# How do we know the universe is infinite?

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1. Jul 26, 2015

### Rupert Young

In this documentary they discussed some research experiments which concluded that the universe is infinite. I didn't really understand it. Can someone explain how we know that the universe is infinite?

Wouldn't this also mean that the universe was infinite at the big bang?

2. Jul 26, 2015

### FactChecker

3. Jul 26, 2015

### Bandersnatch

Since most of us can't watch the doc, can you confirm a guess about its contents?
Was it about measuring flatness of the universe? Perhaps something about geometry, angles in a triangle adding to more/less than 180 degrees? Baryon acoustic oscillations?

If not that, can you quote or paraphrase the part that was unclear?

4. Jul 26, 2015

### Rupert Young

Yes, I remember angles adding to more/less than 180? Was that referring to flatness?

5. Jul 26, 2015

### rootone

As far as I know the case for the (whole Universe, as opposed to observable), being spatially infinite (or not), is still very much debatable.
mathematically it can be argued both ways, observationally we don't have enough real data to draw conclusions.

The observable universe is definitely finite, almost as a matter of definition.

Last edited: Jul 26, 2015
6. Jul 26, 2015

### Chronos

Flatness is only suggestive of an infinite universe. There are finite topologies [e.g., torus] that would also exhibit flatness. There no known way to definitively show the universe is infinite, while there are a number of ways to prove it is not. None of these finite universe models has been validated, so, the general consensus is the universe is probably infinite.

7. Jul 26, 2015

### Chalnoth

I don't think this last bit is accurate. Because the evidence is lacking, which option is preferable is entirely up to personal preferences.

8. Jul 26, 2015

### phinds

Yes, and as Chronos said that does not imply an infinite universe, just that the universe MIGHT be infinite.

You really have to be very careful in getting your science from TV. They have really neat graphics and pics and so forth, and they do get a lot of stuff right, and the programs can be very entertaining but they get a lot of stuff wrong, some of it egregiously so and the problem is that if you don't already know the actual science you can't tell which parts are right and which are wrong.

9. Jul 26, 2015

### Orodruin

Staff Emeritus
It should however be noted that a torus breaks another of the usual assumptions in cosmology, isotropy. With isotropy and homogeneity, there are only three options.

10. Jul 26, 2015

### stedwards

Do you mean an embedded torus, a torus generated by identifying opposite edges of a square, or a hyper torus by identifying opposite faces or a cube? As far as I know, the hyper torus is isotropic and homogeneous, and a candidate for flat space.

11. Jul 26, 2015

### William White

surely the only answer to the question is

"We don't"

(If you are outside of the UK, its quite easy to watch the BBC using a British Proxy)

12. Jul 26, 2015

### Staff: Mentor

13. Jul 26, 2015

### rootone

It works for me, although I did see this doc before.
A second take is well worth it for me, and as far as popsci goes it's good enough.
I'm in Ireland, and availability of BBC stuff is a bit strange, though not usually a problem.

Last edited: Jul 26, 2015
14. Jul 27, 2015

### Orodruin

Staff Emeritus
It is only locally isotropic. A geodesic on the flat torus ends up returning to the original point (with a winding number of one) only in some special directions, making the space non-isotropic.

15. Jul 27, 2015

### Rupert Young

Could someone run through the reasoning for the flat infinite universe, I'd like to understand theory itself?

16. Jul 27, 2015

### phinds

Flatness is not a theory, it's a measurement. To within the accuracy of the measurements, we measure the universe as flat, but that is not a guarantee that it IS flat (be a hell of a coincidence it is isn't, but that's an opinion, not evidence). If it IS flat, that is not a guarantee that it is infinite. See post #6

17. Jul 27, 2015

### Chalnoth

Yes, but that doesn't mean it doesn't match reality. This just means that the torus would have to be significantly larger than the observable universe.

18. Jul 27, 2015

### Finny

As already noted, to the best accuracy we can measure, the portion of the universe we can observe seems flat or close to it...that is, angles of a triangle add to very close to 180 degrees. We assume we live in a typical region of the universe and what we observe locally likely extends further.

Enough has been posted that this Wikipedia article will explain things in a way that is understandable.

Here is a quick synopsis:
"The shape of the global universe can be broken into three categories:[1]

1. Finite or infinite
2. Flat (no curvature), open (negative curvature) or closed (positive curvature)
3. Connectivity, how the universe is put together, i.e., simply connected space or multiply connected.
One should note that any combination of these can occur, that is, a flat universe can be finite or infinite, or any combination.

The exact shape is still a matter of debate in physical cosmology, however, experimental data ...... confirm that the universe is flat with only a 0.4% margin of error

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

What we cannot observe, what we cannot detect experimentally, are regions of space from which we cannot receive light signals. That's because information is limited to the speed of light and if we can't get any confirming measurement [observation] information, all we have is theory.

19. Jul 27, 2015

### Orodruin

Staff Emeritus
True, but impossible to falsify experimentally (as is the infinite Universe) and therefore the distinction s more philosophy than science.

20. Jul 27, 2015

### stedwards

Given the FRW metric, how is the curvature derived from the values of $\Lambda$ and the trace components of the stress-energy tensor, $T_{\mu\mu}$?

21. Jul 27, 2015

### bapowell

Just to clarify: I think it's possible to falsify the infinite universe proposal, for example, by discovering that it's actually finite (via CMB maps that recover a fundamental cell). It is instead not possible to falsify the finite universe, since it could always be just larger than we can probe.

