Talk:Shape of the universe

Tone of article
The language of this article comes off as highly condescending. Rather than slapping the reader around with "What you think is wrong" it would be more approachable to simply state the generally scientifically accepted notions of space-time. Addressing "the reader" repeatedly also begins to sound didactic and overly bookish. I'll throw this up on my list of pages needing massage, but feel free to go at it before I manage to get to it.


 * Hope to have a go at Shape of the universe shortly, if no one else does so before me.
 * Eddie 08:14, 13 Dec 2004 (UTC)
 * Working on this now --Eddie 21:50, 4 Jan 2005 (UTC)
 * Done. Please improve and be bold.  Old text commented out in this page. --Eddie 23:10, 12 Jan 2005 (UTC)

<!-- The term shape of the universe can most usefully refer either to the geometry (curvature and topology) of a comoving spatial section of the universe (a loose term for this is the shape of space) or more generally, to the shape of the whole of space-time.

Language/intuition prerequisites
To understand concepts of the shape of the universe, according to the standard big bang model, the reader should, ideally, first develop his/her intuition of manifolds, and more specifically, of Riemannian manifolds.

However, those definitions are somewhat abstract.

Here is an attempted shortcut to developing that intuition.

The reader's ordinary notions of space and time are likely to be wrong, they are psychological constructions developed from common sense and folk physics. These notions are useful for ordinary living, as they closely approximate reality over distances and times that are at human scales, but this does not make them real.

For example, common sense and everyday observation tells us that the world is big and flat and stationary and not a sphere in rapid rotation, both by spinning around its axis (at around 1000 mph at the Equator) and moving around the Sun (at around 66,000 mph). The real situation with regard to the motion of the Earth was discovered only recently in human history, and took over a century to be generally accepted.

Similarly, science tells us that the Universe behaves very differently from our common-sense experience at very small scales or very high speeds or energies. It even tells us that the local geometry of space can be altered by gravity. It therefore makes sense to ask if the Universe has a different local geometry (curvature) or global geometry (topology) at very large scales from that which we can measure locally.

One way of developing correct intuition is to ignore one's existing intuition and start from scratch, from very simple logic.

The reader should imagine starting off with a very abstract definition of a set, which is more or less just a collection of points, and then adding more and more definitions. These definitions include ways in which the points relate to each other, and eventually include some concepts so that this set has some properties which are like the common notions of a space.

It is then proposed that the reader accept the use of two-dimensional spaces as analogies for real, three-dimensional space, since this way the third dimension of his/her intuition can be used as a psychological tool for imagining different possibilities for two-dimensional spaces. The reader should remember that the use of a dimension for intuition-building does not imply that it has any physical meaning. It is merely one way, among many, of thinking about spaces of different curvature and topology.

Comoving space
Comoving coordinates are necessary for thinking about the shape of the Universe. In comoving coordinates, we can think of the Universe as static, despite the fact that in reality it is expanding. This is simply a useful way of separating geometry (shape) from dynamics (expansion).

Local geometry (curvature)
In simple words, this is the question of whether or not Pythagoras' theorem is correct, or equivalently, whether or not parallel lines remain equidistant from one another, in the space one is talking about.

If we put Pythagoras' theorem in the form
 * $$h = \sqrt{x^2 + y^2} $$

then:

The first and third of these are relatively easy to imagine with two-dimensional analogies. The first is an infinite flat plane. The third is the surface of an ordinary sphere.
 * a flat space (zero curvature) is one for which this is true
 * a hyperbolic space (negative curvature) is one for which $$h > \sqrt{x^2 + y^2} $$
 * a spherical space (positive curvature) is one for which $$h < \sqrt{x^2 + y^2} $$

Global geometry (topology)
In simple words, this is the question which ignores Pythagoras' theorem.

Three different two-dimensional spaces which are all flat spaces, in all of which Pythagoras' theorem is true, are


 * an infinite flat plane
 * an infinitely long cylinder
 * a 2-torus, i.e. a cylinder with two ends which are defined to be stuck to each other ("identified" with each other)

Each of these is globally very different.

The third is finite in 2-volume, i.e. surface area, but has no edges and Pythagoras' theorem is true everywhere in it.

The Twin paradox leads to a new paradox in the context of the global shape of space. See the external links for more on this.

What is the shape of space of our Universe?
We know neither the local nor the global shape of space. We do know that the local shape is approximately flat, just like the Earth is approximately flat. We do not yet know the topology of the universe, and maybe never will.

The shape of the whole of space-time
remains to be written

See also Friedmann-Lemaître-Robertson-Walker.

A typo in Local geometries
I am not familiar with this but I know that there is a typo at Local geometries (...negative than the...)

There are three categories for the possible spatial geometries of constant curvature, depending on the sign of the curvature. If the curvature is exactly zero, then the local geometry is flat; if it is positive, then the local geometry is spherical, and if it is negative than the local geometry is hyperbolic.

--Iiaiialover 02:31, 11 December 2006 (UTC)


 * That's not quite right. See discussion below in Why isn't the Mobius Strip in here as a possible shape of the universe?.-- Cheers, Steelpillow (Talk) 10:56, 7 November 2009 (UTC)

Merged and redirected Topology of the universe
I've merged and redirected Topology of the universe. Actually, I only redirected, as IMHO that article doesn't provide anything, not already covered here. For the case, someone disagree, I quote the entire old article here: According to the general theory of relativity, spacetime is a pseudo-Riemannian manifold. The term topology of the Universe is generally used to mean the 3-manifold of comoving space, even though strictly speaking, it should probably refer only to the underlying topology of this manifold.

We do not yet know the global topology of the Universe, and in fact may never be able to know what it is. However, cosmologists are trying to measure cosmic topology using data from ground-based and space-based telescopes. Results from the WMAP telescope may give an answer by 2004 or 2005.

The adjective global here means that black holes are ignored - only the properties of space on scales of at least hundreds or thousands of megaparsecs are referred to in the term topology of the Universe.

A current hypothesis is that the spatial shape of the Universe is homeomorphic to a 3-sphere.

