# Infinite Universe: What does it mean?

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1. Jul 1, 2014

I know some folks may get tired of questions about the finite/infinite scope of the universe. Sorry for that. But as you know, many concepts are hard to wrap one's head around. Let me make my question as clear as possible from the outset:

-I am NOT asking whether the universe is infinite or finite. I accept that we don't know.
-I only wonder what it would mean to say that the "universe" is "infinite."
-I know that to answer this question depends on the proper use of specific definitions, and I may not be fully aware of what the standard definitions are.

Anyway, in the FAQ tells us: "Standard cosmological models come in three flavors, open, flat, and closed,[Carroll] whose spatial curvatures are negative, zero, and positive. The open and flat types have infinite spatial volume."

And NASA tells us: "If the density of the universe is less than the critical density, then the geometry of space is open (infinite), and negatively curved like the surface of a saddle. If the density of the universe exactly equals the critical density, then the geometry of the universe is flat like a sheet of paper, and infinite in extent."

Now let me just assume an "open" universe, at less than critical density. The above suggests that the universe has "infinite spatial volume," and is "infinite in extent."

Which of the following would it be fair to assume, in this case?:

A) There exists matter/energy at a distance greater than 500 Quintillion (5*10^20) light years from earth. I.e., much much beyond the limits of the "observable universe."
B) Matter/energy may be assumed to extend beyond the limits of the "observable universe," though there's no accounting for its extent. We can assume that the density beyond what is observable is the same or similar to the density that is observable.
C) There is no reason to assume the existence of matter/energy even one micrometer beyond the limits of the observable universe. However, the observable universe is able to expand without limit, and without ever having to contract.

As a tangential question, when a physicist uses the term "infinite", does that generally mean "a damnably large number so far beyond what is measurable that it approximates infinity," or is it expected to fit literally and absolutely the mathematical abstraction of "infinity" (which seems largely paradoxical in its formulation)?

2. Jul 1, 2014

### phinds

Given the assumption of an infinite universe, A is correct, although it would be even more correct to just say something like "goes on forever" rather than pick some finite number

B would be wrong because ... well, "infinite" means infinite, not "really, really large"

C would be ridiculous in any case since it would imply an edge of the universe in a spherical shape with us at the center and that makes no sense

As to your question about "infinity", I say again ... "infinite" means infinite, not "really, really large"

3. Jul 1, 2014

### Mordred

answer B is appropriate, (if you aren't looking at the necessity of infinite)as we also have no idea if the geometry stays the same beyond the observable universe.

we also don't know if the universe is finite or infinite even in terms of knowing our observable universe is extremely close to flat. It could also mean that the universe so large that by all measurements our relatively small observable portion can measure being flat, however we would not be able to measure a curvature. (think of the ant on a ball scenario)

4. Jul 1, 2014

### TumblingDice

The bolding below is my own, because I prefer to steer clear of assuming and assumptions. I'm going yea or nay based on the OP meaning "could accept as certain" wherever "assume" was originally mentioned.

No. Infinite matter/energy solves some problems for some theories and creates some as well. I'm unaware this would be absolutely required or could be proven.

I'm with Mordred - this is "appropriate". It states what we don't know and our better  theories based on what we do know.

Hmm... That word "assume" just doesn't sit well with me. To get this to slip under the wire, change "assume" to "know for certain".
: There's a problem with C, because in an open model, it implies we would be at the center of the matter and energy in the universe. I shouldn't have replied as I did. (I shouldn't have commented on 'C' at all...)

Last edited: Jul 1, 2014
5. Jul 1, 2014

Okay. So far there's a bit of disagreement among responses, but it seems that not all physicists agree that an "open" low-density universe indicates an infinite expanse of matter and energy beyond the observable universe. What is agreed upon is that, in such a model, the observable universe can be expected to go on expanding endlessly.

At the core of this question is the extent to which physics can claim knowledge of that which lies outside of the observable universe.

