# How can the universe be infinite and finite at the same time?

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There has to be an outer limit, and then, what is on the other side of this outer limit?

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Empty space.

the Place the Universe is expanding Into.

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There has to be an outer limit, and then, what is on the other side of this outer limit?

very few think the universe, has no end; so yes most agree with you that it ends someplace.

whats on the other side of course is not known, nor will it likely ever be known. if you prefer the Big Bang Theory, at least the current one, then space itself was part of the singularity, which sprang out giving us the universe. those then says "nothing" however defined, was replaced by space and that this space is the ends of the universe and in constant outward mode.

IMO; the universe ends someplace, not likely to be expanding. space and the universe having always been pretty much as it is today. beyond then empty space...

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Surface of a sphere is a finite infinite.And our universe is expanding into some space thingy...I never knew that .I thought that it was just the space-time expanding itself without a notion of 'beyond'.

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This has been discussed in great detail in other threads, if I get a chance I'll search...

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it shouldn`t take long, we get about 1 a week asking the same thing!

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I do not have anything against the Big Bang Theory and the idea that the universe is expanding. Proven scientific observations are kind of hard to counter, in my opinion, though the implications of the first few seconds of the existence of the universe truly raise many more questions. It surely must have been some kind of self-propelling fusion bomb using some form of material with unknown properties that God set off right as he killed himself, leading to the scattering of more of this unstable material. How else could a sun spontaneously combust from inert matter in deep space?

What I am asking now is how can space be limitless? According to some, once the universe reaches full expansion, it will start to revert and shrink, which would be one long heyday of cataclysmic collisions to observe until the inevitable wallop.

It either keeps on expanding indefinitely, starts shrinking back, or hits a wall, though it could slow its expansion to a crawl till it stops, like a fish outgrowing its tank. Either way, it shouldn't be limited, but if it is infinite, just how could that be?

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One thing at a time!

First, there does not have to be an "outer limit," even if it is finite. It could do something like "fold back" on itself, such that travelling in one direction eventually brings you back to where you started.

Second, it CAN be infinite, and also be expanding. It just means that everything is getting farther away from everything else, getting "less crowded." Or, to put it another way, the universe has infinite volume, but finite density, which can increase or decrease.

Third, it wouldn't stop expanding because it reached some "limit." It would stop expanding because the forces causing it to expand, whatever those might be, become weaker than the forces pulling things together, like gravity.

Fourth, I figure you're probably kidding about "suns spontaneously combusting" and whatnot, but in case you're not, the sun is not "on fire." Fire is a chemical reaction of combining oxygen. The sun is fusion, which is merging atoms together into different atoms (different elements), it happens because the core is so extremely compressed from gravity.

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• 4 weeks later...
Empty space.

the Place the Universe is expanding Into.

lol , now that must be one of the worst statements in science

for the starter of the topic...it is a very long discussion which no answer has been found..so don't worry about it seeming to be mind boggling. In fact, like someone stated about a sphere having an infinite surface w.r.t. two dimensions. In mathematics, advanced differential geometry and manifold topology is the scientific area of working with the universe models today. No, stating that our universe with inherent 3-dimensional space properties is expanding into some similar 'empty space' which would have same properties is NOT an answer (YT2095).

It is a hard question , simply because we are still researching it. Current research works with so-called positive semi definite metrics etc. The issue about finiteness and infiniteness geometrically speaking, has to do with certain experimental variables (look up the omega factor I believe its called). which is determined from what we think we know about the mass distribution and its relative velocities to again, arbitrary reference points (ps. the cosmological principle for example isn't as sound as we tend to assume but thats a different discussion).

Anyway, this omega factor gives an indication of the curvature of space-time, or Einstein's adopted Minkowski space.. It might be positive (open) , negative (closed) giving it predictions about if the universe will expand forever and cool down (enthropy-wise) or actually collapse on itself again.