See also: shape of the Universe, Poincar&eacute; conjecture. Pjacobi 20:59, 2005 Jan 22 (UTC)

Open Universe
The open universe with hyperboloid geometry is unclear to me. Being infinite, the universe would continue forever. But if that was so, then either curvature would have to change its sharpness, or stop curving beyond the center, otherwise the curve would continue around until it contacted itself, making a doughnut shape. Is that sensible?--Ansandre 02:17, 1 July 2007 (UTC)Ansandre
 * That relies on the idea that there's something for the universe to curve into. Where it looks like the hyperbolic universe is curving into itself, it just looks like that when you squeeze a 2-hyperbolic universe into three-dimensional Euclidean space. We only put it in 3D Euclidean space to make it easier to visualize the 2-hyperbola's geometry. In reality, they're not close together, since there's no such thing as distance other than from inside the universe. Does this answer your question? --Zarel (talk) 05:13, 2 September 2009 (UTC)

Closed and Open?
I think that the stubs for Closed universe and Open universe probably need to be redirected to this page, the definitions added in here somewhere; but I don't know enough to be confident doing so. The definitions of closed, flat, and open universes would need to be added here to wherever they're relevant, and there would need to be at least a mention of the connection between a closed universe and an eventual Big Crunch. -- ThirdParty 01:24, 6 December 2005 (UTC)


 * Hi Third Party. If you're keen go ahead. I didn't realise that there are stubs for Closed and Open Universe.  Do you think they could be worked up where they are for the time being and then considered for integration here?
 * You've raised food for thought and I for one am ruminating on it. For instance, you may be well aware, that Olbers paradox is true, so to speak, in a Closed universe? Distant are stars blue shifted - night is as bright as day (the sun/local star being a disc not as bright as the surrounding stars) and everywhere bombarded by x-rays from distant galaxies. --Eddie 08:53, 6 December 2005 (UTC)


 * I've merged these two stubs into this article and turned them into redirects while I rewrote this article a bit (see 'Rewrite' below). Mike Peel 16:50, 25 February 2006 (UTC)

Is it possible to have a closed hyperbolic universe? If not, why not?


 * no, if it was hyperbolic then it would make a gradual turn and then head in a nearly-straight direction on both ends. —Preceding unsigned comment added by 58.173.131.113 (talk) 11:35, 30 June 2009 (UTC)


 * It is possible, actually. The higher toroids (double torus, triple torus and so on) are closed manifolds with negative (i.e. hyperbolic) curvature (a simple torus or doughnut has zero overall curvature). The Universe might be a 3D equivalent. -- Cheers, Steelpillow (Talk) 11:14, 7 November 2009 (UTC)

Multiple images in different age
One of the endeavors in the analysis of data from the Wilkinson Microwave Anisotropy Probe (WMAP) is to detect multiple "back-to-back" images of the distant Universe in the cosmic microwave background radiation. Assuming the light has enough time since its origin to travel around a bounded Universe, ''multiple images may be observed. While current results and analysis do not rule out a bounded topology'', if the Universe is bounded then the spatial curvature is extremely small.

the words in italics:

does any astronomer consider about the light needs time to move ?
 * yes

so that we can see multiple images of the same object but in different age ?


 * Yes. However, the multiple "images" from the cosmic microwave background (CMB) that we are most interested in are those on the surface of last scattering - which is essentially a sphere (2-dimensional sphere) centred on the observer (us, at the Sun), defined by the time light takes to travel to us. This is light emitted at the time when the Universe was much denser. Of course, the light went in all directions, but only some of the light particles photons happened to be sent from spatial positions and in directions which turn out to be useful for us as the observer. In other words, for the CMB, the age of the "images" (but they're really fluctuations rather than individual images) are approximately equal. Boud 12:28, 20 February 2006 (UTC)

stuff removed
from here

Connectedness of the global manifold
A simply connected space is all of one piece, such as a sphere.

The probability of detecting a multiply connected topology depends not only on the scale of the topology but also the degree of complication in the topology. The observer may have a privileged position near a closed path. In a hyperbolic local geometry, a non-simply connected space is unlikely to be detected unless the observer is near a closed path.

A second endeavor in the analysis of data from the WMAP is to separate any multiple images in the cosmic background radiation from potential "back-to-back" multiple images due to a compact space. Current results eliminate many forms of non-simply connected topologies implying that either we are not near a closed light path or the global geometry is simply connected.

One way of thinking of a multiply connected space has circle-shaped "holes" or "handles". If the global geometry is non-simply connected then at some points in the geometry, near the junction of a "handle", paths of light may reach an observer by two routes, a "closed path" - a path through the main body and a path via the handle.

to here (though some is already edited a bit, sorry)

The &pi;-2 homotopy class of the 2-sphere is non-trivial - just as the circle is a multiply connected 1-dimensional space - so you have to be a bit careful in saying that the 2-sphere is simply connected - better not use it as an example.

The problem with the "hole" or "handle" way of thinking is that it's most relevant for an extremely INhomogeneous universe, whereas in observational cosmology we're thinking of a standard approximately FLRW model universe, which is of nearly the same density (hence, curvature) everywhere. A purely topological approach ignores distances, the metric, you can stretch the space arbitrarily as long as you don't cut or tear it. But that's confusing in this case, unless you explain that you are making extremely radical stretching and that you are thinking from a four-dimensional point of view.

A lot of the explanation for correct development of intuition about the subject has been removed from this page - look in the history to find it if you want to bring it back. Some time when i have a moment free i may do this if noone else does (i guess some of it could be moved to wikibooks - but given people's constant misunderstandings, i don't see how we can avoid having a section on intuition development - an encyclopedia is not supposed to persuade people that they are stupid. Boud 12:51, 20 February 2006 (UTC)

Rewrite
I've just gone through the article and rewritten it, with the aim of making it more accessible to the non-mathematician, and to make it conform more with the cosmology section. At the same time, I merged the information about open, closed and flat universes into the page - these are the common terms used by cosmologists to describe the universe. The text probably needs further work, but I'm done for now. Mike Peel 16:50, 25 February 2006 (UTC)

The terms "open" and "closed" are misleading, though it's true that they're commonly used. Boud 19:32, 10 July 2006 (UTC)

I'm new to wikipedia, but I couldn't help adding my two cents: I thought this page was tough reading for a lay person. Perhaps some illustrative analogies or simple examples would help. gabekader —Preceding comment was added at 08:31, March 19, 2007

correcting several errors
i've corrected some errors:


 * figure - omega alone does not determine the overall geometry of the Universe. It's a local property, not a global property.