Let me ask another question, proposing a hypothetical shape to the physical universe. Maybe we can call this "Option D". I'll illustrate in two dimensions, with circles, representing 3D spheres in cross-section:

-Imagine the big circle is the physical extent of a large collection of matter and energy, perhaps the entire universe, finite in extent.
-The smaller circle inside is the observable universe. (This is necessarily defined by our point of view, but there is no separation or boundary).
-They are expanding together.

The question is whether such a structure could be possible, and whether it would be consistent with the "open" universe model we started with.

Of course, from the point of view of expansion, our observable universe would be the same. But I don't know whether having the observable universe off-center would create any observable effect. E.g., could matter beyond the "observable" universe have a gravitational effect upon the observable universe, thereby making it actually observable? I would imagine not, but I don't know.

IF Option D is theoretically impossible, then we're thrown back upon a dilemma. Then my original Option B would only be possible if we placed the observable universe in the center of a larger unobservable universe. THAT would return us to the same privileged position at the middle of everything that was regarded as too absurd to contemplate, which invalidated Option C. The absurdity would be compounded by the fact that we were not only placing ourselves at the center of the universe, but we were drawing an absolute conclusion about the structure of the unknown universe.

I guess, obliquely, this highlights that if the universe is finite AND open, then it must have a center somewhere... unless I've made a huge gaff in my understanding of all this.

I hope my question makes sense.

Last edited: Jul 1, 2014
6. Jul 1, 2014

### phinds

Nope, doesn't work because it presupposes/requires a center and that would violate the experimentally tested Cosmological Principle. The universe may be finite but if so it is unbounded and has no center.

I suggest the link in my signature.

7. Jul 1, 2014

I will return to your link and read it in detail ASAP, but meanwhile, while I thought I understood the balloon analogy, I also thought that finite and unbound only made sense in a closed model of the universe. Can there be an "open" universe which contains a finite amount of matter and energy <i>without</i> a center? Well, okay, more reading for me...

8. Jul 1, 2014

### Staff: Mentor

Yes, if it has a nontrivial topology. For example, spatial slices could have the topology of a 3-torus, which has a finite volume but no center. Observations cannot rule that out completely, because the universe has a finite age so we can only see things a finite distance away. The most we can say is that, if the universe has a non-trivial topology, we see no evidence of it at the farthest distances we can see.

9. Jul 1, 2014

Okay, this is all helpful, thanks everyone.

Let me pause and do a summary, which may not include everything, but is what I've gathered so far:

-If the universe is "open" then it will expand without limit.
-We still can't draw any definite conclusions about what may exist beyond the limits of the observable universe (in fact, I started this because I wondered to what extent we could say something "exists" if it's unobservable).
-Thus, An "open" model of the universe does not necessarily require an infinite expanse of matter and energy, nor does it rule out such a possibility.
-It is still believed that there is no "center" in such a model of the universe, even if its extent is finite.

I've come across a few other questions, which I'll ponder before posting.

10. Jul 1, 2014

### Mordred

you've got it thus far, A center implies a preferred direction and location. Expansion however shows us that there is no preferred direction or location. The universe is homogeneous and isotropic.

homogeneous no preferred location
isotropic no preferred direction.
together they describe a uniform universe, in expansion measurements all non gravitationally bound objects expand away from each other equally, in all directions. As per the balloon analogy, Phinds article covers the inherent risks of taking the analogy too far.

an article I like posting on universe geometry and distance measures that may help is
http://cosmology101.wikidot.com/universe-geometry
page 2 that covers the FLRW metric in a step by step format in regards to distance measurements is
http://cosmology101.wikidot.com/geometry-flrw-metric/

11. Jul 1, 2014

Okay. For such a time as the entire universe is not yet observable (because we have not yet received radiation from the most distant objects) Is it correct to say:

-The number of observable galaxies will always be increasing, regardless of whether the universe is open, flat, or closed, and regardless of whether it is finite or infinite? (I.e., radiation from more and more distant galaxies will eventually reach us regardless of the rate at which they are receding, and thus no part of the "observable universe" will become unobservable due to expansion taking it beyond an observable range).

And, taking a different set of preconditions, given a universe that is finite but larger than the currently observable universe:

-The entirety of a finite universe will eventually become observable, regardless of whether it is open, flat, or closed.