22. Jul 27, 2015

### Chalnoth

I don't know quite what your intention is here. The local shape of the universe has little to nothing to do with whether or not it wraps back on itself (as Finny mentions above). There's no reason to prefer the model of an infinite universe just because our observable universe is very close to flat. A spherical topology with radius of curvature much larger than our observable universe or a toroidal topology also explain the observations. There are a diversity of models for the topology of our universe and not yet any reason to strongly prefer any of them.

The closest thing to an argument on the subject that I've seen is that it's difficult to write down a sensible model of the universe that is infinite: the infinities cause all sorts of problems with the ability of any such model to make predictions. This is one reason why some purely finite universe models have been proposed lately (one example: http://arxiv.org/abs/0906.1047).

Does the difficulty in writing down a sensible model say anything about whether or not the proposition is true? That's a hard question to answer.

23. Jul 28, 2015

### bcrowell

Staff Emeritus
This quote from the WP article doesn't seem right to me, unless they have in mind some loophole such as a cosmology that lacks even local homogeneity and isotropy. If the universe is (locally) homogeneous and isotropic, then there are certain combinations of these three properties that are impossible. For example, you can't have a universe that's finite, flat, and has the trivial topology.

BTW, your user icon looks like a clone of my terrier mutt -- very cute!

It seems to me that the OP asked a very basic, low-level question about cosmology and has not gotten any kind of correct answer so far at anything like the level of the question. The basic, canonical answer would be something like the following.

If the documentary claims this, then it's wrong. We do not know whether the universe is finite or infinite. The reasoning is as follows. We observe that the universe is homogeneous and isotropic on large scales, and we also assume by default that it has a trivial topology (i.e., it doesn't do anything funny like wrapping around on itself like a torus). These assumptions lead to cosmologies called FLRW models. FLRW models come in two flavors, finite and infinite. The finite ones have positive spatial curvature. The infinite ones have zero or negative spatial curvature. Therefore if we want to know whether the universe is finite or infinite, we need to determine the sign of its spatial curvature. Measurements show that the curvature is very close to zero, and the error bars are still consistent with either a positive or a negative curvature. Therefore we don't yet know whether the universe is finite or infinite.

Yes. Making use of only some extremely weak assumptions, general relativity tells us that if the universe is infinite now, then it's been infinite at all times and always will be infinite. Likewise if it's finite now, it always has been and always will be finite.

24. Jul 28, 2015

### bcrowell

Staff Emeritus
25. Jul 28, 2015

### Bandersnatch

Let me elaborate a bit more on this point, since the OP wanted also to better understand the reasoning behind curvature measurements.

If we start with a more familiar 2-dimensional space (i.e., a surface) and try drawing a triangle on it, we may notice that the sum of the angles of the triangle may vary depending on how curved the surface is.
A standard, flat 2D surface (an euclidean surface), such as that we learn about in school, will always have the sum of angles in all triangles net 180 degrees.
If, however, we tried to draw the same triangle on a surface that is positively curved - such as a sphere, we'd notice that the angles add up to more than that. This is best illustrated by the surface of the Earth, and a triangle between a pole, and two points on the equator. It's easy to see how you can make a triangle with all angles equal to 90 degrees, or more.
The following picture from the wiki article on shape of the universe illustrates these two cases, together with one of negative curvature (where angles add up to less than 180 degrees (in the middle):

An important point to notice here, is that when drawing triangles on a large-scale curved surface, such as the surface of Earth, very small triangles look like they're drawn on a flat surface. I.e., it's easy to fool yourself into thinking that the Earth is flat.
Only very large triangles begin to exhibit measurable deviations from the euclidean space. This is, however, just a limitation of our measuring ability. With better, more accurate equipment, it's possible to see the deviation for smaller and smaller triangles (disregarding issues of uneven ground etc.). With less-curved surfaces (e.g. on larger planets), the triangles need to be larger or equipment more sensitive.

Measuring curvature in the 3D space of the universe follows the same logic.
What is needed is a feature on the sky, whose actual size and distance can be deduced. The edges of this feature will constitute two of the three vertices of the triangle (the third one being the observer). With size and distance available, it is relatively easy to calculate how large the feature should look on the sky if the space were flat, and compare with the observed angular size. Any deviations will point to either positive or negative curvature universe.
The feature used in such measurements are the Baryon Acoustic Oscillations - a type of overdense regions in the plasma in the early universe, whose density fluctuations left an imprint on the Cosmic Microwave Background Radiation. Their size can be calculated from the properties of the plasma, and the distance to the CMBR can be also deduced. All that is left is compare the predicted sizes of the blobs with those observed imprinted in the CMBR.
These have the advantage of being probably the largest such triangles we can draw.

So far it appears that they are consistent with the predictions of a flat model of the universe. An important point to observe here is that if the universe is actually flat, we will never be able to tell with a 100% certainty that it is so, since it is impossible to make a perfect measurement that'd exclude all but a single value of curvature - and flatness is such a goldilocks value. All we can do is narrow the error bars on the measurements.
If the universe is not flat, then we may be able to tell, if we narrow the error bars enough to exclude the one case of exactly zero curvature.

So while we might not know or ever find out if the universe is really flat, none of the ongoing successive measurements of ever increasing precision have been able to exclude the 0 curvature scenario, so it is fair to say that the universe looks remarkably flat - and by extension either infinite or so large that we can't tell the difference.