 * a hypersphere is 3D, not 4D.

=== Non-Simply Connected Universe === This is the case of a multiply-connected, or more generally non-simply  connected, topology.
 * i removed the following section since it is not a separate case, it is discussed in the preceding three sections on negative, zero and positive curvature universes:

Boud 19:41, 10 July 2006 (UTC)

various
i've done a bit more cleaning up, trying to preserve the work of people who have tried to help, while also correcting the errors.

Please: anyone making corrections please be careful that you're not changing the scientific sense unless you're reasonably sure that you understand things properly. i'll probably come back to this and start from talking about 3-manifolds, because otherwise everybody will get confused...

Boud 23:31, 30 December 2006 (UTC)

Why isn't the Mobius Strip in here as a possible shape of the universe?
I read that it's a possibility. MC Escher made a drawing of it with ants crawling along it. 64.236.245.243 15:50, 15 February 2007 (UTC)

good Question, i thought of that also. I am working on new ideas that the universe has no shape and is truly infinite in all dimentions, direction,time and matter/anti matter.... —Preceding unsigned comment added by 209.212.21.182 (talk) 19:02, March 23, 2007


 * I think it's a bit of an outdated model, but it would still be nice to mention it. Also, unsigned comment person: I don't even know what to say to you. Ketsuekigata 14:08, 15 November 2007 (UTC)


 * The main reason the Moebius band is not the shape of the universe is that the Moebius band is only 2-dimensional.


 * There are, however, plenty of non-orientable 3-manifolds, and my guess is that it is highly unlikely that physicists have ruled them out as a spatial cross-section of the universe.


 * To respond to the unsigned suggestion that "the universe has no shape and is truly infinite in all dimensions", I will say that the universe could well be "infinite in all directions" and yet have a very complicated shape. The entire concept of manifolds was invented to describe the shape of things that are locally Euclidean -- and our universe certainly appears to be locally Euclidean, at least away from singularities.  It is not clear to me what it would mean to say "the universe has no shape".Daqu (talk) 06:00, 3 July 2008 (UTC)


 * Well, although non-orientable 3-manifolds haven't been ruled out, there's no real reason why the universe would be non-orientable. By Occam's Razor, it probably isn't. It's the same reason why there probably isn't a cheesecake at the center of the earth. It's possible, but the explanation that there's a molten metal core makes a lot more sense. --Zarel (talk) 05:29, 2 September 2009 (UTC)


 * In the section on Possible local geometries it says that a positively curved universe would be spherical. This must surely be wrong - even a 2D universe can be elliptic (non-orientable, e.g. the Boy surface) rather than spherical. In fact, the synthetic geometry of the Boy surface is cleaner than the sphere, since it is a projective geometry. Occam's razor would suggest the 3D analogue of this, projective space, as the most likely. Perhaps unexpectedly this space, like spherical space, is orientable (even though, unlike the sphere, a plane within it is not). -- Cheers, Steelpillow (Talk) 18:14, 6 November 2009 (UTC)


 * I'm with Steelpillow all the way here, Zarel. You say there is no reason the (spatial) universe should be non-orientable. That is so far from a convincing argument that it is ludicrous.  There is also no reason that it should be orientable, either!


 * You claim that by Ockham's Razor you can eliminate non-orientability as being presumably unnecessarily complicated. Please note:


 * 1. It is not clear at all that a non-orientable 3-manifold is necessarily more complicated than orientable ones.  As Steelpillow points out, a non-orientable surface (the projective plane) is the natural setting for elliptic geometry, not an orientable one.


 * 2. Ockham's Razor is a good rule of thumb. But it is never a guarantee that the (apparently) simplest explanation for something is in fact the truth.


 * 3. A non-orientable spatial universe might explain some dualities in physics, or the existence of antimatter.


 * 4. The simplest hyperbolic (constant negative curvature) non-compact 3-manifold is in fact non-orientable: The Gieseking manifold. (It has the least volume among non-compact hyperbolic manifolds, and is the only one that can be constructed from just one ideal hyperbolic simplex.)Daqu (talk) 06:25, 16 August 2015 (UTC)

The Möbius strip isn't in here because its only 2-dimensional. So the question should be renewed as &quot;why isn't R x Möbius strip not considered in here&quot;, and moreover, &quot;why isn't Klein's bottle not considered&quot; either. Even R2 x a twisted closed loop cannot be ruled out. All these manifolds cannot be ruled out by a meta argumentation of the type &quot;there is no reason to ...&quot;, but only by observation. What we really need, is a classification of 3-dimensional manifolds, orientable and non-oriental ones &agrave; la Perelman. Then there must be Singer&Thorpe-type curvature structures to get general relativity. What is nice in this article is the title, which avoides the word topology, already used in mathematics in a different sense: Remember a topology is a set with a set of subsets such that (i), (ii), (iii). So shape is a much better notion. Another, equivalent notion would be the &quot;large scale structure of universe&quot;. — Preceding unsigned comment added by 130.133.155.66 (talk) 17:26, 1 September 2012 (UTC)

indeed, a great circle on a sphere has circumference only twice its diameter...
I may be wrong, or there's a small geometry mistake here. 202.27.54.3 00:02, 15 March 2007 (UTC) Gerry

Don't think of the sphere in terms of its embedding in 3-dimensional Euclidean space. You have to measure the diameter of a circle within the manifold. As an example, consider the equator of a sphere of radius R. Its circumference is 2πR, its diameter is twice the distance between the north pole and a point on the equator, i.e., πR. Hence, the ratio between the equator's circumference and diameter is two. SwordSmurf 13:13, 15 March 2007 (UTC)


 * Agreed. Boud (talk) 14:57, 11 February 2008 (UTC)

