# The flatness of the observable and unobservable univ

1. May 31, 2012

### robertjford80

I was watching this lecture and the professor said that before inflation the universe's shape was spherical or curved and inflation blew it up to the point where the observable universe appears flat but the actual unobservable universe is still a curve or spherical. Did I understand correctly? Is the unobservable universe curved and the observable universe flat?

2. May 31, 2012

### marcus

What you say is roughly right. We don't know for sure that the region we are currently able to observe is in fact, exactly flat.
There is a 95% confidence interval of 0.99 < Omega <1.01

The technical NASA report is what you get if you google "komatsu WMAP 7"

For 3D space to have exactly zero curvature Omega must be exactly 1.
But with 5% probability Omega might not even be in that interval.
And that interval they give more precisely as 0.9916 < Omega <1.0133
so even if it is in that interval Omega could still, for instance, be 1.01, or 1.0132
that's quite a substantial curvature. And it falls within the 95% possibility!

I would guess that the speaker was not telling you something to believe. He was describing a certain SCENARIO in which the universe is spatially finite, like the surface of a sphere with nothing inside or outside, just the surface---but a hyperspere (one higher dimension).

In that scenario, inflation saves the day, because it expands the hypersphere so much that for all practical purposes any local patch is flat, and then lets ordinary Einsteinian geometric evolution proceed.

It is something that certainly COULD have happened. But it is not proven yet. A lot more observation is needed. So he was telling you a very nice story which everybody should hear and think about. But it is not known for a fact to be right. That's my guess. If you find the link to the lecture, please post it! It might be interesting for others to listen to.

Last edited: May 31, 2012
3. May 31, 2012

### robertjford80

But the unobservable universe is probably curved, right? Of course you can't verify that but I'm guessing using a priori reasoning that is the most logical solution?

4. May 31, 2012

### marcus

what I'm saying is that it is consistent with the data so far for the OBSERVABLE portion of space to be curved. All we have is a 95% confidence interval on the measured largescale curvature, and it allows for a very substantial amount of curvature.

Since the universe appears pretty uniform the natural assumption is that if we measure a largescale average curvature here in the part we currently see then it is probably the same all over. Our particular locale is not special.

The part we can see keeps growing of course as more light from more distant stuff comes in. So what was not in the observable region today might be tomorrow the change is very very slow.

I'll tell you how to calculate the CIRCUMFERENCE of the whole universe if that guy's scenario is right.

Suppose the Omega number of what we can measure is up near the top of that interval at 1.0132. Assume that holds for all the rest of space.
Subtract 1 (getting 0.0132) and take the square root (getting 0.1149)
then take a figure for the Hubble length scale like 14 billion lightyears and
calculate 2pi*14/sqrt .0132 = 2pi*14/0.1149 = 765
765 billion lightyears

If the largescale curvature is such that Omega = 1.0132 then that is the circumference of the 3d hypersphere. It contains all space and all matter. It curves around to itself so it has no edge or boundary. If you could get it to stop expanding then a flash of light could in principle circumnavigate in 765 billion years. If it didn't hit anything. But because of expansion nothing, not even light, can make it around, no matter how long it tries.

I think I essentially agree with what you said, just wanted to spell it out in more detail.

5. May 31, 2012

### robertjford80

Thanks for the calculations and I'm aware that if you look far enough you will see the back of your head. But if space is flat then how can the universe have a circumference?

6. Jun 1, 2012

### Ken G

It is not known if you could see the back of your head if you look far enough, you should not at all take that as a given. Also, if space is exactly flat then it does not have a circumference. I think the lecturer you refer to simply was "appealing to incredulity" that the universe really could not be exactly flat, nor infinite, so was imagining it had to be finite but its finiteness has "covered its tracks" by some process like inflation. That's certainly a very nice story, but there is no actual evidence that it is true-- and it is quite likely that there never will be. Even if we ever do detect some small curvature in the universe we can observe, it could easily be nothing but a fluctuation. But if inflation is correct, we will never detect any such curvature, and so will never have the issue to even consider-- and will always have nothing but an appeal to incredulity (an approach with a truly rotten track record in science).

Last edited: Jun 1, 2012
7. Jun 1, 2012

### robertjford80

you're misunderstanding the fallacy of incredulity. the fallacy of incredulity is when someone disbelieves something and the only reason they have for their disbelief is nothing other than the fact that they cannot believe it. It has the following logical structure:

1. There is evidence to support X
2. However, I cannot believe X
3. Therefore X is false

The flatness of the universe or the impossibility of curved space does not fall into the above fallacy because there are good reasons for believing in the flatness of the universe namely the experiments done with the CMB.

8. Jun 1, 2012

### twofish-quant

Same way that the earth has a circumference even though it looks flat. From observations we can say that it looks flat within a certain tolerance, but it may be that there is some roundness that we can't detect (yet).

Also it turns out that you can't see the back of your head even if the universe is curved. The time it takes light to travel around the universe is always longer that then age of the universe before it collapses.

9. Jun 1, 2012

### robertjford80

Well, what reasons do we have for believing that the universe is round?

