Saddle and flat universe edges?

[msailer1234]

Hi,

I have become very interested in cosmology recently and I had a question about the possible shapes of the Universe. I understand the critical density plays a role in the shape. This is what I know (or think I know). At the critical density of energy and matter, the universe is flat. If it is less than the critical density it is saddle shaped. If it is greater than the critical density, it is spherical and finite curving back on itself so that traveling any direction would hypothetically bring you back to the same point.

My question is, what is the geometry and characteristics of the flat and saddle universe in regards to boundaries? Does the saddle universe also curve back on itself in a certain way in theory? Or do these seemingly open universe concepts have infinite dimensions of space and/or space time?

Additionally, if you could direct me to some great journal articles on the subject that are relatively (no pun intended) easy to understand, that would be fantastic! (no worries if you can't think of any)

Thanks!

 

[Bandersnatch]

My question is, what is the geometry and characteristics of the flat and saddle universe in regards to boundaries? Does the saddle universe also curve back on itself in a certain way in theory?

Both these cases are spatially infinite without boundaries (all three have no boundaries). The flat one obviously so. The saddle-shaped has hyperbolic geometry, so it doesn't curve back upon itself much like the hyperbola doesn't.

Or do these seemingly open universe concepts have infinite dimensions of space and/or space time?

Note that when discussing the shape of the universe, it's only the 3-dimensional spatial slice of equal time that is under consideration. So neither space-time nor additional dimensions have any need to be bothered.

Additionally, if you could direct me to some great journal articles on the subject that are relatively (no pun intended) easy to understand, that would be fantastic! (no worries if you can't think of any)

(I'm assuming here you meant the subject of cosmology in general, not of this question in particular)
As far as journal articles with a pedagogical bent go, I highly recommend Lineweaver and Davis' 'Expanding confusion' and (with Webb) 'The Tethered Galaxy Problem'. Both discuss some unintuitive and interesting properties of the expanding universe. Some background knowledge might be necessary.

If you're looking for something slightly more lightweight, there's also a few great articles on our Insights blog, bridging the gap between popular and textbook treatments. E.g.:
Inflationary Misconceptions and the Basics of Cosmological Horizons
A Poor Man’s CMB Primer
Approximate LCDM Expansion in Simplified Math

 

[Grinkle]

I very much enjoyed The Poincare Conjecture - In Search of the Shape of the Universe

Accessible enough up until the author starts discussing the modern (1990's) attempts at proofs at the (far) end of the book then it became murky.

That ending didn't detract from my experience reading the book, it was well worth the time.

https://www.amazon.com/dp/080271532X/?tag=pfamazon01-20

 

[msailer1234]

Is a flat or saddle shaped universe compatible with the big bang theory? It seems like that would require an infinite amount of energy which would not be possible with a finite age of the universe.

 

[Grinkle]

Is a flat or saddle shaped universe compatible with the big bang theory? It seems like that would require an infinite amount of energy which would not be possible with a finite age of the universe.

Expansion theories of the early universe do not assume any particular size of the early universe - they say that the early universe was denser than it is today; that is different from saying it was smaller than it is today. There is no theory that I know of to guide us on whether the universe is finite or infinite. We take as axiomatic (I think its an axiom as opposed to proven somehow) that if the universe is of infinite extent today then it must always have been of infinite extent, and if it is finite today then it was always finite.

But I don't think finite precludes non-closed. Finite and expanding can continue without bound, as far as I know.

 

[Bandersnatch]

Is a flat or saddle shaped universe compatible with the big bang theory? It seems like that would require an infinite amount of energy which would not be possible with a finite age of the universe.

They are. The infiniteness of 'stuff' in the infinite universe doesn't play a role.
Please relate your line of thinking that led you to believe it wouldn't be possible so that we may troubleshoot it.

 

[msailer1234]

They are. The infiniteness of 'stuff' in the infinite universe doesn't play a role.
Please relate your line of thinking that led you to believe it wouldn't be possible so that we may troubleshoot it.

I thought the main principle of the big bang was that all of space and time came from a singularity if you look back in time. After the big bang, space expanded from a point rather than matter just moving further away. This is why we have the background radiation. I also thought a finite amount of energy in the universe is necessary to have the total energy add up to 0. What am I misunderstanding?

 

[msailer1234]

Expansion theories of the early universe do not assume any particular size of the early universe - they say that the early universe was denser than it is today; that is different from saying it was smaller than it is today. There is no theory that I know of to guide us on whether the universe is finite or infinite. We take as axiomatic (I think its an axiom as opposed to proven somehow) that if the universe is of infinite extent today then it must always have been of infinite extent, and if it is finite today then it was always finite.

