B Does an infinite universe contradict a Big Bang origin?

[DaveC426913]

TL;DR Summary

I have heard some say, right here in PF, that the universe may be infinite in extent. How does that jive with the Big Bang starting off very small in extent?

I grew up in a time when we thought the universe was finite in size - even if unbounded. I am now hearing (from some right here on PF) that scientists think maybe the universe is infinite in extent.

But if the Big Bang bubble was once a finite size and expanded (smaller than an atom, big as a basketball, larger than a city block, etc.) how can it become infinite in extent?

Perhaps something in here about "expanding everywhere all at once", and "it's only the observable universe that was once basketball sized"?

Confused.

 

[Ibix]

But if the Big Bang bubble was once a finite size

It wasn't. If the universe is now infinite it always was, just denser. If it is now finite and boundaryless, it always was.

 

[Ibix]

"it's only the observable universe that was once basketball sized"?

Correct.

 

[DaveC426913]

So TBBT applies to our observable universe?

That doesn't seem right. Our observable universe is a horizon problem, limited by speed of light, which BB expansion was not limited by. Why would that tiny volume have such a high temperature if not because it was the whole universe compressed into that space?

I realize I'm talking through my hat. I've gotten tripped up by someone who has asked a seemingly simple question about which my knowledge is (obviously) limited. I can't even manage a "lies to children" answer.

 

[Ibix]

So TBBT applies to our observable universe?

No, it describes the whole universe which is everywhere uniformly filled with matter (at least in an idealised model). It may be finite and closed or infinite. The observable universe is the bit of it we can see, which is finite in extent.

 

[DaveC426913]

No, it describes the whole universe which is everywhere uniformly filled with matter (at least in an idealised model). It may be finite and closed or infinite. The observable universe is the bit of it we can see, which is finite in extent.

I'm sorry, your responses seem to me to contradict each other. (that doesn't mean they are contradictory, just that they seem to be, from where I'm standing.)

I don't understand how the BB can apply to an infinite volume if we are able describe the BB has having a finite volume.

Is it kind of like the whole universe before the BB was infinite but did not contain properties of length, width, height or time associated with our spacetime, and then everywhere (perhaps) all at once, every point in the infinite universe erupted with these properties, inflating at supra-light speeds?

 

[Ibix]

we are able describe the BB has having a finite volume.

We aren't. The big bang was everywhere in the universe, whether that universe is finite or infinite. The whole thing (finite or infinite) was filled everywhere with hot dense matter, which has cooled and spread out now.

The observable universe is a finite patch of that whole. That is the thing that was once the size of a baseball, but it was always the same as everywhere else, filled with the same stuff everywhere else was.

 

[PeroK]

I'm sorry, your responses seem to me to contradict each other. (that doesn't mean they are contradictory, just that they seem to be, from where I'm standing.)

I don't understand how the BB can apply to an infinite volume if we are able describe the BB has having a finite volume.

Is it kind of like the whole universe before the BB was infinite but did not contain properties of length, width, height or time associated with our spacetime, and then everywhere (perhaps) all at once, every point in the infinite universe erupted with these properties, inflating at supra-light speeds?

Here's a simple mathematical analogy involving the infinite real number line. The distance between two points on the number line is $d(x, y) = |x - y|$. Imagine, however, that we map the number line to itself using a scaling factor $\alpha$, where $x \to \alpha x$. In this case, we assume $\alpha < 1$.

If we think of the integers on the original number line as points of matter, then on the new number line these integers are mapped to points that are closer together. We still have an infinite number line, but the points of matter are closer together.

If now we make $\alpha$ a function of time, where the current time is $t_0$ and $\alpha(t) = \frac t {t_0}$, then we have a simple, crude mathematical model of a "big bang" for the number line. The further back in time we go, the closer together all the points of matter are. But, we still have an infinite number line with a countably infinite set of points representing matter.

Note that at $t = 0$ every point is mapped to $0$. This represents a singularity, in that at $t = 0$ the mapping no longer represents something physically viable. So, this model cannot apply all the way back to $t = 0$. At some point, for small enough $t$, some other model is needed.

 

[DaveC426913]

I have concluded that I lack the background and knowledge to be able to explain this - even in simplistic terms - to someone who knows even less than I do.

Thanks for your efforts though.

My recommendation to my listener and myself is: read more.