Finally, given that last point, if and when a finite but unbound universe becomes entirely observable, will we expect to see "echoes" or "reflections" of distant objects starting to appear? Could we then test for whether our observation encompasses the whole universe by comparing regions of distant space that are 180-degrees opposed from a given observation point?

12. Jul 2, 2014

### Staff: Mentor

Professor Susskind in a video lecture on Cosmology (search Susskind and Cosmology on youtube.com) said that if the universe just beyond the observable horizon was empty, that would cause anisotropy in the CMB. There would be photons exiting our observable region, but none entering. Further, that CMB observations of homogeneity and isotropy imply that the universe must be homogenous and isotropic out to at least 10 times the radius of the observable horizon.

Also, the expansion of the universe continues and it accelerates. Distant galaxies recede fastest and some disappear beyond the observable event horizon every day. Eventually, all galaxies (except the Milky Way and perhaps Andromeda) will disappear to us.

13. Jul 2, 2014

### phinds

Actually, my understanding from Marcus is that you have that backwards. Galaxies that are just outside the current observable universe will BECOME part of the OU as the Hubble "constant" changes into the future, so the OU is gaining galaxies, not losing them.

Last edited: Jul 2, 2014
14. Jul 2, 2014

### Lino

Phinds (or anyone) could you elaborate on this please? I appreciate that if there was no expansion that this would be the case, and I appreciate that objects at the inside "edge" of the OU are visible even though they are receding FTL. But how does the OU get more observable galaxies, when those outside of the OU are already receding FTL?

15. Jul 2, 2014

### marcus

You have some good ideas here but mixed them up so that one of the statements is wrong. What is called the observable universe is different (and much larger than) what is contained in the cosmic event horizon (CEH).

Most of the galaxies which we can see are out beyond the CEH. The CEH is around 16.5 Gly. A galaxy inside that range can send us a signal TODAY that will get here. We can TODAY send a signal to them that will eventually reach them.

The CEH is expected to stabilize around 17 Gly, it will not grow by much. There are today galaxies that are passing out of range, crossing the horizon. We will continue to see them for a long time after they have crossed, we just won't be able to see them as they were at any time after they cross over.

The radius of the observable region of the universe is called the "particle horizon" and it is much larger than 17 Gly. It is around 46.28 Gly as of today (if you could pause the expansion process long enough to measure it). And it is increasing. It is on track to increase to around 62 Gly, as I recall. That is in today's distance. So a matter which today is 60 Gly from us today will eventually become detectable, or at least would if we are still around and have sensitive enough instruments, very far in future.

The currently observable region of the universe is defined to include not just LIGHT but also neutrino signals and any kind of signal that travels at c that we might detect if we had the right instruments. Currently we actually see matter that is only about 45.33 Gly, that is how far the matter is (today) that emitted the ancient light we are receiving today and call the CMB (1+z= 1090). But if we had detectors that could see cosmic neutrinos we would be seeing closer to the theoretical max, like 46.28 Gly.

You can round these numbers off (they are approximate) I am spelling out surplus decimals so you can SPOT them on the table. Can you see 46.2789..≈ 46.28 in the particle horizon column? And can you see the distance NOW 45.33 of the matter that (as a hot gas) emitted the ancient CMB light we are now seeing, stretched by a factor of 1090?

$${\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}$$ $${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline S&T (Gy)&D_{now} (Gly)&D_{hor}(Gly)&D_{par}(Gly) \\ \hline 1090.000&0.000373&45.331596&0.056714&0.000856\\ \hline 339.773&0.002496&44.183524&0.178562&0.006124\\ \hline 105.913&0.015309&42.012463&0.552333&0.040144\\ \hline 33.015&0.090158&38.051665&1.651928&0.248752\\ \hline 10.291&0.522342&30.917756&4.606237&1.491191\\ \hline 3.208&2.977691&18.247534&10.827382&8.733318\\ \hline 1.000&13.787206&0.000000&16.472274&46.278944\\ \hline 0.312&32.884943&11.117770&17.224560&184.082917\\ \hline 0.132&47.725063&14.219438&17.291127&458.475874\\ \hline 0.056&62.598053&15.535514&17.299307&1106.892899\\ \hline 0.024&77.473722&16.092610&17.299802&2639.025517\\ \hline 0.010&92.349407&16.328381&17.299900&6259.261851\\ \hline \end{array}}$$

