# Is the Universe Flat or Curved?

• kaushik_s
In summary: But, you are right, there are other models. In summary, there are several different models and theories about the shape and structure of the universe. Some suggest that it is flat, while others propose a spherical or even trumpet-like shape. However, there is still much that is unknown and unproven about the universe, and many of these theories are based on speculation and limited evidence.
kaushik_s
hi,

I am a bit confused on what the current model of the universe is. some are saying it is round, while others are saying it is flat. which is true?

If the universe is flat, then is it that only some part of it is flat or the whole universe is flat?

how can we prove it theoratically and mathematically?

Observations are consistent with a spatially flat universe. But observations also suggest that there is much more universe "beyond" what we can actually see, so whether or not it continues to be flat ad infinitum is unknown and may not be knowable.

Hi,

The COBE and WMAP satellites launched by NASA in 1992 and 2003 measured the Cosmic Microwave Background, and determined that the Universe must be either flat or extraordinarily close to it. If it was even slightly curved in the beginning, it would have become more and more curved over time, so it seems the universe it flat

Also, remember what people mean when the say the Universe is round: they don't mean it is in the shape of a ball ,or anything like that. It is actually impossible to picture. To get an idea of what a round(or closed) universe would be likely, think of a 2 dimensional example: imagine a person who lives on the surface of a sphere - but that is all there is, no center of the sphere or outside. To him, the universe has no boundaries, but if he continuously travels in one direction, he will eventually cross through either the top or the bottom, and then eventually return to his position.

For the 3 dimensional version of this, you would need to be able to picture a fourth dimension, which we can't do. But what you can do is know that in a round universe, you will never see a boundary, and that parallel lines will eventually cross over far enough distance.

If the universe is flat, as the evidence suggests, then it can be infinite or finite. If it is infinite you can easily picture it, it just goes forever in every direction. If it flat and finite, we once again can not imagine the whole universe, but it would be like a 3 dimensional version of the world pacman lives in - finite, but no boundaries.

kaushik_s said:
hi,

I am a bit confused on what the current model of the universe is. some are saying it is round, while others are saying it is flat. which is true?

There are probably many different ideas of what you could mean by a Universe that is flat, round, finite, infinite, etc. My personal preference is to look at the possibility of closed space like curves. If you travel long enough in a straight line in one direction (i.e. traveling along a space like geodesic), then you could end up where you started from; space would be compact.

But, you would never know when you reached your departure point in a finite, unbounded universe. It would be like walking around the Earth on foot. It would take so long your point of origin would no longer be recognizable by the time you returned. The expansion of the universe further compounds the problem.

kaushik_s said:
hi,

I am a bit confused on what the current model of the universe is. some are saying it is round, while others are saying it is flat. which is true?

If the universe is flat, then is it that only some part of it is flat or the whole universe is flat?

how can we prove it theoratically and mathematically?

I'm not sure if anyone has answered your question but I think the shape of the universe and if it is flat are two different things. You can have a round (spherical) universe that is flat. I think the standard model describes a universe that is spherical and expanding but it could contract or be flat. I think flatness has more to do with the density of the universe than it does with the shape. I think

Hi,
thanks to all of you for the reply

recently, I did some research on google on the matter, and i found out that in the recent model proposed by physicists, they are now thinking that the universe has a shape similar to a flat trumpet like shape. In this model, they think the universe is narrow at one end and widens on going from one end to the other end.

What do you people think of this !

welcome to pf!

kaushik_s! welcome to pf!
kaushik_s said:
… In this model, they think the universe is narrow at one end and widens on going from one end to the other end.

no, that's a size-time graph of the size of the universe, not a picture of space

kaushik_s said:
Hi,
thanks to all of you for the reply

recently, I did some research on google on the matter, and i found out that in the recent model proposed by physicists, they are now thinking that the universe has a shape similar to a flat trumpet like shape. In this model, they think the universe is narrow at one end and widens on going from one end to the other end.

What do you people think of this !

No one thinks this is actually true :) Sometimes popular magazines pick up weird publications to promote, that is all.