But I don't think finite precludes non-closed. Finite and expanding can continue without bound, as far as I know.

A finite flat universe doesn't seem to make sense to me. There would have to be edges which is a really weird thing to think about. Do you know of any articles that discuss this that you could recommend?

 

[Bandersnatch]

I thought the main principle of the big bang was that all of space and time came from a singularity if you look back in time. After the big bang, space expanded from a point rather than matter just moving further away. This is why we have the background radiation. I also thought a finite amount of energy in the universe is necessary to have the total energy add up to 0. What am I misunderstanding?

1. The big bang singularity is temporal. It's a point in time, not in space. As Grinkle mentioned above, a universe that is infinite now, was always infinite (but more tightly packed). The observable universe converges to a spatial point as one rolls back the time, but that's not the singularity.
2. It's critical energy density, not critical energy. I.e., it's independent of the actual size.

 

[Grinkle]

Do you know of any articles that discuss this that you could recommend?

https://www.physicsforums.com/insights/big-bang-happen/

https://www.physicsforums.com/insights/balloon-analogy-good-bad-ugly/

https://www.physicsforums.com/insights/brief-expansion-universe/

https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/

edit:

I don't know that you will find a lot of specific discussion around resolving human brain limitations in visualizing complex geometrical stuff. It is the case that a geometry can exist without being embedded in a higher dimensional geometry. So a 3d universe can exist and expand without automatically requiring the universe to be having a pre-existing and larger fourth dimension to be expanding into. I can't picture it, either, if that is any consolation. For myself, I gave up the notion that my inability to mentally image something is evidence that something can't exist. It was a hard notion to give up.

 

[msailer1234]

1. The big bang singularity is temporal. It's a point in time, not in space. As Grinkle mentioned above, a universe that is infinite now, was always infinite (but more tightly packed). The observable universe converges to a spatial point as one rolls back the time, but that's not the singularity.
2. It's critical energy density, not critical energy. I.e., it's independent of the actual size.

1. Okay, I think I understand what you're saying. I found this short FAQ post that helped me understand: http://www.astro.ucla.edu/~wright/infpoint.html
2. I understand critical density is what dictates the shape. If our observable universe started from a singularity, but the full universe is infinite, wouldn't that imply all matter came from the same point? Would that point be infinite by definition?

 

[PeterDonis]

I thought the main principle of the big bang was that all of space and time came from a singularity

No, it isn't. There is a singularity in a particular idealized model that is often used for pedagogy, but there is not a singularity in the actual model cosmologists use to describe our actual universe. More precisely, that model does not require an initial singularity or make any claims about whether one is there or not. The term "big bang" in the actual model refers, not to an initial singularity, but to the hot, dense, rapidly expanding state that is the earliest state of the universe for which we have good evidence. We don't know for sure what preceded that state, but the best current hypothesis is that it was preceded by an epoch of inflation. We don't know whether an initial singularity preceded inflation or not; some inflation models, like "eternal inflation", do not have one.

If our observable universe started from a singularity, but the full universe is infinite, wouldn't that imply all matter came from the same point? Would that point be infinite by definition?

Your reasoning here is based on a mistaken premise as far as our best current model of the actual universe is concerned; see above.

However, even in the idealized model I referred to above, that is used for pedagogy, your reasoning above is not quite correct. The initial singularity in this model is not, strictly speaking, part of the universe; it is a mathematical limit that does not exist physically. The scale factor of the universe goes to zero, mathematically, in this limit, which is why many pop science treatments refer to the initial singularity as a "point"; but if you dig deeper into the math, this limit has some properties that are not well described by the term "point": for example, the limits of worldlines of different objects, when extended into the past, do not actually meet; they each end up at a different place in the limit.

 

[PeterDonis]

If our observable universe started from a singularity, but the full universe is infinite, wouldn't that imply all matter came from the same point?

There are other issues here as well. I don't think the FAQ entry you linked to is strictly correct when it says that our observable universe came from a point. Ordinary language isn't really suited for describing the idealized model being referred to. A better way to describe what is going on mathematically would be to say that, in the limit as the initial singularity in the idealized model is approached, the size of the observable universe as seen from a particular worldline goes to zero--or, to put it another way, if zero time has elapsed since the initial singularity, then light has had time to travel zero distance, so you can only see zero distance away from you. But that doesn't mean that all of the universe that is observable to us now was a point at the initial singularity.

Also, in the above you seem to be assuming that the observable universe, meaning what we can observe today, contains all of the matter in the universe. It doesn't. The diagrams in the article you linked to should make that clear.