Torus
I don't know much, but I don't think the surface of a torus is flat. Why is it listed under the possible shapes of bound flat universe? If it is flat, I request a proof or explanation. Aurora sword 07:24, 22 May 2007 (UTC)
 * I assume taht they have to have flat surfaces because the other two shapes (Cylinder and Mobius Strip) are flat. Aurora sword 07:26, 22 May 2007 (UTC)
 * I'm pretty sure a 4D torus can be flat. As far as I understand, a toroidal universe would mean a cubic honeycomb that repeats itself infinitely, but could still be "flat" in 3D (parallel lines neither meet nor diverge, and all that. Unless they go near anything that has mass, but that's another story). :-) - ∅  ( ∅ ), 06:41, 18 January 2008 (UTC)


 * Try drawing a diagram showing Pythagoras' Theorem on a piece of flat paper. Write down the lengths of the 3 sides of the triangle, either numerically or algebraically. Now roll it up to make a cylinder. The three side lengths have not changed. So Pythagoras' Theorem is still correct and the paper is flat. Now define the two ends of the cylinder to be equal to one another, and you have a 2-Torus. Pythagoras' Theorem is still true. So the 2-torus is flat. The embedding of T^2 in euclidean 3-space is just an aid to intuition, it's not part of T^2 itself. Hope this helps. Boud (talk) 14:55, 11 February 2008 (UTC)


 * One proof of this uses the Euler characteristic of a surface decomposition to show that the torus has the same topological curvature as an infinite flat plane. -- Cheers, Steelpillow (Talk) 11:23, 7 November 2009 (UTC)


 * There is no such thing as "topological curvature". Curvature is a geometric concept that can be attached to a surface (or points of a surface in a higher dimensional manifold) only if distances between any two points on the manifold have been defined — and in a particularly nice way (making it into what is called a Riemannian manfold).


 * But if the torus is a Riemannian manifold, then it is not true that the torus must have the same curvature as a flat plane (which would be 0 curvature). The only thing that must be true is that the torus must have average curvature equal to 0.  But the curvature can vary arbitrarily much over the torus.


 * P.S. Also, as for what ∅ said: "A toroidal universe would mean a cubic honeycomb that repeats itself infinitely" — This is not true, any more than an ordinary torus "repeats indefinitely". Both must have finite extent (the technical term is that they are "compact".) And a flat (zero-curvature) 3D torus does not need to be based on a cube, but rather on any parallelepiped.


 * However, It is indeed true that, to anyone living inside one, a toroidal universe based on a cube would look like a cubic honeycomb that repeats itself infinitely.


 * By "based on a cube" I mean that is the result of identifying corresponding points on opposite faces, for each of the three pairs of opposite faces. That is, if the cube is all points (x,y,z) in R3 with each of x, y, z lying in the unit interval [0,1], then we identify each (x,y,0) with (x,y,1); each (0,y,z) with (1,y,z); and each (x,0,z) with (x,1,z).Daqu (talk) 08:20, 16 August 2015 (UTC)

Another shape.
There is another shape (the name eludes me) where it is a spherical universe but it a dip in it. Does anyone know what I'm talking about? —Preceding unsigned comment added by 69.19.14.42 (talk) 02:37, June 24, 2007

Hyperbolic Universe Consistent with 1998 Measurements?
If you look at the Supernova Cosmology Project's website, it seems that the later conclusions drawn from the 1998 observations support a flat universe with vacuum energy, not with a hyperbolic universe. This article seems to favor the hyperbolic model, whereas my understanding is that the current most accepted model is flat. Ketsuekigata 13:53, 15 November 2007 (UTC)

The terms flat and curved apply only to the spatial part of the Robertson-Walker metric. Even if this spatial part is flat (Euclidean) there is still the extra dt² term and a minus sign which makes the universe hyperbolic. To put it another way flatness usually refers to the vanishing of the Riemann-Christoffel tensor so that Minkowski space is considered flat. But when you take into account the dt² term you still have the metric for a hyperbolic space. Indeed Minkowski space is hyperbolic although the textbooks mostly incorrectly think it is a kind of Euclidean space.JFB80 (talk) 17:00, 7 November 2010 (UTC)

Subsections in introduction
Someone boldly deleted the subsections in the introduction and also deleted its subsection on "Well defined 3-dim concept of space". Since the introduction is in development it is important to have a subsectioning. So that people can identify what the introduction is about, what is missing and what contains errors. —Preceding unsigned comment added by Caco de vidro (talk • contribs) 23:18, 17 January 2008 (UTC)
 * No text was deleted, I merely reverted the following:
 * the conversion of prose to a list
 * the addition of useless and distracting section headers
 * the rewording of one sentence.
 * See WP:MOS, WP:LEAD and WP:LAYOUT. (Also WP:SIG.) - ∅  ( ∅ ), 06:20, 18 January 2008 (UTC)

Curvature of the Universe?
Shouldn't this be named Curvature of the universe? Its a more commonly used term than shape and is a more accurate description. Or at least redirect it here. ErgoSum88 (talk) 08:11, 30 January 2008 (UTC)


 * No. Curvature does not fully determine the shape of the Universe. A 2-plane and a cylinder (more formally R times S^1) are both flat spaces. They have identical curvature (zero) but they are different shapes. See the first sentence of the article. Boud (talk) 14:37, 11 February 2008 (UTC)

CMB Analysis Shows Shape is Flat
This article looks good to me, but shouldn't it be mentioned somewhere that the observed angular size of the CMB temperature variations (as shown by the first acoustic peak) is just what is expected, which implies the angles of the corresponding triangle add pretty close to 180, so the shape of the universe is flat to a fairly high degree of accuracy, at least the universe from here to the surface of last scattering? DCCougar (talk) 01:45, 4 April 2008 (UTC)
 * That only shows that the Universe cannot be tightly curved. A very gentle curvature is not ruled out. -- Cheers, Steelpillow (Talk) 11:25, 7 November 2009 (UTC)

And the answer is.....?
This article yaps on about the theory, but does not provide a simple answer to the question: what is the shape of the universe? I suggest there should be a paragraph at the top which answers this question in simple laymans terms, even if only to say "Nobody knows" or "Different scientists say different things" or "It could be A or it could be B" or whatever. 80.2.206.224 (talk) 00:18, 13 May 2008 (UTC)