 

[PeterDonis]

the whole universe before the BB

There was no such thing. The BB is a boundary of the spacetime that describes our universe, at least in the model we are discussing. There is no such thing as "the universe before the BB".

 

[javisot20]

TL;DR Summary: I have heard some say, right here in PF, that the universe may be infinite in extent. How does that jive with the Big Bang starting off very small in extent?

I grew up in a time when we thought the universe was finite in size - even if unbounded. I am now hearing (from some right here on PF) that scientists think maybe the universe is infinite in extent.

But if the Big Bang bubble was once a finite size and expanded (smaller than an atom, big as a basketball, larger than a city block, etc.) how can it become infinite in extent?

Perhaps something in here about "expanding everywhere all at once", and "it's only the observable universe that was once basketball sized"?

Confused.

"Universe" and "observable universe" are not the same. We are the center of the observable universe, by definition, whereas the universe has no center.

Furthermore, the expansion of the universe is an intrinsic property of spacetime (not a receding edge).

The cosmological principle tells you that right now you can move in any direction without stopping, observe the distance from that new position, and see the CMB at a certain distance. This does not change no matter how much you move with your observable universe (of which you are the center).

 

[DaveC426913]

There was no such thing. The BB is a boundary of the spacetime that describes our universe, at least in the model we are discussing. There is no such thing as "the universe before the BB".

Substitute "Whatever there was that brought the Big Bang into existence".

-

We are describing two distinct things here. The whole universe and the observable universe.

If the Big Bang's expansion is a description of what happened when our local Observable universe inflated rapidly, then how did it happen everywhere at once in an infinite universe - if some (most) if those parts are far from our OU?

 

[PeterDonis]

Substitute "Whatever there was that brought the Big Bang into existence".

According to the model we are discussing, nothing brought the BB into existence. That will be true for any model that has an initial singularity. The spacetime is simply there, period, from infinitesimally after the initial singularity on. Nothing brings it into existence. (The initial singularity itself is not part of the spacetime, which is why I said "infinitesimally after" just now.)

If you want to consider a different model, such as eternal inflation, that does not have an initial singularity at all, the question you are asking doesn't even arise; the model extends infinitely far into the past, and nothing brings it into existence.

Either way, the issue raised in the quote above simply does not apply.

 

[phinds]

If the Big Bang's expansion is a description of what happened when our local Observable universe inflated rapidly

It is NOT. It is a description of how ALL of the universe inflated rapidly.

 

[PeterDonis]

If the Big Bang's expansion is a description of what happened when our local Observable universe inflated rapidly

It isn't.

More precisely, the term "Big Bang" has two meanings, neither one of which fits what you say in the quote above.

Meaning #1: the BB is the initial singularity. That comes before everything else in the model, including inflation if we are considering an inflation model with an initial singularity. And the initial singularity is everywhere, not just in our observable universe.

Meaning #2: the BB is the hot, dense, rapidly expanding state that is created at the end of inflation, when the false vacuum inflation state decays to true vacuum and all the energy density from the false vacuum gets transferred to the Standard Model fields. But such a state is still not limited to our observable universe. Even in eternal inflation models where there are an infinite number of such BB events, and the universe we observe was produced by just one of them, the events still are not limited to the observable universe of any particular observer. And, as I noted in post #13 just now, in such models there is no initial singularity; the model extends infinitely far into the past (from our point of view in our own little universe produced by one BB event, inflation extends infinitely far into the past from our BB event).

 

[DaveC426913]

According to the model we are discussing, nothing brought the BB into existence. That will be true for any model that has an initial singularity. The spacetime is simply there, period. Nothing brings it into existence.

OK I'll accept that.

So, the whole universe and the observable universe are still distinct entities. If the observable universe was initially in some hot, dense, compactified state, but the whole universe was not (since it's infinite), what happened everywhere else in the whole universe outside our observable?

i.e. the whole universe is infinite in extent, but the OU is stil only basketball-sized, what's happening to the whole universe outside that basketball?

 

[DaveC426913]

It is NOT. It is a description of how ALL of the universe inflated rapidly.

This is directly contradictory to what someone said above. here, for example:

The observable universe is a finite patch of that whole. That is the thing that was once the size of a baseball, but it was always the same as everywhere else, filled with the same stuff everywhere else was.