Now, after the psychobabble, the more important question is what you initially are trying to do...visualise with the imagination how 'inside' the universe and 'beyond' it can be.

aka Visible universe and there which original light has not reached (this is with the assumption of a centre point , big bang event).

An eternal, infinite universe is of course much easier to imagine, but would then defy much of the astronomical data. ***** edited

Yes, I am not answering anything in this post...just threw out some thoughts and some concepts you can google further and/or think about)

lakmilis

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I do not have anything against the Big Bang Theory and the idea that the universe is expanding. Proven scientific observations are kind of hard to counter, in my opinion, though the implications of the first few seconds of the existence of the universe truly raise many more questions. It surely must have been some kind of self-propelling fusion bomb using some form of material with unknown properties that God set off right as he killed himself, leading to the scattering of more of this unstable material. How else could a sun spontaneously combust from inert matter in deep space?

What I am asking now is how can space be limitless? According to some, once the universe reaches full expansion, it will start to revert and shrink, which would be one long heyday of cataclysmic collisions to observe until the inevitable wallop.

It either keeps on expanding indefinitely, starts shrinking back, or hits a wall, though it could slow its expansion to a crawl till it stops, like a fish outgrowing its tank. Either way, it shouldn't be limited, but if it is infinite, just how could that be?

lol, like your way of expression :X

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• 2 weeks later...
There has to be an outer limit, and then, what is on the other side of this outer limit?

Let's say the universe's topology is isomorphic (geometrically similar) to a sphere (it's likely not, but that's another topic). You don't want to think of yourself as an observer floating around in that sphere, but as an observer on the surface. Let's also pretend you're two dimensional; your natural perception of reality is constrained to the surface of that sphere.

Now it should be obvious to you that this surface has only a finite area. It should also be obvious to you that if you pick a direction and start walking, you'll never run into a boundary--no edge to speak of. You'll just keep circumnavigating this sphere forever. These two facts about the surface of a sphere our 2D version of you has discovered are analogous to what cosmologists mean when they say the universe may be finite in one sense and infinite in another.

The trick is to remember that we occupy a four dimensional space-time, a higher dimensional analogue to our sphere's surface, that might curve and twist in ways that permit its total content--a higher dimensional analogue to area and volume--to be finite while simultaneously permitting an observer to eternally move inertially (under no influence other than gravitation due to the curvature of space-time).

Ghetto edit: replaced isotropic with isomorphic

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Let's say the universe's topology is isotropic (geometrically similar) to a sphere (it's likely not, but that's another topic). You don't want to think of yourself as an observer floating around in that sphere, but as an observer on the surface. Let's also pretend you're two dimensional; your natural perception of reality is constrained to the surface of that sphere.

Now it should be obvious to you that this surface has only a finite area. It should also be obvious to you that if you pick a direction and start walking, you'll never run into a boundary--no edge to speak of. You'll just keep circumnavigating this sphere forever. These two facts about the surface of a sphere our 2D version of you has discovered are analogous to what cosmologists mean when they say the universe may be finite in one sense and infinite in another.

The trick is to remember that we occupy a four dimensional space-time, a higher dimensional analogue to our sphere's surface, that might curve and twist in ways that permit its total content--a higher dimensional analogue to area and volume--to be finite while simultaneously permitting an observer to eternally move inertially (under no influence other than gravitation due to the curvature of space-time).

At what point is space-time observable? What I mean by this is what in reality can show the existence of such truly? Like how I can pick up a rock and through it, so I know I can do that, I cant physically touch the rock and look at it, bust it apart and so on. At what point in physics is space-time observable like that? I mean I have a general understanding, barely, of what scientists mean by space-time, but what allows them to know for sure that it exists, I never really attempted to look for that until your post actually, so if you know, like have a link to something, could you post it?

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At what point is space-time observable? What I mean by this is what in reality can show the existence of such truly?