 

[msailer1234]

There are other issues here as well. I don't think the FAQ entry you linked to is strictly correct when it says that our observable universe came from a point. Ordinary language isn't really suited for describing the idealized model being referred to. A better way to describe what is going on mathematically would be to say that, in the limit as the initial singularity in the idealized model is approached, the size of the observable universe as seen from a particular worldline goes to zero--or, to put it another way, if zero time has elapsed since the initial singularity, then light has had time to travel zero distance, so you can only see zero distance away from you. But that doesn't mean that all of the universe that is observable to us now was a point at the initial singularity.

Also, in the above you seem to be assuming that the observable universe, meaning what we can observe today, contains all of the matter in the universe. It doesn't. The diagrams in the article you linked to should make that clear.

Thank you for your response, but I fully understand the observable universe is not all there is. I do not know what part of my post made you believe I thought that.
Additionally, it seems there are some opposing views in mainstream science and the big bang. I also see how the terminology is not prefect in trying to describe the big bang.

Your reasoning here is based on a mistaken premise as far as our best current model of the actual universe is concerned; see above.

I don't think I adequately explained what I meant with my example. I had been taught the following:
1. All the energy in the universe should add up to 0
2. The current theory suggests everything may have come from a quantum fluctuation
3. Our observable universe can be thought of as a "bubble" on a huge expanding balloon full of many (possibly infinite) other bubble universes that we will never be able to interact with because of inflation

My question is referring to the idea that all the energy of the universe adds up to 0 assuming that hypothesis is correct (with negative energy of gravity cancelling out all the positive energy of mass and light). I am getting the sense that this may not be the most accepted view.

To clarify my question, I am asking that given a universe model that is either saddle or flat shaped, how does it not approach a paradox if we reverse time and have an infinite universe collapse to a finite point? I understand we don't know much about the very early universe, but it seems like this paradox is still there.

 

[Bandersnatch]

To clarify my question, I am asking that given a universe model that is either saddle or flat shaped, how does it not approach a paradox if we reverse time and have an infinite universe collapse to a finite point?

It doesn't collapse to a finite point. All distances scale down towards 0 in the limit, but a spatially infinite universe stays infinite.

 

[msailer1234]

It doesn't collapse to a finite point. All distances scale down towards 0 in the limit, but a spatially infinite universe stays infinite.

I would define that as a paradox.

 

[PeterDonis]

t seems there are some opposing views in mainstream science and the big bang.

You'll need to cite some mainstream science sources to back up this claim. I'm not aware of any significant disagreements in mainstream cosmology about the big bang, defined as I defined it earlier, and what came after it. The disagreements are about what came before it--was it inflation, and if so, what particular kind of inflation model.

I had been taught the following:

Taught from what source?

1. All the energy in the universe should add up to 0

That depends on how you define "all the energy in the universe" and how you add it up. You might want to read this:

http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

2. The current theory suggests everything may have come from a quantum fluctuation

That's one speculative hypothesis, but that's all it is, a speculative hypothesis. It is certainly not established by any evidence at this point.

3. Our observable universe can be thought of as a "bubble" on a huge expanding balloon full of many (possibly infinite) other bubble universes that we will never be able to interact with because of inflation

"Many bubble universes" is an ok description of an "eternal inflation" model, but the "bubble" we are in, in this kind of model, is much more than just our observable universe.

My question is referring to the idea that all the energy of the universe adds up to 0

The "shape" of the universe, which is what you were asking about up to now, has nothing whatever to do with the energy of the universe adding up to 0. The particular mathematical trick that that ordinary language phrase describes works for any "shape" of the universe.

To clarify my question, I am asking that given a universe model that is either saddle or flat shaped, how does it not approach a paradox if we reverse time and have an infinite universe collapse to a finite point?

And this has nothing whatever to do with whether you think the mathematical trick for "energy adding up to 0" is physically meaningful or not.

You seem to have, not one well-defined question, but a bunch of vague questions that seem to be based on misunderstandings.

I would define that as a paradox.

Apparently "paradox" to you means "I don't understand it". That's not a good definition. The model being described is perfectly consistent mathematically.

At this point you really need to cite some sources for where you are getting your understanding from. You seem to have some significant misconceptions, but we can't help you to correct them unless we know where they came from.

 

[phinds]

I would define that as a paradox.

Why? What about it seems paradoxical to you?

 

[Bandersnatch]

I would define that as a paradox.