 

[PeterDonis]

the whole universe and the observable universe are still distinct entities.

Yes.

If the observable universe was initially in some hot, dense, compactified state, but the whole universe was not (since it's infinite)

No. The whole universe was initially in some hot, dense, compactified state.

Of course it is possible, mathematically, using the laws of GR, to construct a model in which a tiny bubble of the initial size of our observable universe at the BB is hot, dense, and rapidly expands, but everything outside is something else, such as vacuum. But such a model does not match observations. Our observable universe would not look the way it does, in all respects for which we have data, if it were a "bubble" expanding into vacuum. Things like the relationship between redshift, apparent brightness, and angular size of galaxies would be very different in such a model from what we actually observe. That's why cosmologists don't use such a model.

 

[phinds]

This is directly contradictory to what someone said above. here, for example:

No, it is not. You are misreading what has been said. The OU is no different than ANY similar sized chunk of the universe located anywhere in it. ALL such chunks inflated since the entire universe inflated.

 

[PeterDonis]

This is directly contradictory to what someone said above. here, for example:

How so?

 

[PeroK]

So, the whole universe and the observable universe are still distinct entities.

The only difference is that the current observable universe is the region we have observed so far. It's like the ocean we can see as far as the horizon. That's not distinct from the rest of the ocean. In this case, the ocean may be infinite in extent or just larger than the region within the horizon.

If the observable universe was initially in some hot, dense, compactified state, but the whole universe was not (since it's infinite)

This is a fundamental misunderstanding of the nature of an infinite universe. An infinite universe can be in a hot dense state. If a truly infinite universe troubles you, just think of one that is large enough to be practically indistinguishable in terms of our observations from an infinite one.

, what happened everywhere else in the whole universe outside our observable?

The assumption is that the universe, whether finite or infinite, is the same everywhere.

i.e. the whole universe is infinite in extent, but the OU is stil only basketball-sized, what's happening to the whole universe outside that basketball?

The OU is simply the region we can see. What's beyond that is assumed to be more of the same.

 

[DaveC426913]

No. The whole universe was initially in some hot, dense, compactified state.

OK. So how does that jive with it being infinite in extent, as some are beginning to assume?

 

[PeterDonis]

how does that jive with it being infinite in extent, as some are beginning to speculate?

Um, just fine?

As others have already posted, there is no issue whatever with a spatially infinite universe being in a hot, dense state. The model we have that includes such a thing is perfectly consistent and makes good predictions. So we use it. What's the problem?

 

[DaveC426913]

Um, just fine?

As others have already posted, there is no issue whatever with a spatially infinite universe being in a hot, dense state.

Is it a hot, dense, compactified state?

The model we have that includes such a thing is perfectly consistent and makes good predictions. So we use it. What's the problem?

Please don't misunderstand my position; I'm not saying anything about it being wrong, I'm just trying to get my head around it. My head is the problem.

 

[Ibix]

OK. So how does that jive with it being infinite in extent, as some are beginning to assume?

It's got an infinite amount of matter uniformly filling an infinite space. It used to be higher density, now it's lower density.

Is what's troubling you some variant on "what's it expanding in to"?

 

[DaveC426913]

It's got an infinite amount of matter uniformly filling an infinite space. It used to be higher density, now it's lower density.

OK, so the Big Bang happened everywhere at once. Every point in the whole universe inflated at the same time to form spacetime, yes? I'm trying to get my head around this idea that something (the same thing) happened - at every point, in that uniform, infinite space - at the same time.

Is what's troubling you some variant on "what's it expanding in to"?

No.

It's how did it happen everywhere all at once in a universe that is, as you say, a "uniformly-filled infinite space" (which sounds to me like it is infinite in extent, not compactified)?

 

[PeroK]

Is it a hot, dense, compactified state?

I don't know what compactified means. An infinite universe is not compact in the topological sense.

 

[DaveC426913]

I don't know what compactified means. An infinite universe is not compact in the topological sense.

The whole 'smaller than an atom' thing. If it wasn't compactified, how can it have inflated?

To-wit:

ALL such chunks inflated since the entire universe inflated.

 

[Ibix]

It's how did it happen everywhere all at once in a universe that is, as you say, a uniformly-filled infinite space?

We'll get back to you on that.

