for your input guys, even though I didn't start the thread with intention of teddies being fired out of prams at relativistic velocities! The latest images from Hubble show a Pooh bear traveling past Uranus.

Where does the supposition that within the 'surface' of the sphere, there is nothing, come from? Or for that matter, beyond the sphere (or even the flared cone) of 'space'?

18. Mar 31, 2007

### George Jones

Staff Emeritus
When people use the term "closed" in the context of cosmology, they usually mean compact. If spacetime is compact, then it admits closed timelike curves, which could mean paradoxes; I gave a proof of compactness https://www.physicsforums.com/showpost.php?p=1254758&postcount=82". When people used the term "closed" in the context of cosmology, they also are usually referring to spatial sections.

As others has pointed outde Sitter space, has topology R x S^3.

MeJennifer, is this what you mean?

Even with zero cosmological constant and dark energy, closed Friedmann-Robertson-Walker universes that have both a Big Bang and a Big Crunch have topology R x S^3, i.e., open time and closed spatial sections. It may seem that, in these models, time should be represented by a closed interval in R, but the Bang and Crunch singularities are not part of the spacetime manifold, they're more like boundary points that aren't included. Thus, time is an open interval in R, and this has the same topology as R.

Last edited by a moderator: Apr 22, 2017
19. Mar 31, 2007

### marcus

LOL
I felt sure it would be worthwhile responding to your question. And it turned out to be, very!
Thanks for starting the thread

Branches of science go thru phases and right now cosmology is a data-fitter's field. If you put an extra term in the classic 1915 Einstein GR model (actually a term he put in originally himself without a really good reason) you get amazingly good fit to four or five different sets of data gathered different ways.

And the more that comes in, the better the fit.

So you may get swell-heads who say "I dont like Lambda! I don't like w!
It's against my personal taste of how the universe should run! Mother Nature should have consulted me about what model to use!"

And the answer, at this stage of history, is simply "Nature didn't ask you. Our job is to fit the data. This fits better than anyone had a right to expect."

The next historical phase is already visible but most people don't know or pay attention because there is no press coverage. There are already people who are looking at the Einstein model with the Lambda number (or the equivalent thing that hellfire mentioned where you also get a w number) and saying how could this effective equation arise in a beautiful and fundamental way?
In other words, what LOOKS to superficial eyes like a fudge factor, or two fudge factors, is something that deep eyes see as a possibly arising as, say, quantum corrections when the 1915 model is made more beautiful by quantizing it----or in some other fundamental way.

But the way science works, you don't worry about the next swing of the pendulum, when you are in data-fitting mode you just focus on that and get a really good effective equation. So we have to make sure that our value for Lambda is really right, and that it really fits, and that there arent some other factors, like w, that have to be put in for trim, and so on.

then, after 10 years, a reliable effective equation is turned over to the deep vision people and they transform the Einstein equation into something else (probably that talks to the quantum physics of matter)

From two guys, Willie Ockham (13th century IIRC) and Bernie Riemann (1850s).

If you dont need it, you don't assume it. You dont make unnecessary assumptions and add unnecessary clutter to a theory.

Riemann figured out a way of defining a continuum, and giving it more or less arbitrary geometry, FROM THE INSIDE. Shapes can be defined and measured and studied using just the intrinsic experience of moving around inside them. Riemann was a Mozart of mathematics and Einstein just USED Riemann's new 1850 invention of any-shape geometry.

Riemann says you dont need any external higher dimension warehouse to put things.

Ockham says, well since we don't need it then it is only for children and sci-fi people to fantasize about it, ***zap*** it doesnt exist!

Any of us can still choose to believe in the unnecessary higher dimension surroundings, if we want to and it makes us happy, as a kind of religious mysticism thing. The scientific approach is not fundamentally about belief it is more about discarding unnecessary clutter and getting predictive models. there is admittedly a suggestion of monkish asceticism here But it seems to work.

Hey Corkie! That was a great question. Thanks for helping us stir the pot!

Last edited: Mar 31, 2007
20. Mar 31, 2007

### MeJennifer

You are missing the point.
The point is that lambda runs counter to the principle of relativity, it invalidates the theory rather than supporting it.
Adding something to the Einstein field equations does not fine-tune the theory of relativity, it invalidates it!

