Is the universe infinite in size?

[ercatli]

I am an occasional visitor here, and I hope this is the best place to ask a question please. I have been doing some reading on cosmology, and I have found what seems to me to be a contradiction, yet clearly that must be my lack of understanding.

Accounts of the early stages of the big bang say that it began as an infinitely small size which began expanding and cooling. This was not an expansion into empty space, but was an expansion of 3 dimensional space itself. The progress of the universe can then be described - at this time the size was so big, the average temperature was this, and this was what was happening with fundamental particles, formation of structure, etc.

All this is challenging to understand, but makes sense to me.

But if I focus on a different question, the size of the present universe, I find that there is conjecture whether it is finite or infinite. I understand that, depending on the total mass/energy of the universe and the cosmological constant, the universe may be either closed (it will eventually collapse back), open (it will expand forever) or flat (it will slow down and reach a static state at time infinity). And I understand that if the universe is closed, then it is finite in size, but if it is open, then it is infinite in size.

I further understand that the best scientific measurements so far indicate the universe is very close to flat, but could still be open or closed. I am not here concerned about which is the case. But rather, that if it turns out that the universe is open, and infinite, this seesm to contradict what I learned about the big bang and the growth of the universe from small to large, but still finite and measurable.

So my questions are:

1. Does the scientific account of the big bang include a finite universe of measurable or calculable size?
2. Do some current understandings suggest (though not prove) that the universe might be infinite in size?
3. If both of these are true, how are they compatible? Did the size of the universe pass from finite to infinite at some stage in the 14 billion years since the beginning of the big bang? (I find that quite bizarre!)

Thanks for any light you can shed.

 

[marcus]

.

Accounts of the early stages of the big bang say that it began as an infinitely small size which began expanding and cooling. This was not an expansion into empty space, but was an expansion of 3 dimensional space itself. The progress of the universe can then be described - at this time the size was so big, the average temperature was this, and this was what was happening with fundamental particles, formation of structure, etc.

All this is challenging to understand, but makes sense to me.
...

According to the standard picture it is the space and matter which we can now observe which was once a small volume of very high density.

Popular accounts seem never to make this plain, but the state at the start of expansion would have been infinite volume if (as is possible) the present universe is infinite volume.

When they give you all wow Mr. science stuff about it all being concentrated in a small volume, the "all" they mean is the finite portion of the universe that we are getting light from. That doesn't have to be (and probably isn't) the whole kaboodle.

 

[marcus]

So you probably understand that the contradiction you began with is not actually a contradiction. It is just misconception caused by bad popularization writing. Pop-sci journalism gives the impression that the high-density state could not be infinite volume. But beyond that contradiction, which I hope is resolved, you have some general questions.

...So my questions are:

1. Does the scientific account of the big bang include a finite universe of measurable or calculable size?
2. Do some current understandings suggest (though not prove) that the universe might be infinite in size?
3. If both of these are true, how are they compatible? Did the size of the universe pass from finite to infinite at some stage in the 14 billion years since the beginning of the big bang? (I find that quite bizarre!)
...

1. Yes. The standard model (called LCDM) has several cases. One or more cases are infinite spatial volume. At least one case has positive spatial curvature and finite volume.
The radius of curvature is estimated to be at least 100 billion lightyears.

So far they only have a 95% confidence interval lower bound on the radius of curvature.

This is 2008 WMAP data from a NASA CMB mission, if you want links or details please ask.
It is based on the best most up-to-date figures I know of. Hopefully with more data the estimates will improve.

If you want to know what lowerbound volume of space this translates into, please ask. It is for the whole universe (in the finite case) and it is substantially larger than the currently observable chunk we can see.

2. Yes! the standard cosmo model LCDM (lambda cold dark matter) includes, for instance, an infinite spatial volume zero curvature case, the flat case. When they fit the data they get nearly as good fit with the flat model as they get with a finite volume model with very slight positive curvature.
There is no statistically significant difference. (As analogy, to someone up close, a very large balloon would look flat.)

3. Finite spatial and infinite spatial cases are the same model just with a different curvature parameter plugged in. Both fit the data pretty darn well.
No! the universe did not switch from being finite to infinite.
Big bang theory does not require that everything start from a small finite blob. That is only the pop-sci version.
the theory says expansion started from a high density state, you could have high density in an infinite volume. It's just harder to imagine and journalists earning their money refuse to tell you anything that is hard to imagine.

if volume is infinite now then it was infinite back then too.

 

[DaveC426913]

And I understand that if the universe is closed, then it is finite in size, but if it is open, then it is infinite in size.

I believe this statement is incorrect.

If the universe is open, that does not mean it is infinite in size. (Though it does mean it can eventually grow infinitely.)

 

[marcus]

... And I understand that if the universe is closed, then it is finite in size, but if it is open, then it is infinite in size.
...

That is a statement about definitions and it agrees with what SpaceTiger taught us while he was PF moderator and concurrently a cosmology grad student at Princeton. All we need to do is agree on something that conforms to professional usage. What you say is certainly what I'm used to.