We start with 16 equations that relate the shape of space-time with matter or energy occupying. We can write this concisely as:

$G_{ab} = \kappa T_{ab}$ (don't worry what [imath]\kappa[/imath] means, it's just a bunch of scaling constant anyway)

[imath]G_{ab}[/imath] gives you the shape of space-time and [imath]T_{ab}[/imath] gives you the corresponding distribution of matter and energy. Let's say [imath]T_{ab}[/imath] is chosen to represent a planet of mass [imath]M[/imath]. Well, you compute [imath]G_{ab}[/imath] to get the associated curvature of space-time. You can observe space-time by firing a beam of light across the region [imath]G_{ab}[/imath] describes. The light will travel along the most direct path from its origin in the direction you aimed for. With the right instruments, you can convince yourself that the light bends as the surface it's traveling across does. Voi la, you've just observed space-time.

Like how I can pick up a rock and through it, so I know I can do that, I cant physically touch the rock and look at it, bust it apart and so on.

Space-time isn't material. Material is encoded in the right side of the equation [imath]T_{ab}[/imath]. Space-time is hybrid construct of dimensions of measure. It's the thing that on which you place a coordinate system. Many physicists and cosmologists find it perfectly legitimate to talk of space-time as a physical thing, but personally I think that's confusing. They're not trying to say that space-time is an object with mass or energy, they're simply trying to say that space-time is coordinate-free constraint on the motion of objects described by [imath]T_{ab}[/imath].

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The best estimates by physicists of the value of omega, the variable that tells us whether we're in an infinite open universe (omega value equal to 1) or a finite closed universe (omega value greater than or less than 1) suggests we're in a finite closed universe.

In such a universe, go far enough in one direction and you'll get back to the place you started. Space would loop back on itself.

This is, perhaps, not an intuitive topology. Then again, neither was a spherical earth.

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The best estimates by physicists of the value of omega, the variable that tells us whether we're in an infinite open universe (omega value equal to 1) or a finite closed universe (omega value greater than or less than 1) suggests we're in a finite closed universe.

An open universe does not mean that the universe is infinite, it simply means that the curvature for the observable universe is isomorphic to a saddle surface. We can't say with any certainty how mass-energy out of causal contact curves space-time, and if expansion continues unabated we never will.

This is, perhaps, not an intuitive topology. Then again, neither was a spherical earth.

A spherical Earth was intuitive enough for anyone actually concerned with territory beyond the horizon. There's a reason why Earth's spherical isomorphism was realized (with a reasonable estimate of its circumference) by the early third century BC.

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We start with 16 equations that relate the shape of space-time with matter or energy occupying. We can write this concisely as:

$G_{ab} = \kappa T_{ab}$ (don't worry what [imath]\kappa[/imath] means, it's just a bunch of scaling constant anyway)

[imath]G_{ab}[/imath] gives you the shape of space-time and [imath]T_{ab}[/imath] gives you the corresponding distribution of matter and energy. Let's say [imath]T_{ab}[/imath] is chosen to represent a planet of mass [imath]M[/imath]. Well, you compute [imath]G_{ab}[/imath] to get the associated curvature of space-time. You can observe space-time by firing a beam of light across the region [imath]G_{ab}[/imath] describes. The light will travel along the most direct path from its origin in the direction you aimed for. With the right instruments, you can convince yourself that the light bends as the surface it's traveling across does. Voi la, you've just observed space-time.

Space-time isn't material. Material is encoded in the right side of the equation [imath]T_{ab}[/imath]. Space-time is hybrid construct of dimensions of measure. It's the thing that on which you place a coordinate system. Many physicists and cosmologists find it perfectly legitimate to talk of space-time as a physical thing, but personally I think that's confusing. They're not trying to say that space-time is an object with mass or energy, they're simply trying to say that space-time is coordinate-free constraint on the motion of objects described by [imath]T_{ab}[/imath].