I agree. The first sentence in the article seems to paraphrase down to: "The shape of the universe is the study of the shape of the universe", which doesn't make sense. Okay, but what IS the shape of the universe whose shape is being studied? Or what do we think it is? I realize the rest of the article implies the answer is "We don't know, that's why this whole field of study has come up around it." But it would be nice to actually say that up front, and summarize the tentative conclusions so far. Phil59 (talk) 15:22, 14 September 2008 (UTC)


 * Yes please answer this. The whole article is incomprehensible without a high-level math degree. The first paragraph needs to very directly state "the universe is shaped like X" or "nobody knows the shape of the universe" or "we know the universe is X but not whether it's Y or Z in addition". 98.240.217.220 (talk) 20:00, 24 July 2023 (UTC)
 * To be more specific, the opening section vaguely says that the shape of the "universe" is debated, but does not specify if this is the local observable universe, the entire universe, or somewhere in between. 98.240.217.220 (talk) 20:05, 24 July 2023 (UTC)


 * I would say that the simplest answer of that style is "We have no idea what the shape of the Universe is", but the problem is that different cosmologists have different cv/grant funding/bibliometry/publicity/promotion pressures for trying to give oversimplified answers. Saying "we don't know" doesn't look so good when asking government agencies for funding the next generation of telescope projects. It's established since 2019 that the Universe cannot be spatially flat in a literal sense, since that would prevent galaxies from forming: An interpretation of ΛCDM as literally 3-Ricci flat would forbid structure formation. The statement that the "Universe is flat" is commonly made as a lie-to-children - it's not literally true, it's just a stepping stone in explaining (with advantages and disadvantages). The main confusing thing about curvature being "close" to a zero Omega_{m0} (curvature density parameter) is that it still allows (almost) any of the constant curvature 3-manifolds of any of the three signs of curvature.Overall, it's not so easy to simplify the lead without introducing the basic concepts. And I have a WP:COI (since I work in this research topic) so I have to be extra careful in any editing, especially if the edits are contested. Boud (talk) 16:05, 25 July 2023 (UTC)

Comment re Thurston geometries seems misleading
One paragraph of the article reads:

"In general, local to global theorems in Riemannian geometry relate the local geometry to the global geometry. If the local geometry has constant curvature, the global geometry is very constrained, as described in Thurston geometries."

But there are essentially only 3 different geometries with constant curvature: positive, zero, and negative. By contrast, there are 8 essentially different kinds of Thurston geometries (3 of which are these constant curvature ones).

(All of these geometries are local ones.)Daqu (talk) 05:37, 3 July 2008 (UTC)

Confusing definition of density parameter Ω
The article defines the density parameter as follows:

"Omega is the average density of the universe divided by the critical energy density, i.e. that required for the universe to be flat (zero curvature)."

It's confusing to read that the "density parameter" is defined in terms of the average density of the universe, but is not the same as this.

As long as a definition is being given, it might as well be clear. By "average density of the universe" does that mean mass per volume? If so, why not say so.

Also, what is the connection between "critical energy density" and the kind of density referred to in the phrase "average density of the universe" ? Are mass and energy being considered equivalent (via E = m c2) ?

Whatever the answers, I think the definition of Ω could be much clearer than it is.Daqu (talk) 05:49, 3 July 2008 (UTC)

Early Universe
Was looking for info about how theories about the shape of the universe interacts with theories about the universe's, um, formation. Intuitively one can imagine a compact topology's beginning (eg the point becomes a sphere) more easily than an infinite one's.--Mongreilf (talk) 15:19, 21 December 2008 (UTC)
 * I'd add that one can't imagine an infinite topology at all. And besides, why would one wanted if a compact topology suffices?
 * Another point is why do we need an early universe if we also can imagine the universe existing always easier than created from nothing against the law of conservation of energy? Are we already accepting creation "science"? And if "yes" then "why?" Jim (talk) 20:25, 24 August 2009 (UTC)
 * Our failure to grasp infinity, either intuitively or mathematically, does not mean that we can rule it out in situations such as this one, where we know so little about what is really going on. However, IMHO "infinite size" is just a finite mathematician's way of thinking about something indefinitely larger than anything else he can think of.
 * Gravitational energy is negative. It is possible that the amounts of negative and positive energy are the same, so the net overall energy of the Universe is zero. Douglas Adams remarked, in one of the Hitch Hiker's Guide to the Galaxy seres, that in the context of Quantum probability, "it may be that the universe exists simply because it can". -- Cheers, Steelpillow (Talk) 11:40, 7 November 2009 (UTC)

Don't explain true physics with false math
I spotted in a section Global geometry subsection Spherical universe the following statement: "In a closed universe lacking the repulsive effect of dark energy, gravity eventually stops the expansion of the universe, after which it starts to contract until all matter in the observable universe collapses to a point, a final singularity termed the Big Crunch, by analogy with Big Bang." It happens to be an idea from a pre-letavistic gravitation, MTW type, which we now know was wrong. In Einstein's gravitation there are no repulsive effects (or attractive) and all such effects disappeared from physics after 1915, to become apparent, and stayed only in some textbooks like MTW's "Gravitation" that predicted decelerating expansion allegedly caused by the "attractive gravitation" (as in the quoted statement).

Since 1998, when observations by Supernova Cosmology Project demonstated that decelerating expansion is not observed we should be more careful with our language since attraction and repulsion sound like from 17th century when wise men tried to convince Newton (aginst his better judgement) that "some forces can act at a distance" which was needed to justify religious beliefs of people of that time. Einstein showed that gravitational forces act only while one mass pushes at another (which means never in free fall).

It is silly to try to explain 21st century true physics with 17th century false math (as MTW did) while we have available for almost 100 years Einstein's work to learn from and have all the puzzles explained through the simple Einstein's physics in which the most complicated math is a square root :). Jim (talk) 19:34, 24 August 2009 (UTC)

Move? 2010

 * The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section. 