In the table you can see the CEH stabilizing at around 17.3 Gly. And you can also see that in years 92 billion distances will be about 100 times their present size which means that the present distance of the farthest matter then observable will be 0.01 times 6259 Gly. In other words the distance NOW of that matter is 62.59 Gly. that is a rough indication of the ultimate extent of the observable region of the universe---matter that is NOW about 62 Gly. That is what is meant about the amount of matter in the observable region constantly growing as more light comes in from more distant matter. The particle horizon is now about 46.28 Gly and it is expected to extend to include stuff that is now as far as 62 Gly

Last edited: Jul 2, 2014
16. Jul 2, 2014

### marcus

Look at the table in preceding post and try adding the CEH and the particle horizon of the present (S=1) row.

16.47 + 46.28 = 62.75

The particle horizon says that if some matter sent out a flash of light right near the time expansion started then by now, in year 13.7 billion, the light could have traveled a distance 46.28.
It is more than 13.7 Gly because of expansion. That is what the particle horizon tells us, that we could today be receiving signal from some matter that is NOW 46.28 from us.

well, if some matter is now just inside 62.75 Gly from us and around year zero it sent a flash of light in our direction. That light could have traveled 46.28 (in the unlikely case it didn't get scattered) and so it would now be just inside 16.47 Gly from us. SO IT IS GOING TO EVENTUALLY MAKE IT!

That is what today's cosmic event horizon of 16.47 Gly tells us, any flash of light that is TODAY within that range will eventually get here.

17. Jul 2, 2014

### marcus

So you see why the OU is gaining matter?---the currently observable matter is all the matter currently out to 46.28 Gly. And it is destined to become all the matter that is currently out to 62.75 Gly. Because light or some kind of signal (neutrino?) from that matter could in principle be already within the "safe, home-free" radius of 16.47 Gly.

So the observable region has to grow. To become a region whose contemporary radius is 62.75.
And that region is of course also subject to expansion. So when distances are 100 X what they are now it will have a radius of 6275 Gly.

18. Jul 2, 2014

@Marcus: If I understand you, then what you've said suggests that the observable region has to grow... and then shrink again!

Check if this is right. A galaxy which is currently 62.75 Gly away will eventually become observable, because light (or neutrinos, or....) that was emitted from that galaxy is within the 16.47 Gly. Okay, fine. but what about the light (or neutrinos...) that that same galaxy emits now. THAT light will never reach us. What about the light that it emitted very shortly after the big bang. THAT light will also never reach us, because it has not yet reached a range of 16.47 Gly.

So... it sounds as though, 16.47 billion years from now, the extent of the observable universe will reach its limit and then retreat again. For 16.47 billion years, we we will see more, and more, and more of the universe and then... less, and less, and less. (By "retreat", I don't mean in Giga-light-year distance, but only in the sense of the amount of the physical universe that is observable. I.e., galaxies will be passing out beyond the limit of what is observable).

Is that correct?

19. Jul 2, 2014

If what I said immediately above is true--and it seems to be--then my questions in message #11 have been answered (my assertions were false). I'd have to revise as:

-The number of observable galaxies is increasing, but will not necessarily always do so. If the universe is "open" eventually some galaxies in the "observable universe" will become unobservable due to expansion taking them beyond an observable range.

-If the universe is "closed" and finite, the entirety the universe will eventually become observable.

-If the universe is not closed, (if it is "flat," or "open,") then even if the universe were finite, it would not necessarily become entirely observable. I.e., in an "open" universe, it may never be possible to determine whether the universe contains a finite amount of matter and energy.

20. Jul 3, 2014

### marcus

That light (emitted very shortly after start of expansion) is the only light we could ever see from that matter because it needs the whole 13.8 billion years to get from where the emitting matter is to within the 16.47 Gly range.