Does such only act on light, I mean the curvature being the proof that is? Just sounds kind of weird really. I mean space-time supposedly leads to gravity, but that would mean curvature equal at all points on a body, in respects to geology and gravity anomalies how does that pan out? So is light the only thing space-time will bend, seems kind of odd is all, plus that last bit as a coordinate free constraint? I can only think in more primitive terms such as mass, or matter and energy really, the more multidimensional language used still pretty much eludes me past my taking such as yet more solely mathematical based constructs used to explain to label information really.

I can understand it as a mathematical construct or model to help explain, but I am simply confused overall as to its physical properties. To many times physics and math simply makes me think of a Rubix Cube to be honest. I mean I can read an article on biofilm and have not so much trouble, but when it comes to some concepts in physics I get lost, I think its the translation from the math that causes so much trouble, it must be funny though or frustrating to try and explain this stuff sometimes though huh? Well anyways thanks.

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Does such only act on light, I mean the curvature being the proof that is?

A massive body's motion through space-time is also affected by the curve. Simplest example is a satellite orbiting the Earth. I chose light only to show that there is a curve to begin with.

Just sounds kind of weird really. I mean space-time supposedly leads to gravity, but that would mean curvature equal at all points on a body, in respects to geology and gravity anomalies how does that pan out?

Not quite sure what you're saying here. Could you clarify?

So is light the only thing space-time will bend, seems kind of odd is all, plus that last bit as a coordinate free constraint?

My point was that light travels along a path that is bent by a gravitating body. That curved path is the most direct path through space-time from the light beam's origin through some distant point. A massive body will take a less direct path, but that path is still curved in space-time.

I can only think in more primitive terms such as mass, or matter and energy really, the more multidimensional language used still pretty much eludes me past my taking such as yet more solely mathematical based constructs used to explain to label information really.

Math really helps with this kind of discussion. There are some semantic analogies out there that capture part of the problems in these kind of discussions, but nothing that really captures all of them without resorting to some math.

I can understand it as a mathematical construct or model to help explain, but I am simply confused overall as to its physical properties.

It's physical property is topology, a fancy word for shape. That is, space-time is simply geometry. The reason I used light in my explanation was to as a way to illuminate the geometry of space-time. And as you know, geometry affects how things other than light--massive bodies--move. An analogy would be a ball bearing rolled along the curve of a sink. The sink has a geometry, right? Well, so does space-time, and its geometry of a region of space-time is the result of the distribution of matter and energy inside it.

To many times physics and math simply makes me think of a Rubix Cube to be honest. I mean I can read an article on biofilm and have not so much trouble, but when it comes to some concepts in physics I get lost, I think its the translation from the math that causes so much trouble, it must be funny though or frustrating to try and explain this stuff sometimes though huh? Well anyways thanks.

It's actually a valuable exercise for people like me who are working with or still studying the material. Also, I think it's important that scientists try to accurately but clearly break down their knowledge for people who, by and large through their tax dollars, pay their bills. You can learn a lot while trying to explain ideas to others, and on top of that it's a great way to capture that gee-whiz experience that makes the whole exercise fun in the first place.

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The best estimates by physicists of the value of omega, the variable that tells us whether we're in an infinite open universe (omega value equal to 1) or a finite closed universe (omega value greater than or less than 1) suggests we're in a finite closed universe.

Really? According to Alan Guth's article "Eternal inflation and its implications" (http://arxiv.org/pdf/hep-th/0702178), the omega constant is found to be approximately 1.012 (+0.018/-0.022), hence the universe seems to be rather flat.

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Really? According to Alan Guth's article "Eternal inflation and its implications" (http://arxiv.org/pdf/hep-th/0702178), the omega constant is found to be approximately 1.012 (+0.018/-0.022), hence the universe seems to be rather flat.

If Omega were exactly 1.012 that would say a finite positive curved universe with a radius of curvature of about 130 billion LY. But I would prefer not to rely on Alan Guth's authority.