The result of the move request was: No consensus to change the name of this article Graeme Bartlett (talk) 07:03, 10 January 2010 (UTC)

Shape of the Universe → Shape of the universe —
 * To conform with Age of the universe; unnecessary capitalization  Imagine Reason (talk) 14:23, 1 January 2010 (UTC)
 * Disagree; Universe use the capatalised version throughout. 84.92.117.93 (talk) 18:16, 1 January 2010 (UTC)
 * Oppose. 84.92.117.93 pulled the move request for Age of the universe (Talk:Age_of_the_universe) with the understanding that this was a topic discussion was best resolved at the topic lead, and I would agree. The capitalization of universe is currently inconsistent. Suggest a naming consensus be reached at the topic lead (Universe) first, for all affected articles, before this move is initiated.--Labattblueboy (talk) 14:01, 7 January 2010 (UTC)
 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

no mention of dodecahrdron multiverse
i have added a seperate article in the end about a dodecahedron multiverse.plz help in expanding the article and if possible a seperate article here are some links http://goldennumber.net/classic/universe.htm http://news.nationalgeographic.com/news/2003/10/1008_031008_finiteuniverse.html http://physicsworld.com/cws/article/news/18368 http://en.wikipedia.org/wiki/Wilkinson_Microwave_Anisotropy_Probe http://en.wikipedia.org/wiki/Dodecahedron http://arxiv.org/abs/0801.0006 http://en.wikipedia.org/wiki/Homology_sphere#Cosmology manchurian candidate 04:59, 6 June 2010 (UTC) —Preceding unsigned comment added by Manchurian candidate (talk • contribs)


 * It's already in the final section, properly weighted. ScienceApologist (talk) 16:37, 14 June 2010 (UTC)


 * The Poincare dodecahedral space papers consider standard FLRW models. They do not consider multiverse scenarios. These are two totally separate ideas. Boud (talk) 21:25, 18 September 2010 (UTC)

TODO: T^3 models by Aurich et al.
The Ulm group has recently published many papers in favour of the T^3 model. i or someone else should add these in here... Boud (talk) 22:17, 18 September 2010 (UTC)

Why infinite?
The introduction claims: the presently most popular shape of the Universe found to fit observational data according to cosmologists is the infinite flat model. I do not see how the given source backs up that statement. It rather seems to say: "the universe is quite flat". But there are compact ("finite") manifolds which are flat, like the 3-torus. --131.152.41.173 (talk) 17:08, 24 September 2010 (UTC)


 * Indeed, that statement is not backed by the given source at all. I have replaced the bad ref with a proper one. Good catch. Feel free to hone the statement. DVdm (talk) 18:16, 24 September 2010 (UTC)

Move? 2011

 * The following discussion is an archived discussion of the proposal. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section. 

No consensus to move. Vegaswikian (talk) 22:00, 16 March 2011 (UTC)

Shape of the Universe → Shape of the universe —
 * caps per MoS Smjg (talk) 17:43, 9 March 2011 (UTC)
 * Comment isn't Universe a proper noun? 184.144.163.245 (talk) 04:55, 10 March 2011 (UTC)
 * Defend It's "universe" – not a proper noun – according to my direct first-hand experience, Wikipedia usage and the vast majority of dictionaries. What does your dictionary say about it?  Moreover, if we were to treat it as a proper noun, we would have to change many WP articles (titles and content) to reflect this. — Smjg (talk) 19:52, 10 March 2011 (UTC)
 * We're talking about a particular universe, since "universe" is a common noun, and it is a class of object, not a particular object. There are many conceptual universes out there, the particular universe this article deals with is "The Universe"/"Universe". This also needs clarification between Everett universes, Hubble universes, and our universe as a whole (the sum of Hubble and Everett universes), which may exist in an omniverse or multiverse of M-branes, or budding inflationary zones. Same as the Sun is the star in our solar system, the Solar System, while a sun is the star of a solar system. There are the particular and the generic forms. 184.144.160.156 (talk) 02:05, 11 March 2011 (UTC)
 * Are you sure about this? Most of the aforementioned dictionary definitions and mentions here on WP seem to be talking about the universe, rather than a universe as a general entity. — Smjg (talk) 11:38, 11 March 2011 (UTC)
 * Object there is an old requested move on the talk page with just this, that did not pass. Therefore this requires a discussion, since an old discussion occurred with this exact same proposal. 184.144.163.245 (talk) 04:56, 10 March 2011 (UTC)
 * By heading with "Object" you've made it sound as though you're objecting to the move, hence the comments that follow. If you're only objecting to the speediness of it, it's better to just follow the instructions for contesting a request and head your point with "Comment" if anything. — Smjg (talk) 19:52, 10 March 2011 (UTC)
 * That is the procedure for objecting to speedy renaming. The person who moved the discussion here did not make a clear cut between the speedy section and the discussion that occurs after it. 184.144.160.156 (talk) 01:56, 11 March 2011 (UTC)
 * That discussion was over a year ago, WP:CCC  C T J F 8 3  05:01, 10 March 2011 (UTC)
 * Comment consensus cannot change without a consensus discussion. This was nominated for speedy renaming, not regular renaming. You said that CCC, but that cannot occur without a discussion, so what's your point? 184.144.160.156 (talk) 10:21, 10 March 2011 (UTC)
 * Ahh...I misunderstood the IPs comments. C T J F 8 3  16:21, 10 March 2011 (UTC)
 * The above discussion is preserved as an archive of the proposal. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

Spherical Expanding Universe
I'm not an expert in this matter, but this section seems to be wrong. It cites no sources and has some remarkable sentences. -"An observer can never get to the edge of the Universe if it is expanding at the speed of light" Speed of expansion is not expressed in the same units as the speed of light, so you can't compare them.

It is also applying special relativity to the speeds found by the expansion of the universe. To my knowledge there is no length contraction or time dilatation due to the expansion, since these are not the speeds that special relativity is concerned with. These speeds can even exceed the light speed, as is confirmed by this wiki article http://en.wikipedia.org/wiki/Faster-than-light#Universal_expansion ZVdP (talk) 11:16, 8 August 2011 (UTC)

More examples, less theory
This article needs more practical every-day examples in order to be remotely understandable by non-physicists.