Before 1998, people would say closed to mean both spatial finite and doomed to crunch.
(Without dark energy those two go together.)
After 1998, closed simply means spatial finite--spatial closure. And a closed universe can expand forever. Because of dark energy.

that is how we learned to use the terminology. It is different from the old-fashioned pre-1998 way of talking. One has to be clear or confusion will result.

...If the universe is open, that does not mean it is infinite in size. (Though it does mean it can eventually grow infinitely.)

Dave it seems to me that you are using the terms open and closed in a way more in line with the pre-1998 usage. This is not a issue of correct/incorrect, but rather a semantic one.

Perhaps I don't understand you, but I think you are trying to say that "open" means something about the future---that expansion will continue and a crunch will not occur.

But this leads to confusion because everybody tends to think of open and the opposite of closed! And for many of us, closed means spatial finite. Therefore open must mean spatial infinite.

Maybe closed and open are outworn jargon and destined to be abandoned by cosmologists.

If you care strongly, maybe you could find some recent authoritative cosmology source material that represents how cosmologists are talking these days. I hope the professionals are not in a semantic muddle themselves.

 

[Chronos]

The universe is observationally finite, so far as we know. No compelling evidence to the contrary has yet been presented.

 

[Wallace]

I believe this statement is incorrect.

If the universe is open, that does not mean it is infinite in size. (Though it does mean it can eventually grow infinitely.)

For the most part I agree with the jist of Marcus' reply, but let me put it in a slightly different way.

We have two distinct things in cosmology, observations and theories. Clearly our theories and influenced by observations but the two are not the same.

So, observationally all we can say is that the Universe is at least a certain size (a sphere encompassing the volume between us and the surface of last scattering, from where the CMB photons we observed come from). Observationally we know the Universe is at least that big, but we could never observe it to be infinite.

Now, we also have a theory, General Relativity, that let's us place the observations we have in a framework governed by physical laws. The Universe we observe appears to be well described by a solution to GR in which energy is, on largeish scales, distributed homogenously and on similarly large angular scales the Universe is isotropic (looks the same in all directions). This is known by some subset of the Friedmann-Lemaitre-Robertson-Walker (FLRW) model.

Now in this model the situation is cut and dry. If the spatial curvature of surfaces of constant time are postively curved, then the Universe is finite, otherwise it is infinite. As marcus alluded to, there exists some terminology (flat, closed and open) that can be a little confusing due to the apparent presence of dark energy, but in that terminology a closed universe is always finite and open and flat universes are always infinite. But this is a model dependant statement, if the FLRW model is wrong then so are these assertions. They are statements about a mathematical model, not about the real Universe, since we have only observed a finite volume of the Universe.

In the end, we will probably never know for sure if the Universe is truly infinite in the way people normally think of the word 'know'. However, the FLRW model appears to work quite well. There are alternatives, and some of these say different things about the spatial extent of the Universe. For now, and for any point in the future in which the FLRW is generally thought to be valid, then the shorthand statement;

"If the universe is flat or open then it is infinite"

is an acceptable abbreviation of the perhaps more correct, pedantic and cautious;

"If the FLRW model is a good model of our universe and our observations demonstrate that our best fit model has hypersurfaces of constant time that are flat or negatively curved then the model requires that the Universe is inifinte in spatial extent"

 

[Wallace]

Maybe closed and open are outworn jargon and destined to be abandoned by cosmologists.

If you care strongly, maybe you could find some recent authoritative cosmology source material that represents how cosmologists are talking these days. I hope the professionals are not in a semantic muddle themselves.

FYI marcus, I still hear people say 'flat, open, closed' in talks and papers. It is generally assumed that cosmologists will immediately translate this into: k=-1,0,+1 or equivalently $$\Omega_k<0, \Omega_k=0, \Omega_k >0$$ and not to 'the Universe will suffer a big crunch or not' hence this causes no confusion. It is outdated terminology in a sense, but not one that causes any confusion amongst cosmologists. As you point out though, this is a ripe oppurtunity for misunderstanding when translated to pop sci.

 

[DaveC426913]

Dave it seems to me that you are using the terms open and closed in a way more in line with the pre-1998 usage. This is not a issue of correct/incorrect, but rather a semantic one.

That would make sense. My defs might be a bit rusty. I'll brush up.

 

[ercatli]

Thank you everyone for your answers - they were clear and helpful. I was particularly helped by the clarification of definitions of closed and open, and the clear distinction between observable and calculable. But I have a couple of further questions please.

According to the standard picture it is the space and matter which we can now observe which was once a small volume of very high density.

Popular accounts seem never to make this plain, but the state at the start of expansion would have been infinite volume if (as is possible) the present universe is infinite volume.

I understand that mathematically, we cannot go back before Planck time (= 10^-43 secs), but that it is assumed/believed that time, matter, energy and space all began at t=0. I had previously understood this to mean that all matter, energy and space were contained within the singularity, but now I understand you to be saying that it was "only" all of these that lie within that part of the universe observable by us.