And just for reference (in case you did not read the article completely), they are postulating a very weird topological structure for the universe just to explain the leftmost datapoint on this plot. Now, the blueish region on the plot corresponds to natural statistical uncertainty (poetically called "cosmic variance"), arising from the random nature of the initial density fluctuations. You can see that it almost manages to cover the data point, meaning that the data is already almost within the expected error margin.

tiny-tim said:
kaushik_s! welcome to pf!no, that's a size-time graph of the size of the universe, not a picture of space

No, I'm pretty sure that's not true... The 3-space metric they consider is
ds2 = (dx2+dy2+dz2)/z2

bill alsept said:
You can have a round (spherical) universe that is flat. I think the standard model describes a universe that is spherical and expanding but it could contract or be flat. I think flatness has more to do with the density of the universe than it does with the shape. I think
No, you can't. You cannot globally cover the sphere with the metric of flat space. In other words, a sphere has different geometry than the plane. Of course, it is possible that the sphere be sufficiently large that it locally looks flat, but there is still not an exact equivalence. The standard model of cosmology makes no a priori claims as to the global geometry of the universe. Recent CMB measurements coupled with those from the HST indicate that the *observable* universe is flat to within 1%. This measurement, however, tells us nothing of the global geometry of the universe.

Asking if the universe is round or flat is like asking if a body of water is round or flat

Whitewolf4869 said:
Asking if the universe is round or flat is like asking if a body of water is round or flat

why is that?

Because the nature of the universe is to equalize in much the same way water neutralizes

Whitewolf4869 said:
Because the nature of the universe is to equalize in much the same way water neutralizes

What do you mean by equalize? I thought the universe was expanding.

In other words its not relevant water is water and space is space and it doesn't mater what shape the container is

I don't think the question is what shape the universe is contained within, it's what the curvature of the universe is on the large scale.

This discussion is becoming nonsensical. It is perfectly valid to question the global geometry of the universe. Anyone who says otherwise must be unaware that general relativity is a geometric theory of spacetime, and that the content of the universe determines its global geometry.

It's not about "containers". The distinction is between flat and curved geometries: for example, is the Earth round or flat? Is that a sensible question? If you think so (as I hope you do), then the question regarding the geometry of the universe is equally sensible -- in fact, it's simply a higher-dimensional analog.

how are you observing the universe?
and yes its is very sensible to be curious about the geometry of the universe

Whitewolf,

I don't mean to be rude, but please don't spread misinformation when you are not knowledgeable on a topic. Your responses in this thread have been cryptic, vague, and worst of all, completely incorrect. I think bapowell's nice concise answer is basically the end of the geometric discussion.

However, there is an interesting point here that I'd like to make, which is that the curvature of the universe (positive, negative, or zero) is a separate question from the topology of our universe. For example, since we know the universe is flat (curvature is zero), the easiest solution to have is the simple plane. But there are other solutions, for example, the universe could be shaped like a torus! There are other, more exotic global topologies of the universe, and it's interesting to think about but often difficult to experimentally verify (since one can always make the radius of the doughnut, for example, very large such that there is no hope to observe its global structure on the timescales available to us).

Were the observations Whitewolf4869 asks about done by COBE, WMAP, etc. ?
Can flat universes have different possibilities for topologies like flat surfaces can ?
At any fixed time, is the spatial universe a 3 manifold ?

Nabeshin said:
However, there is an interesting point here that I'd like to make, which is that the curvature of the universe (positive, negative, or zero) is a separate question from the topology of our universe.

Yes that is what I was saying in post#6

doesn't flat mean that the universe on average is not warped by gravity. It is warped locally by every particle of mass but on the average the warped space and the unwarped space even out. If true, that seems to me that the unwarped space is getting additional space from other dimensions.

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neginf said:
Were the observations Whitewolf4869 asks about done by COBE, WMAP, etc. ?
Yes. WMAP+HST (Hubble Space Telescope) furnish the best constraints yet on the geometry of the observable universe.
Can flat universes have different possibilities for topologies like flat surfaces can ?
Yes. For example, a geometrically flat universe is consistent with toroidal topology, as Nabeshin points out.
At any fixed time, is the spatial universe a 3 manifold ?
Yes. The spatial geometry at an instant in time (spacelike hypersurface) is a 3-manifold.

It occurs to me that, in a torus which is a 2-d surface wrapping a 3-d space (exactly like the surface of a doughnut, in terms of dimensions), the curvature is sometimes like a sphere's (curving the same direction on both axes) and sometimes like a saddlepoint (axes curving opposite directions).