It is not really hard to explain a closed, hypersphere-like universe to a layman, it just has to be done (use an "ant on a soccer ball" analog) — Preceding unsigned comment added by 82.139.196.68 (talk) 21:58, 23 December 2011 (UTC)

Flat universe
Is flat universe three dimensional? is it like a "membrane" or a "thick" wafer?--144.122.104.211 (talk) 22:07, 29 May 2013 (UTC)
 * If our universe was flat, it would be three-dimensional. There's nothing stopping you from theoretically imagining a flat universe with any number of dimensions, though, since you can define n-dimensional Euclidean space for all non-negative integer n.
 * The illustration in the article depicts a two-dimensional flat universe, however, because it's quite difficult to visualize three-dimensional curved space, and it's easier to have all the example universes be of the same dimensionality. Double sharp (talk) 09:49, 15 May 2014 (UTC)
 * Thank you.--95.10.139.121 (talk) 17:35, 26 May 2015 (UTC)

Requested move 2013

 * The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section. 

The result of the move request was: Page moved - unanimous support for move. &mdash; Amakuru (talk) 11:14, 21 October 2013 (UTC)

Shape of the Universe → Shape of the universe – Despite the results of the previous move requests above, I'm requesting this move once again, mostly as a result of the move discussion at Talk:Age of the universe. The word universe is lowercased in the text of this article, and it's desirable that the title and the text should agree. To say nothing of WP:NCCAPS. Deor (talk) 21:10, 11 October 2013 (UTC)
 * See also Talk:God becomes the Universe. Anthony Appleyard (talk) 21:26, 11 October 2013 (UTC)
 * Support - *entirely* the comments of Deor above - and renaming the article with a lower-case "universe" - Enjoy! :) Drbogdan (talk) 02:51, 12 October 2013 (UTC)
 * Support - Per the rather overwhelming evidence for usage given at Talk:Age of the universe, especially in style guidelines which specifically state that universe should not be capitalized, whereas not a single source could be shown that suggests that it should. - Aoidh (talk) 05:38, 12 October 2013 (UTC)
 * Support per the desirability of consistent capitalization and the result of the other move request. 168.12.253.66 (talk) 16:36, 12 October 2013 (UTC)
 * Support per the sources in the above linked discussion. Reliable style guides, dictionaries, and other sources almost all unilaterally recommend lower case here.  -- Jayron  32  00:39, 13 October 2013 (UTC)
 * Support. In addition to the references from the previous discussion, the American Astronomical Society (pretty much the last word in astronomical designations, and referred to as the authority by the Chicago Manual of Style), uses lowercase "universe" in its own materials.   - WPGA2345 -     ☛   03:19, 14 October 2013 (UTC)
 * Support per above reasons and those in Talk:Age of the universe. --Article editor (talk) 23:06, 14 October 2013 (UTC)
 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

Capitalization of universe
There is currently a discussion about the capitalization of Universe at . Please feel free to comment there. —sroc &#x1F4AC; 13:15, 19 January 2015 (UTC)

Discussion of capitalization of universe
There is request for comment about capitalization of the word universe at Wikipedia talk:Manual of Style/Capital letters. Please participate. SchreiberBike talk 00:49, 4 February 2015 (UTC)

Notification of request for comment
An RfC has been commenced at MOSCAPS Request for comment - Capitalise universe.

Cinderella157 (talk) 03:23, 22 March 2015 (UTC)

Ridiculous premise
The introductory section includes the following passage:

"The shape of the global universe can be broken into three categories:


 * 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."

This contains a number of mistakes and omissions:

Let's assume that the only manifolds in question are complete (all geodesics can be continued indefinitely).

Then:

* A complete flat manifold can be either open or closed * A complete manifold having everywhere negative curvature (constant or not) can be either open or closed. * A manifold having everywhere positive curvature can be either open or closed. (It is true that a complete manifold having constant positive curvature must be closed, i.e., of finite extent and without boundary.) * There is much more to the topology of a complete manifold than just whether or not it is simply connected. It can be simply connected or not, and still have complicated higher-dimensional holes. (Consider for example the product of two sphere S2×S2. Or the connected sum of two of these, S2×S2 # S2×S2. Or complex projective space ℂℙ2, or the connected sum of two of these ℂℙ2 # ℂℙ2. All four of these are simply connected.)Daqu (talk) 22:53, 26 June 2015 (UTC)
 * So how do you suggest that it be changed? Should 2. be split so that flat, positive  or negative curved appears as one category; with open or closed as another.  I don't think we can assume your definition of complete applies to the Universe. However do you have other suggested categorizations for the shape?  I suppose we need references to support that this is the way it has been described. Graeme Bartlett (talk) 11:30, 27 June 2015 (UTC)
 * "It is true that a complete manifold having constant positive curvature must be closed, i.e., of finite extent and without boundary." Cosmological models are normally homogeneous and isotropic, so they normally do have constant curvature across a spatial curface. Also, your statement, although true, can be weakened significantly, at least in the Riemannian case. The Myers theorem only requires a lower bound on the curvature.--76.169.116.244 (talk) 16:59, 28 July 2015 (UTC)

Inaccuracy in lead
The lead contained an inaccurate claim that overstated the logical independence of the three factors listed (finite/infinite, curvature, and topology). There *are* links between curvature and topology; they are not completely independent things. In the Riemannian case, this is what the Myers theorem is about. In cosmology, a positively curved model (assuming homogeneity and isotropy) must be spatially finite. I've corrected the incorrect statement and added a reference.--76.169.116.244 (talk) 17:02, 28 July 2015 (UTC)

The flatness of the Universe isn't a result, but the cause of everything on it
The flatness of the Universe isn't a result, but the cause of everything on it. The Universe means "eternally flat spacetime". The Universe may create (as during the Big Bang when it defaulted) or cancel some mass (blackboard delete some mass and spit it elsewhere), and it does that because it permanently is flat on the large scale.

All secondary phenomena (Big Bang, gravity, black hole radiation) exist due to the permanence of the fundamental Universal flatness.

Why did they Universe when it defaulted during Big Bang was so homogeneous? Because defaultness means to force homogeneity, and force homogeneity means Big Bang!