1. Are you saying that, in the models where the universe is infinite in extent, that infinite space, and perhaps more energy and matter, were outside this singularity, or also inside it?

Either way, we seem to have something that appears difficult, perhaps even contradictory. For, in the infinite universe models, it seems there are only two possibilities:

2a. either infinite space was contained within the singularity, or

2b. the singularity wasn't very singular at all - in which case, were there an infinite number of singularities?

Or perhaps my understanding of the term "singularity" is deficient?

Please be patient with me. I am not a physicist (I am an engineer) but I have read some books by competent cosmologists (Rees, Susskind, etc) and I am trying to understand better. I am also aware we are deaing with things that cannot always be understood with our visualising minds, even if they can be calculated mathematically, so I know I am asking difficult questions for you to explain to me, but I appreciate the effort.

Thanks a lot.

 

[Chronos]

Singularities are generall considered mathematical artifacts. In quantum physics, singularities are forbidden by the uncertainty principle. The uncertainty principle also yields predictions like Hawking radiation and the Unruh effect, which can be tested by observation, and generally accepted as valid. I think it would be safe to assert we can only observe a finite portion of whatever this universe arose from, and can say little to nothing about the characteristics of this 'egg'.

 

[Wallace]

Hi ercalti. On the question of whether the Universe is infinite or not I drew a clear distinction between observational evidence and model predictions. The same reasoning applies to your question about 'the singularity'.

Unfortunately, in both the popularisation of the Big Bang and Black Holes, this idea of 'the singularity' has been garbled from its scientific usage into something very different. As Chronos suggests, a 'singularity' is not a physical thing, it is a mathematical concept. You can have singularities occur in all kinds of mathematical equations and models, but a singularity is no more 'real' than the roots of a function.

So, what we have is a theory that describes very well the observations and inferences we can draw from observations. However, there is a problem with the theory, that we we go back far enough in time, a bunch of quantities go to either zero or infinity. So, the scale factor of the universe goes to zero, density goes to infinity etc. What is too often missed in popular accounts of this though, is that this makes no sense physically. It is highly unlikely that the real Universe did this. The only thing it tells us is that our theory is inadequate to describe what happens once we go back far enough. Our theory is incomplete.

The problem is one of nomenclature, in popular accounts 't=0' is taken as being 'when the Big Bang happened' which is complete non-sense. The very name 'Big Bang' is a very poor description of the theory it describes. In fact, the theory explains pretty much everything EXCEPT the 'Bang' part, since we know it breaks down in this region (because the equations go singular). In fact, as far as professional cosmologists are concerned, 't=0' is defined as being today, and then we count backwards in time. The theories work up until about 13-14 Billion years ago, where we reach a point where the theory breaks down.

This shouldn't be taken to mean the theory is wrong, just that it is not complete. What we suspect is the case is that there is some higher theory, some true 'quantum gravity' theory that looks very much like General Relativity when the density of energy is not extremely high, but starts to look different for sufficient energy, in much the same way as Relativity agrees with Newtonian physics as long as you aren't going too fast. We hope that when/if such a theory is developed it will not be singular when we go back too far in history and may give us some deeper insight about where the Universe came from. Marcus can give you some good information about one possible theory along these lines that he is very interested in, although there are many others being developed and the situation is far from settled. Finding the right theory will probably be the quest of fundamental physics for much of the next century.

So, don't try and visualise 'the singularity' as it doesn't exist in a physical sense. It is just the sign that our theory is not yet complete. Instead we should stop at the point that our theory currently describes well. That is, in the beginning the whole universe was in a hot dense state. Possibly the extent of this early universe was infinite, in which case it is still infinite, possibly it was finite. It is unfortunate that pop sci seems to focus largely on the one place where the theory says nothing, and not on the rest of the 14 billions years in which is says a lot! Of course the crappy name is also to blame, 'The Big Bang' theory really should be called something like 'The universe expanding from an initially hot dense state' theory, but that is not so catchy...

Does that help? I know it's hard to unlearn years of sloppy pop-sci mythology, it's a sorry state of affairs really.

As an aside, this also means that when people say 'the Universe is 13-14 Billion years old' what they are really saying is that the best fit model we have that is a solution to General Relativity goes singular 13-14 Billion years ago. In fact the theory says absolutely nothing about whether this time was the beginning or not. Also the qausi mystic rubbish that gets repeated over and over like 'time and space began with the Big Bang' is utter non-sense. It is the misrepresentation of unphysical mathematical behaviour of an incomplete model. But it has sold a lot of books written by people who should (and probably do) know better.

 

[ercatli]

Wallace:

Does that help? I know it's hard to unlearn years of sloppy pop-sci mythology

Yes that did help, as did other posts. And it led me to search further, and I found confirmation of much of what you and others said, for example http://map.gsfc.nasa.gov/universe/bb_concepts.html" . It is good to keep learning.