If you assume that space is uniformly filled with matter then you can only have a spherical, flat, or open universe. All but the spherical one is infinite in extent. All of them start from a high density state and have a singularity at the beginning. The evidence suggests that we're in a flat universe, but doesn't rule out a very, very large closed one.

The singularity, though, suggests that the maths goes wrong somewhere. How it goes wrong and what actually happened are a matter of debate. The leading candidates are variants on inflation, which either push the singularity back in time or don't have a singularity. They use a period of extremely rapid growth (aka inflation) to explain how everything is the same everywhere. But Peter knows more of the detail than I do.

 

[Ibix]

compactified

Compact has a specific meaning in maths, which isn't relevant to this case. It was just hot and dense.

 

[DaveC426913]

Compact has a specific meaning in maths, which isn't relevant to this case. It was just hot and dense.

OK (sorry if I'm going around in circles) I still don't see how a (whole) universe that is infinite in extent can undergo "a period of extremely rapid growth (aka inflation)".

 

[Ibix]

I still don't see how a (whole) universe that is infinite in extent can undergo "a period of extremely rapid growth (aka inflation)".

And I'm having trouble understanding what you want to know here if it isn't some variant on "what's it expanding into". Universes filled with matter (or other stuff in the case of inflation) expand or collapse - it's just what they do.

 

[DaveC426913]

Universes filled with matter (or other stuff in the case of inflation) expand or collapse - it's just what they do.

But not if they're infinite in extent. They can't expand or collapse.

Or is it some variant on finite but unbounded?

I understand how a universe can start off in a compact, hot dense state (smaller than an atom) and expand to be finite (say, 140Gly in diameter, or whatever the OU is now) but unbounded - without it having to have something to expand into.

The easiest way I can envision that is if it wraps around, so if you were in a (magical) spaceship a few million years after the BB, you could cross the universe and arrive back where you started. (It may not be the correct way, but it's a way.)

Still, finite but unbounded is not infinite.

 

[Ibix]

But not if they're infinite in extent. They can't expand or collapse.

Yes they can. Imagine a line of stakes in the ground each 1m from the next. Come back a while later and you find the stakes are now 1.1m apart. That's expansion, whether there's a finite number of stakes or an infinite number of them.

 

[DaveC426913]

Yes they can. Imagine a line of stakes in the ground each 1m from the next. Come back a while later and you find the stakes are now 1.1m apart. That's expansion, whether there's a finite number of stakes or an infinite number of them.

Ah. A Hilbert's hotel thing.

I think that strikes at the crux of my confusion.

 

[Orodruin]

Ah. A Hilbert's hotel thing.

I think that strikes at the crux of my confusion.

Indeed, and the point is it is space itself that is expanding and becoming larger (in the usual cosmological coordinates). It doesn’t need anywhere to expand, it is just growing. So all of the matter in the universe becomes less dense - thereby also cooling down. Volume per mass grew and so density went down.

 

[javisot20]

Ah. A Hilbert's hotel thing.

I think that strikes at the crux of my confusion.

An infinite universe can expand, no edge of the universe is necessary for that to happen, expansion is an intrinsic property of space-time.

1- Choose a point in the universe to carry out observations with your best telescope.

2- You will observe very young galaxies in the distance, and CMB will be further away. On a large scale you determine that the universe has a certain content of matter and energy, and certain properties

3- Imagine at that moment you move instantly in any direction, for example to Andromeda, to mount your telescope again and observe the distance

4-You will see the same thing, young galaxies in the distance and the CMB further away, in addition, the content and properties of the large-scale universe will be the same as what you determined in the other point.

5- If the cosmological principle is correct, and it seems to be, you can move in any direction as much as you want and conclude the same thing

 

[DaveC426913]

Thanks all. I grok it now.

Not sure I'm in a position to explain it to someone with even less of a grasp of cosmology than i, but still...

 

[PeroK]

But not if they're infinite in extent. They can't expand or collapse.

I gave you an example of the number line expanding over time.

In any case, the mathematical basis of cosmology is precisely this. That we have an infinite universe with galaxies dotted around approximately uniformly at a large enough scale. But, as time goes on the galaxies become further apart. There is no mathematical contradiction.

That said, it's not really possible to visualise an infinite universe. You have to rely on the mathematics. And not to rely on intuition for the finite objects we are familiar with.

PS I nearly mentioned the Hilbert Hotel.