When speaking of the universe, I often see "negative curvature" represented as a saddlepoint-style brane, and "positive curvature" like a sphere's. Does this mean that in a torus-shaped universe, some areas would be observe to have negative curvature and others to have positive curvature? Or am I confusing my geometries?

cephron said:
It occurs to me that, in a torus which is a 2-d surface wrapping a 3-d space (exactly like the surface of a doughnut, in terms of dimensions), the curvature is sometimes like a sphere's (curving the same direction on both axes) and sometimes like a saddlepoint (axes curving opposite directions).

When speaking of the universe, I often see "negative curvature" represented as a saddlepoint-style brane, and "positive curvature" like a sphere's. Does this mean that in a torus-shaped universe, some areas would be observe to have negative curvature and others to have positive curvature? Or am I confusing my geometries?

The way you measure curvature is to see how the action of transporting vectors along the manifold changes them. In particular, if the transform is not commutative, then the manifold is curved.

Another simple way is to see how many degrees do a triangles angles sum up to. Anything but 180 degrees means that the manifold is curved. For a torus, all triangles sum still up to 180 degrees, as you can probably convince yourself by drawing donuts and triangles.

Thanks for the replies everyone !

But, I am not a very experienced person in this matter. So if you people don't mind, can you please explain stuff in a more simple English.

I too get quite confused when people talk about the shape of the universe - it seems that different folk use different meanings.

Could someone clarify, perhaps by posting some simple diagram what a flat universe might look like ? ie, are we talking about, say, a pancake shape ?

Also a round one - are we talking about a sphere shape ?

Thanks.

Edit - even if 'flat' means pancake shape, surely it must be a zillion ly in 'flatness' width, so even that 'flat' seems a misnomer.

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alt said:
Could someone clarify, perhaps by posting some simple diagram what a flat universe might look like ? ie, are we talking about, say, a pancake shape ?
The shape and geometry of the universe are ultimately different things. For example, a flat universe could be in the shape of a flat sheet or a donut. What we actually measure with cosmological observations is the intrinsic geometry of the local universe. The best way to distinguish different intrinsic geometries is to consider whether the Euclidean postulates and their consequences hold: for example, in a flat geometry, the interior angles of a triangle sum to 180 degrees. In curved geometries, this no longer holds.

Whitewolf4869 said:
In other words its not relevant water is water and space is space and it doesn't mater what shape the container is

Actually, it does matter quite a bit. In immediate practical terms, probably more so for a body of water than for space, since the size/shape of the container says a LOT about what you can/cannot DO in that body of water/space. It's tough to get a battleship into a bathtub for example.

Understanding the "shape" of the universe may well lead to understanding of other things of more immediate relevance.

Your point of view seems contemptuous of science.

bapowell said:
The shape and geometry of the universe are ultimately different things. For example, a flat universe could be in the shape of a flat sheet or a donut. What we actually measure with cosmological observations is the intrinsic geometry of the local universe. The best way to distinguish different intrinsic geometries is to consider whether the Euclidean postulates and their consequences hold: for example, in a flat geometry, the interior angles of a triangle sum to 180 degrees. In curved geometries, this no longer holds.

OK, thanks. I understand that. So are you saying that to say 'flat universe', one means it in terms of flat geometry, 180 deg triangles, etc ?

alt said:
OK, thanks. I understand that. So are you saying that to say 'flat universe', one means it in terms of flat geometry, 180 deg triangles, etc ?
Yes, that's exactly right.

Does the universe's flatness mean that non Euclidean geometry isn't important in physics?

kaushik_s said:
I am a bit confused on what the current model of the universe is. some are saying it is round, while others are saying it is flat. which is true?

If the universe is flat, then is it that only some part of it is flat or the whole universe is flat?

how can we prove it theoratically and mathematically?

According to the depicted universe described in special relativity, particulary concerning the Lorentz transformations, the universe is flat with a .08 margin of deviation due to the differentiation between co-motion systems. In a difference of say, a rotational axis, certain points experience alternate rates of fluctuations to compensate for their differing inertial reference frames, specifically, when evaluating that circular system of rotation, when an side undergoes a contraction by:
L0√1-v2/c2
the radius will grant an invalid conclusion in the description of the area of a circle, namely A=∏r2, which is mathematically impossible in the Euclidean geometry of a classical universe, hence the necessitation of a curved space-time.

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