The max distance a flash of light can be from its source, at present, is 46.28 Gly and this would only be if the signal was emitted around "year zero" around start of expansion and so could have been traveling for the entire 13.8 Gy.

Better not to think about light "from galaxies" when we are talking about light emitted in very early universe. the matter that emitted the light when it was a hot gas may have condensed into stars and galaxies in the meantime. But it is emitted by the matter when the matter is hot ionized gas. this is hypothetical because the U was not sufficiently transparent until around year 370,000. Light would have been scattered and unable to make it thru. So we have to be thinking about neutrino signals or something else. the particle horizon 46.28 is a theoretical maximum distance from source of unspecified signal emitted in year zero.

21. Jul 3, 2014

### marcus

Immediately above means post #18 where something you said actually was not true. You said:
"What about the light that it emitted very shortly after the big bang. THAT light will also never reach us, because it has not yet reached a range of 16.47 Gly."

I just now explained what was wrong.

Another bit of advice: after 1998 it turned out that the terminology "open" and "closed" universe could be confusing and not very useful. I try to avoid using those terms.

Before 1998 people thought that a finite volume universe like a 3D hypersphere had to collapse eventually. so they called it "closed" because it was closed in two senses, spatially and in terms of its future contraction, so closed in time as well.

But that was found to be wrong. the U can be spatially finite and still expand forever. So when you say "closed" it is not clear what you mean. Do you mean the "closed" universe that expands forever or the "closed" universe that eventually starts contracting and goes to a crunch?

IMHO better to use more words and avoid jargon that has become confusing.

22. Jul 3, 2014

Okay, I understand what you're saying about jargon, except I'm picking up the language as I go, and folks in these threads and other sources seem to use the terms in various ways.

New revision:

-The number of observable galaxies is increasing, but will not necessarily always do so.

-If the density of the universe is below the critical density, so that it expands forever, eventually some galaxies in the "observable universe" will become unobservable due to expansion taking them beyond an observable range. (However, they will not suddenly go black... from what I've just been reading, they will gradually red-shift until no observable radiation can be received).

-If the universe is more dense than critical density, so that it will cease to expand and will eventually "crunch," and if it is finite, the entirety the universe *may* eventually become observable. (It just occurred to me that an exceedingly large but finite universe--that may have always been exceedingly large--could expand and then collapse so that much of the matter would never have become observable from the beginning to the end of time... hmmm...)

-If the universe has a low density, so that it expands forever, then even if the universe were finite, it would not necessarily become entirely observable. I.e., it may never be possible to determine whether the universe contains a finite amount of matter and energy.

So, if THIS is roughly correct, then with regards to the question of whether the universe contains infinite matter and energy, the question remains unsolvable in most scenarios.

23. Jul 3, 2014

### marcus

Being more dense than critical density does not imply it will cease to expand. It can be more than critical density and continue expanding forever. This was discovered in 1998. I just wrote to you about this, Zadig.

24. Jul 3, 2014

Hmmm... someone may need to provide a link or information about jargon then, because even your earlier post got me to reconsider the use of the word "closed," but it wasn't so clear to me that I must also reconsider "critical density."

What is the meaning of "critical density," and why is it critical? It seems that NASA's site, and most users in these forums, use critical density to mean the density of the universe that would cause the universe to "crunch." Are there two critical densities, one which is "critical" to the question of a finite but unbound universe, and another one which is "critical" to the question of limiting the expansion of the universe?

It's odd that incorrect usage of terms like "closed," and "critical density" are persisting for over 16 years after they've been invalidated. And this is what causes confusion for they layman, like me, who has to ask questions such as "what does infinite universe mean?" when it seems obvious that these kinds of language need pretty clear and precise definitions to be understood.

Anyway, thank you for your continued patience with this. I hope you can see that some challenging concepts become even more challenging to comprehend when language breaks down and misconceptions abound.

25. Jul 3, 2014

### Chronos

A closed universe is classically viewed as spatially finite. Choosing a coordinate system that renders this sensible is a bit complicated.