The only one I can think of is that it is more logical that space expands in all three dimensions rather than just 2.

10. Jun 1, 2012

### twofish-quant

Maybe.

The idea of inflation is that it doesn't matter what the shape of the overall universe is. If you take any curved shape and blow it up, it looks flat. So it could be that the unobserved universe has positive, negative, or zero curvature. If you "blow up" the universe, it looks flat.

Same thing happens with the earth.

The reason this is a nice idea is that it avoids "fine tuning". One problem is that if the universe starts out non-flat, it becomes more and more non-flat over time, and to say that the universe "magically" started flat seems weird. If you assume that the universe expanded a huge amount, then it doesn't matter what the universe started like, since any shape if you expand it enough, looks flat.

It so happens that saying that the universe expanded a lot solves about four or five other mysteries.

11. Jun 1, 2012

### Ken G

Actually, there is no need for point #1 in your description, that has nothing to do with it. It's just #2 and #3. In this case, #2 is that it is hard to believe that the universe could be infinite, so the lecturer is incredulous on the issue. But science doesn't care what he/she is incredulous about, it merely asks, what is the evidence? Since there is no evidence whatever that the universe has curvature, there is no reason to include curvature in any description or model of the universe, at present. What's more, this will likely always be true (if one believes in inflation).
You misunderstand, I said the incredulity is around the universe being flat, not around it being curved.

12. Jun 1, 2012

### robertjford80

Good, then we're in agreement.

13. Jun 1, 2012

### twofish-quant

Very strongly disagree with both statements. The current numbers are consistent with zero curvature, but they are also consistent with small curvature.

1) The universe as a whole is flat, but we need to include geometric curvature since that's an essential part of general relativity which the theory that we use to calculate the universe.

2) One consequence of GR is that the universe is unstable to curvature with no cosmological constant, which is to say that if you have small amounts of curvature, the amount will increase. Now if you include a cosmological constant, then it becomes stable to curvature, but it's possible that dark energy isn't the cosmological constant.

So models of the universe must take into account the *possibility* that universe is curved. One reason is that a universe that has curvature of plus or minus 0.00000001 is *different* than a universe that has a curvature of 0.0, and we can't exclude a universe with 0.000001.

And there are reasons for that. If you create a universe at random, there is no reason that anyone can think of that the universe should have zero curvature.

Inflation will reduce the curvature factor a lot, but something with positive curvature will stay positive and something with negative curvature will stay negative. The only way that inflation will produce a universe with exactly zero curvature is if it starts out with exactly zero curvature, and that involves some "fine tuning".

14. Jun 1, 2012

### twofish-quant

That's not quite true. One thing that makes a bad scientific theory is "magic." I can come up with a theory in which my coffee cup just happens to fall when I drop it by "magic". The problem with that theory is that it doesn't explain why the coffee cup doesn't go sideways or go up when I drop it.

This principle works with cosmology. One reason that people find exactly flat universes to be troubling is that in order to have a universe that is *exactly* flat, you have to assume that it came into being by "magic". Whereas if you have a universe that isn't exactly flat but really, really, really close, then you have "non-magical" explanations.

Inflation predicts that the universe will be close to, but not exactly equal to zero.

Also you need to include curvature in your theories to show that the universe isn't curved. If you don't ask "what does a curved universe look like" you can't show that the universe isn't curved.

15. Jun 1, 2012

### twofish-quant

Because if GR is a correct description of gravity, then the universe will have to be round under certain conditions. GR says that gravity "curves" space, so the space-time around any gravitational body will curve slightly.

It's not a matter of "belief." In order to show that the universe is flat, you have to consider the possibility that it's round. From our observations, we can eliminate "large amounts of roundness" and as we get better measurements those measurements will get tighter and tighter.

Or not. If the measurements get sensitive enough, then we may actually detect roundness.

It actually does. "Roundness" is a metaphor.

If you draw a triangle in "flat" space then the angles will add up to be 180 degrees. Gravity distorts space, so that if you draw a triangle around the earth and measure the exact angles, it won't add up to be exactly 180 degrees.

The deviation from 180 degree is "roundness". It's *as if* you draw a triangle on a sphere.

16. Jun 1, 2012

### robertjford80

I'm aware that there are local patches of curveness in space, such as near the sun, but the universe as a whole, that's a different question

17. Jun 1, 2012

### Whovian

Models for inflation suggest that the Universe is "round." (EDIT: Looks like I'm crazy. Ignore this post, as the previous statement was invalid and as all arguments follow from it, this post is invalid.) As these seem to be the best fit to observational evidence so far, we'd have to assume the Universe is "round" unless known otherwise. The CMBR experiments only suggest that the Universe is nearly flat, not necessarily completely flat.

Last edited: Jun 1, 2012
18. Jun 1, 2012

### Ken G

Where do you get that? Models of inflation say no such thing, they just say that we will never detect any spatial curvature on the largest scales in our universe. That's it, that's what they predict-- they say nothing at all about the existence of roundness.