Why? Take two arbitrarily chosen points in an infinite space, separated by distance D. Divide all distances in that space by an arbitrary factor (say, 2). This makes the initial distance D become D/2. Has the space become any less infinite? Now, let's relabel the new, shrunk, distance as D, and repeat the process. Do it as many times as you want. Is there a step at which the space in which the two points are located stops being infinite?

 

[msailer1234]

Why? Take two arbitrarily chosen points in an infinite space, separated by distance D. Divide all distances in that space by an arbitrary factor (say, 2). This makes the initial distance D become D/2. Has the space become any less infinite? Now, let's relabel the new, shrunk, distance as D, and repeat the process. Do it as many times as you want. Is there a step at which the space in which the two points are located stops being infinite?

I understand the concept of approaching zero, but it doesn't seem to explain anything as to why the universe is like this because it never gets completely back to 0. Or it doesn't seem like it gives any room to even ask that question which seems like a paradox.

Taught from what source?

Everything I know about cosmology (which isn't much otherwise I wouldn't be on a forum) is from the MOOC by Brian Schmidt and Paul Francis: https://www.edx.org/xseries/astrophysics.

That depends on how you define "all the energy in the universe" and how you add it up. You might want to read this:

http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

That is a great article, thank you for sharing!

That's one speculative hypothesis, but that's all it is, a speculative hypothesis. It is certainly not established by any evidence at this point.

I found that speculative hypothesis from an interview with Lawrence Krauss.

"Many bubble universes" is an ok description of an "eternal inflation" model, but the "bubble" we are in, in this kind of model, is much more than just our observable universe.

Yes I understand that, there's more to the bubble than what we can just see.

The "shape" of the universe, which is what you were asking about up to now, has nothing whatever to do with the energy of the universe adding up to 0. The particular mathematical trick that that ordinary language phrase describes works for any "shape" of the universe.

I think I am starting to see that now.

And this has nothing whatever to do with whether you think the mathematical trick for "energy adding up to 0" is physically meaningful or not.

You seem to have, not one well-defined question, but a bunch of vague questions that seem to be based on misunderstandings.

I see nothing wrong with this. I stated above that I do not know much about cosmology, but am becoming interested in it. I thought some things were connected at first that might not be connected with total energy and the shape of the universe.

Apparently "paradox" to you means "I don't understand it". That's not a good definition. The model being described is perfectly consistent mathematically.

At this point you really need to cite some sources for where you are getting your understanding from. You seem to have some significant misconceptions, but we can't help you to correct them unless we know where they came from.

That's not very helpful saying my definition is I don't understand it. I am trying to understand which is why I am asking on this forum.

See above, but my post also asked for more sources so I can help understand because I don't have a lot of knowledge. You guys have shared some sources which are great and I will be looking into. Part of learning is getting it wrong at first.

 

[PeterDonis]

I see nothing wrong with this.

There's nothing wrong with starting out with a not very good understanding and trying to improve it. But that's not how your posts are coming across. See below.

That's not very helpful saying my definition is I don't understand it. I am trying to understand which is why I am asking on this forum.

When you use the word "paradox", that's a strong claim: you're saying there is something wrong with the model. You do not have the basis to make such a strong claim; the only basis you have is that you don't understand how the model works. So you should not be using the word "paradox". You should be saying things like "I don't understand how the model with an initial singularity works; can you help me to understand it?"

 

[msailer1234]

When you use the word "paradox", that's a strong claim: you're saying there is something wrong with the model. You do not have the basis to make such a strong claim; the only basis you have is that you don't understand how the model works. So you should not be using the word "paradox". You should be saying things like "I don't understand how the model with an initial singularity works; can you help me to understand it?"

I think I'm done using Physics Forums. As I described I'm interested in the subject and will continue learning, but this was a weird response.

 

[PeterDonis]

this was a weird response.

What's weird about it? You apparently did not realize what your use of the word "paradox" implied, and were thus confused about the responses you were getting. I was trying to clarify.

I understand that you might not have realized what the word "paradox" implied when you used it. But it did have that implication, whether you realized it or not. So making you aware of that should help you in future.

 

[phinds]

I think I'm done using Physics Forums.

That would be unfortunate for you since PF is exactly the kind of place you need to dispel some of your misconceptions. You will not find a better science forum on the internet.

 

[Drakkith]

I think I'm done using Physics Forums. As I described I'm interested in the subject and will continue learning, but this was a weird response.

Don't take Peter's response as saying, "You're wrong and you should know better."
Take it as, "In science and math, the word 'paradox' means something specific, so be careful about using it."

We can get a little picky with our terminology here at PF. Just bear with us and you'll get used to it.