But isn't this case quite different from the case of dark energy?

Of course these points are not just coordinate singularities. But if you claim that only one dimension is the culprit at these two points then you must also claim that the format of the metric matters in GR right?

Last edited: Apr 1, 2007
21. Mar 31, 2007

### Wallace

Sorry but this is not true at all. Genereral relativity permits the presence of energy that can be described by it's equation of state defined as it's pressure divided by the density. This is how matter, radiation are dark energy are described in GR. If you want to claim that dark energy is not permitted in GR you are going to have to disallow radiation to exist in the universe I'm afraid.

22. Mar 31, 2007

### MeJennifer

Energy and mass are already represented in the Einstein field equations, aren't they? So then why would you need the cosmological constant to describe energy? Simple question right? Do you have a simple answer for me? Or is the answer simply to make it fit?

As soon as you use the cosmological constant you must postulate some special kind of energy or some a-priory curvature.
You invalidate the equivalence between mass-energy density of space-time and space-time curvature.
This equivalence, that is the foundation of the theory of general relativity.

It is ok if have your own theory, but don't call it standard general relativity if it is not. Even when we know Einstein initially proposed it, later Einstein clearly rejected the idea of a cosmological constant in his theory, he thought it his biggest mistake.

IMHO, all those who claim that the cosmological constant is part of the standard theory of general relativity do great injustice to Einstein's legacy.

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23. Mar 31, 2007

### marcus

Wallace
A propos the two moderators (Janus, SpaceTiger) don't hesitate to mention it to one of them if you ever feel you are being harrassed, it is one of the things the "report" button is for. And quite apart from the "report post" function a short PM simply to say hello is not always out of place.

Anyway I just recalled that one of the mods, Janus, has a couple of very apposite quotations, from Betrand Russell and from Alexander Pope, that serve as his signature.

Janus' sig:

The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts.--Bertrand Russell
.
A little learning is a dangerous thing;
Drink deep, or taste not the Pierian spring;
There shallow draughts intoxicate the brain,
And drinking largely sobers us again. -- Alexander Pope
==================

SpaceTiger is just finishing his degree in cosmology at Princeton, or else he did last year. I cant remember which. I think you are a working cosmologist, so you may know quite a few of the same people.

I havent seen much of either Janus or SpaceTiger recently (the latter must surely be busy if finishing thesis and/or looking for jobs, or he may already into his first postdoc, it's hard to keep track.)

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24. Mar 31, 2007

### marcus

Speaking just as a longtime member and not in any official way I want to venture a plea for Jennifer to be nice, and not so vehement. This forum is really a wonderful place but it doesnt work without basic courtesy.

Wallace I admire your patience and kindness enormously. I've had to put Jennifer on ignore, not wanting to be confronted with tirades that seems to me to make very little sense.

Jennifer you are attacking Wallace for allowing the cosmological constant Lambda to occur in the Left Hand Side of the Einstein equation.
One can get the same effect simply by not having Lambda occur at all! In which case one inserts an extra energy term in the Right Hand Side.

None of this is against the spirit of Einstein, whom we doubtless all revere, or his legacy. I find your vehemence disconcerting, not to say possibly insulting to Wallace or others, and beg you to restrain it. Perhaps you could find something else to talk about?

25. Apr 1, 2007

### hellfire

I would like to point out again that you can have also a cosmological constant behaviour without a cosmological constant but with a matter scalar field acting as a cosmological constant. In that case, the modification of general relativity is not in its geometrical part but in its matter content, allowing for violation of energy conditions.

IMHO the inclusion of a cosmological constant as geometrical modification of the Einstein-Hilbert action can be actually considered against the original spirit of general relativity. On the one hand due to the original indentification or relation between curvature and matter content. On the other hand, due to the fact that $\Lambda \neq 0$ does not provide the correct newtonian weak field limit which was a basic criterium for the original formulation of general relativity. Only if $\Lambda$ is small enough, the deviation would be negligible (see e.g. Wald section 5.2). Moreover, due to a deviation from simplicity, adding an extra term to the original Einstein-Hilbert action.

Let us try to keep the discussion about objective criteria and arguments. By the way, may be it would be a good idea to continue this discussion in the relativity forum (split this thread?).

Last edited: Apr 1, 2007
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