19. Jun 1, 2012

### Ken G

All scientific theories resort to magic, it is inescapable. The difference is that the magic referred to in science is quantifiable and repeatable. That's it, we don't call it magic if it is quantifiable and repeatable. But you are not talking about anything quantifiable or repeatable, what is quantifiable and repeatable is that we have no evidence for any non-flatness in our universe, that's it.
That is not true at all. All origins stories are going to involve some step that is essentially magical, what matters is whether or not it gives us testable hypotheses. Now, what testable hypotheses is your creation story giving us? None, zilch.
No, it predicts the curvature will never be observable. It certainly does not say it isn't zero, it says we have no idea so there are no testable hypotheses around the issue. That further says that there is no point in including curvature in our models, since it is a complication that offers us no testable advantages. Pure unadulterated Occam's Razor.
That is true but irrelevant, as you can see like this: "If you don't ask what do unicorns look like, you can't show that unicorns don't exist." But we don't need to go through a list of what every possible creature might look like to do science, for science has no need to say what unicorns look like if it has no reason to invoke unicorns in the first place.

20. Jun 1, 2012

### Ken G

No one has suggested that we don't do observations to narrow down the range of possible curvature. The point is that as long as we observe no evidence for curvature, there is no reason to say that the universe is round. Science makes models, it does not say "what is." The cosmological models that fit the data and obey Occam's Razor are flat models, and nothing more can be said on the topic of roundness.

Getting back to the OP, the answer is that the observable universe appears to be flat, so our best models are flat, and we have no idea what the unobservable universe does. What's more, if inflation happened, this will forever be the state of affairs.

21. Jun 1, 2012

### twofish-quant

This is incorrect.

The inflationary solution to the flatness problem is that the universe underwent a huge amount of expansion. When you expand the universe then the flatness increases.

The important thing is that topologically the universe doesn't change. If the universe was not flat to begin with, then after inflation, it's still not flat.

The amount of flatness that you are left with depends on the initial conditions and the amount of inflation, but until you've pinned down the initial mechanism, there's no reason to think that the flatness of resulting universe is undetectable.

22. Jun 1, 2012

### twofish-quant

Absence of evidence is not evidence of absence. We have observational constraints on the levels of flatness, which are consistent with zero but do not rule out non-zero models.

CMB correlation functions. Nucleosynthetic abundances. GUT particle predictions.

The inflation mechanism is still quite vague, and figuring out the flatness or lack therefore of the universe will pin down the mechanism.

There's also theoretical consistency. It turns out that you *can* do a lot of cosmology assuming that GR is wrong and that the universe is Newtonian. The trouble is that when you do that, you run into huge problems when you start putting in a finite speed of light.

This is false. Inflation predicts no such thing. Let's ask Alan Guth what he thinks.....

http://arxiv.org/abs/1203.6876
What can the observation of nonzero curvature tell us?

It turns out that curvature is a very good probe of the details of the inflation mechanism.

Alan Guth seems to disagree.

Also see

http://arxiv.org/abs/1104.3629
The Primordial Curvature Perturbation from Vector Fields of General non-Abelian Groups

http://arxiv.org/abs/1104.3494
Observational signatures of a non-singular bouncing cosmology

(There are dozens of other papers)

In any case, you can't remove curvature since you are using a gravity model that is based on the concept of curvature. A lot of the experimental tests in cosmology involve measure density perturbations, and even if you are in a universe that is "flat" at the large scale, you have to take into account local curvature if you want to use GR (i.e. the back reaction problem)

http://arxiv.org/abs/1112.5335
Backreaction in late-time cosmology

http://arxiv.org/abs/1203.2635
Inflationary perturbation theory is geometrical optics in phase space

http://arxiv.org/abs/1203.0125
Effect of cosmic backreaction on the future evolution of an accelerating universe

23. Jun 1, 2012

### twofish-quant

There's no reason to say that the universe *isn't* rount.

It's possible to say "I don't know"

This is a false statement. Flat models do not obey Occam's razor.

This is also a false statement. I've posted several papers that state otherwise including one by the person that invented inflation.

If inflation happened then the amount of curvature is going to depend on the inflation mechanism. Once we've pinned down the amount of flatness, we can say more about the details of what happened at the early universe, and if we are lucky we may even be able to make statements about what caused the big bang.

One good thing about Guth's paper is that it's mostly a theory paper, but the last section includes a description of the observational limits on curvature that we'll see in the next several years.

The other thing is that our models assume that GR is the correct theory of gravity and increasingly they assume that dark energy is the cosmological constant. If either assumption is false then all bets are off.

24. Jun 1, 2012

### twofish-quant

You can think of the total curvature of the universe as an "average" of the curvature of the objects inside of it.

One major area of research is how much "local" changes in curvature can influence the large scale evolution of the universe. It's call the "back reaction" problem.

Also the statement isn't that the observable universe is flat and the non-observable universe is round. The statement is that entire universe may be round but since we are seeing a small patch of the whole universe it looks flat. (Like the Earth). However, if the universe is round, then we may be able to detect it if we look at more sensitive measurements, and whether we see roundness (or not) makes a difference.

25. Jun 2, 2012

### Ken G

The statement is that the observable universe is flat, and the non-observable universe is irrelevant.