I would recommend you go directly to working observational cosmologists, who analyse the data directly. Also Guth is somewhat the "elder statesman". My guess is that Guth is just quoting some result from David Spergel, or Ned Wright, Joanna Dunkley----one of those younger people currently leading the field.

Ned Wright recently published a "best fit" figure of Omega = 1.011 based on combining four or five different data sets. It could be that Guth has a citation to Wright. I'll take a look.

Another thing is the width of the ERROR BAR. I have seen quite a bit narrower in the literature than what Guth gives. I don't trust him because he has his inflation ax to grind (his claim to fame). So I would go direct to the working cosmologists and see what size error bar you find.

===================

I don't have time to check to see who Guth is citing as his authority, but it could be this

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

If you are curious about more nitty gritty issues you could have a look. I will get back to this later. It is actually pretty interesting. Some very recent papers by cosmologists do confront the possibility that Omega > 1

and that the universe, though "nearly" flat spatially, may actually be spatially positive curved and spatially finite.

Data is still not good enough to distinguish but the issue arises when people analyze the data because assuming exact flatness can bias the results.

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If Omega were exactly 1.012 that would say a finite positive curved universe with a radius of curvature of about 130 billion LY.

Yeah, I see your point. However, from what I have understood of cosmology, the measures of this value have always given results very close to 1, and the universe seems to be accelerating. I am no cosmologist, so I really have no clue other than referring to what I have read.

I would recommend you go directly to working observational cosmologists, who analyse the data directly. Also Guth is somewhat the "elder statesman". My guess is that Guth is just quoting some result from David Spergel, or Ned Wright, Joanna Dunkley----one of those younger people currently leading the field.

His data is described in the article "Cosmological parameters from SDSS and WMAP" by Tegmark, et al.

http://arxiv.org/abs/astro-ph/0310723 (in the table on page 9).

I don't trust him because he has his inflation ax to grind (his claim to fame). So I would go direct to the working cosmologists and see what size error bar you find.

I thought the inflationary cosmology was rather strong, compared to many of the other models that exist? It has a great explanatory power, doesn't it?

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Yeah, I see your point. However, from what I have understood of cosmology, the measures of this value have always given results very close to 1, and the universe seems to be accelerating. I am no cosmologist, so I really have no clue other than referring to what I have read.

I don't think the fact that there is an accelerating scale factor is directly relevant, Viking. Past measures of Omega HAVE typically given values slightly on the up-side of one, with the errorbar somewhat lopsided towards the upside. This is CONSISTENT with the true value being exactly one (and for simplicity it is often convenient to assume that.

It is also CONSISTENT with a spatially finite positive curved universe where the volume of space is large and the curvature very small. The measurements that have been taken over the years are just what would have been expected in that case too.

I think you might find it interesting to study more RECENT estimates than what Guth quotes. He quotes a 2003 paper. Things have progressed, esp with the release in 2006 of the three-year WMAP data. I will get you a link.

His data is described in the article "Cosmological parameters from SDSS and WMAP" by Tegmark, et al.

http://arxiv.org/abs/astro-ph/0310723 (in the table on page 9).

That 2003 paper of Tegmark only had ONE year of WMAP data. Also the Sloan Digital Sky Survey (SDSS) has been proceeding rapidly in the intervening years. There are now several important sets of data we didnt have in 2003 and the errorbar on Omega has been narrowed down considerably from what Tegmark said in 2003

I thought the inflationary cosmology was rather strong, compared to many of the other models that exist? It has a great explanatory power, doesn't it?

I'd suggest keeping an open mind. Inflation is not a cosmology in the full sense. It is a brief SCENARIO attached at the beginning of standard cosmology to answer some puzzles

horizon problem (how temp equilib different sectors of sky)

flatness problem (why nearly flat)

structure formation (whence came observed density fluctuations)

Inflation is an elegant answer to these riddles, but it replaces one puzzle by another: no-one has ever seen an "inflaton" field. no-one has a clear idea of how it actually would have worked---so it remains at the status of a scenario.