 

[jfmcghee]

That said, it's not really possible to visualise an infinite universe. You have to rely on the mathematics. And not to rely on intuition for the finite objects we are familiar with.

This is the part that gets me every time, even though I know better. I know that this is not possible, but it's almost impossible not to start doing it. And it makes it that much harder to try to explain to someone else, especially if they are not exposed to subjects where this kind of thinking is "normal."

 

[Orodruin]

That said, it's not really possible to visualise an infinite universe. You have to rely on the mathematics. And not to rely on intuition for the finite objects we are familiar with.

This is the thing though. People misunderstand what ”intuition” actually is. Intuition is built through familiarity with something. Everyone has intuition about mundane processes occurring all around us. But for things not occurring around us all the time - intuition needs to be trained before it can be effective. For dealing with infinite universes and advanced physics topics, intuition comes from exposing oneself to them, solving problems and going through arguments. Having done so, one can have intuition for such things - not so much without.

 

[timmdeeg]

Assuming that we will never be able to decide if we life in a very large sphere or if the universe is flat in the euclidean sense my intuition is just switched off. So, ad acta.

 

[256bits]

Indeed, and the point is it is space itself that is expanding and becoming larger (in the usual cosmological coordinates). It doesn’t need anywhere to expand, it is just growing. So all of the matter in the universe becomes less dense - thereby also cooling down. Volume per mass grew and so density went down.

I gave you an example of the number line expanding over time.

Much like the 2D representation of the expanding balloon surface, but that is a finite universe representation, is it not?

The left side/right side of the observable universe had no time to communicate during expansion, but are surprisingly similar. Inflation is theorized to explain the similarity.

So is there a horizon problem hidden within the infinite universe, or within the large universe models.
If our observable universe was hot and dense, as well as the infinite universe being the same, how did all the parts of the infinite universe, or large universe, communicate to all start to expand and become less dense, less hot .

 

[PeroK]

Much like the 2D representation of the expanding balloon surface, but that is a finite universe representation, is it not?

That represents a finite universe. The key concept there, which again can be hard to grasp, is that the universe is only the balloon's surface. And that surface can be defined mathematically as a 2D manifold in its own right, without being embedded in a space of higher dimension (i.e. 3D).

 

[WWGD]

That represents a finite universe. The key concept there, which again can be hard to grasp, is that the universe is only the balloon's surface. And that surface can be defined mathematically as a 2D manifold in its own right, without being embedded in a space of higher dimension (i.e. 3D).

Doesn't it have to live, be embedded within some version of spacetime?

 

[PeroK]

Doesn't it have to live, be embedded within some version of spacetime?

You can't always do it with only one additional dimension. See, for example:

https://en.wikipedia.org/wiki/Whitney_embedding_theorem

 

[Hornbein]

I like the infinite raisin bread dough model. The yeast expands the dough which causes all the raisins to move away from one another. There is no center.

 

[PeterDonis]

You can't always do it with only one additional dimension. See, for example:

https://en.wikipedia.org/wiki/Whitney_embedding_theorem

In the case of models of our universe, however, the analogue of the "balloon" is a 3D spacelike hypersurface that is embedded in a 4D spacetime. This is true whether the universe is spatially finite or spatially infinite.

It is also true that the analogue of the "balloon" can be analyzed as a 3D manifold in its own right, independent of its embedding in spacetime. But it still is so embedded, for this particular case.

 

[WWGD]

In the case of models of our universe, however, the analogue of the "balloon" is a 3D spacelike hypersurface that is embedded in a 4D spacetime. This is true whether the universe is spatially finite or spatially infinite.

It is also true that the analogue of the "balloon" can be analyzed as a 3D manifold in its own right, independent of its embedding in spacetime. But it still is so embedded, for this particular case.

Well, I guess we have to define terms carefully, clearly. I thought " The Universe" is the totality of all there is. How then can it be embedded in something containing it. Maybe we're not using the right language to talk about it, or at least I'm not understanding the current usage of it. Edit: Pretty sure this topic has been brought up way before this post of mine.

 

[PeterDonis]

I thought " The Universe" is the totality of all there is.

That's a common definition, yes. But the term is ambiguous. See below.

How then can it be embedded in something containing it.

The universe at one instant of time, which is a spacelike 3-surface, is embedded in the 4D spacetime that describes the entire history of the universe.