Meanwhile people continue trying to come up with alternative solutions to the horizon problem etc.

But the truth-status of various inflation scenarios is not the issue here. Let's focus on what has been measured especially as concerns Omega.

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Viking, here a link to some more up-to-date information

http://arxiv.org/abs/astro-ph/0603449

Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology

D. N. Spergel, R. Bean, O. Doré, M. R. Nolta, C. L. Bennett, J. Dunkley, G. Hinshaw, N. Jarosik, E. Komatsu, L. Page, H. V. Peiris, L. Verde, M. Halpern, R. S. Hill, A. Kogut, M. Limon, S. S. Meyer, N. Odegard, G. S. Tucker, J. L. Weiland, E. Wollack, E. L. Wright

91 pgs, 28 figs. Accepted version of the 3-year paper as posted to this http URL in January 2007

(Submitted on 19 Mar 2006 (v1), last revised 27 Feb 2007 (this version, v2))

David Spergel is a way prominent guy, but you get the idea already from his being lead author. So is Charles Bennett. this is a blue ribbon paper.

It is an authoritative paper on the third year WMAP data which were released March 2006 simultaneously with this paper explaining the implications of the data for cosmology.

I underlined Ned Wright and Joanna Dunkley because they have authored related papers bearing on the spatial finite/infinite issue.

the remarkable thing is that in one of the figures it gives a 68 percent confidence interval for Omega that is ALL TO THE RIGHT OF ONE. It is something like [1.01, 1.04].

for several reasons this is not to take too seriously. for one thing 68% is not 95%. But it is suggestive.

In their conclusions they said "nearly flat."

Flat is still the dominant picture among rank-and-file cosmologists, for several reasons. But it is being challenged by prominent people within the profession.

Here is the number of that figure, and the page, in Spergel et al.

Yes, here it is: page 50, Figure 16.

68 percent interval for so-called Omegak [- 0.041, - 0.01]

which means that the 68 percent interval for Omega is [1.010, 1.041], or not to put to fine a point on it: [1.01, 1.04]

A recent Ned Wright paper gives a "best fit" LCDM to all the available data that is relevant, which has Omega = 1.011

Here is the Ned Wright paper in case anyone wants

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

He points out that the data so far is CONSISTENT with the spatial flat infinite picture. We cannot yet rule out EITHER the flat case or the finite case. He has the "best fit" Omega = 1.011, thing in a table near the end.

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So it actually seems like the universe might be closed, instead of being flat. If this turns out to be the case, then is it possible that the universe is heading towards a Big Crunch in the far future?

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No, recent mapping of cosmic microwave background radiation and the observation of distant supernovae; as standard candles (objects of known luminosity), shows (quite conclusively) that the expansion of the universe is accelerating. The positive value for the cosmological constant, is attributed to quantum vacuum itself, which exerts a force repelling gravitationally on larger scales. This is all proof of the continual expansion of the universe theory...

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So it actually seems like the universe might be closed, instead of being flat. If this turns out to be the case, then is it possible that the universe is heading towards a Big Crunch in the far future?

Spatial finite does not imply Big Crunch. Big Crunch is very unlikely, can almost be ruled out. With positive cosmological constant (or "dark energy") you can have solutions which are spatially closed and expansion continues indefinitely.

I agree with grifter's post.

However you ask "is it possible?" and it is very hard to say that something is not possible. Suppose that there is a "dark energy particle" and it DECAYS after a long long time----or that the cosmo constant is not really constant and it goes from being positive (as now measured) to negative after a long time. These ideas are too speculative for my taste to even think about. But if something like that happens then we might not have expansion forever. Logically, a Big Crunch is a remote possibility.

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