Why the Universe is so easy to understand? Watch porn, because the "Theory of Everything" will never be accomplished. Our Universe is an algorithm of topological algebra; infinite other versions exist. Also SUSY and superstring-brane-M theory force quantization at a simplistic - non probabilistic way on the Planck scale and are wrong. No sub-Planck scale exists. Particles have a probabilistic behavior. Imagine the void as an old empty tape. Even an empty tape if played loud, reproduces noise! Particles are patterns that exceed the Planck-noise level. No generic "Theory of Everything" will ever be discovered, except if you have infinite ink and infinite paper to describe the infinite topological algorithms which generate a larger infinity of universes (because an algorithm may generate googolplex results. — Preceding unsigned comment added by 2A02:2149:8434:BB00:C97C:5A2D:829B:9E0A (talk) 11:03, 19 October 2017 (UTC)

New paper shows evidence for a closed universe
Someone with better writing skills than I could incorporate this into the article perhaps? https://www.nature.com/articles/s41550-019-0906-9 Xanikk999 (talk) 01:47, 5 November 2019 (UTC)

Physical energy shape scale
The Great shape of scale and cube 37.236.119.15 (talk) 20:53, 7 August 2023 (UTC)

A source to consider
A source to consider: Planck evidence for a closed Universe AXO NOV  (talk) ⚑ 12:32, 27 September 2023 (UTC)

This is a pretty messy article
There's a lot that wasn't needed imo. Working on rewriting it, moving forward it should focus on 3 things.

1.) The local vs global geometry of the universe: a.) What is the difference between them? 2.) How general relativity only constrains the local geometry via the FLRW metric (justified by the large scale homogeneity of the universe) to be a space of constant curvature solely based on the average energy densities of matter, radiation, and dark energy, 3.) How general relativity with the FLRW metric DOES NOT constrain the global geometry if we allow for multiply connected spaces, and how it does constrain it if we restrict ourselves to simply connected spaces (to hyperspheres of constant curvature, either open and flat, closed and positively curved or negatively curved open). List examples of finite multiply connected spaces with constant zero curvature given the observational evidence points to a flat universe. 4.) Experimental searches for global topology/results.

As it stands the article is just disconnected and was definitely not approachable by anyone who doesn't have a physics background, limiting it's usefulness. We don't need to make things unnecessarily complex; we can explain the concepts in a way that everyone can understand. Chuckstablers (talk) 04:20, 30 October 2023 (UTC)


 * I had a quick run through your changes. As said in my edit comment, please complain if you see problems in my edits (WP:COI). Your changes mostly look OK to me. I put a few brief explanations in the edit comment.Looking through your comment immediately above: the hypersphere (S^3) is of positive curvature. Probably what you meant is what typically goes under names such as the comoving spatial section or a hypersurface or a spatial 3-volume.For point 4), I'm strongly biased in terms of the experimental searches :), since a big fraction of the work is by me and co-authors, so I didn't add anything to the global search paragraph beyond repeat references, even though a lot of work was done over the more than two decades since 1993 (the first two COBE cosmic topology articles). However, I did add a paragraph on topological acceleration, which provides a local method of determining global topology. This paragraph only refers to my+coauthors' work, because I'm fairly sure that nobody else has done any peer-reviewed articles on local methods of determining the global topology of the Universe. Obviously, you should add any if you find them, and I would be pleased to hear about them. (There is VR2023, but that uses what is argued to be a necessary extension of general relativity to take topology into account in the Newtonian limit; it cannot claim to be strictly GR. Qualitatively, it confirms the earlier results that global topology has a signature in local acceleration, though in a different way, since the gravity model is an extension of standard GR.) Boud (talk) 23:15, 30 October 2023 (UTC)
 * I have no issues with your changes at all. Thanks for adding what you did. I'm not an academic and wouldn't pretend to have the same knowledge base as you do, so please correct me where I'm wrong.
 * Overall I'd like for the article to focus on the differences between local geometry/global geometry, topology, what general relativity does to constrain local geometry, how it doesn't constrain the global topology of the universe (I believe, correct me if I'm wrong, that you can have a multiply connected space in an FLRW like metric that has the same spatial curvature everywhere just like the FLRW metric, it's just multiply connected with a specific topology and obeys the same equations for the scale factor), and current observational evidence regarding topology, curvature, and shape of the universe. In a way that actually flows and is accessible for the average reader. Trying to think of ways to structure the article. If you have any ideas please let me know. Chuckstablers (talk) 02:10, 31 October 2023 (UTC)
 * You're correct that for a given sign of curvature of an FLRW model, there is a family of different spaces (one simply connected, the others multiply connected). Once the values of the specific FLRW parameters are given (Hubble constant and current-day Omega parameters), then the scale factor evolution a(t) is known for all t for the model, but the specific space is not known. The nuance is that the real Universe is not exactly FLRW (since Earth and the Milky Way, and the cosmic web more generally, exist), so locally measurable properties do, in principle, constrain the global topology (but showing if local effects from the global topology would have strong enough signals to be distinguished from other local kinematical properties has not yet been done). Boud (talk) 00:33, 2 November 2023 (UTC)

Self contradictory statement
“The observable universe is a roughly spherical region extending 46.5 billion light-years in all directions from any observer”. If the observer is on the edge of the sphere containing all matter in the universe then there is nothing in the entire hemisphere that is tangent to the sphere at his location to observe so it is impossible for him to observe matter in all directions. Larry715 (talk) 03:42, 16 May 2024 (UTC)
 * (1) The observer is at the centre of the observable Universe, not the edge. (2) The edge of the observable Universe is defined by the finite age of the Universe: the assumption of the FLRW models is that no matter the topology and curvature, there is no spatial boundary in an FLRW universe. The roughly spherical shape of the spatial section (in comoving coordinates) is defined by the age of the Universe being approximately the same in all (4&pi; steradians) directions. Boud (talk) 11:14, 16 May 2024 (UTC)
 * The sentence says any observer, not an observer at the center of the universe. Any observer would include, for example, an observer at the edge of the universe. Larry715 (talk) 10:19, 24 May 2024 (UTC)
 * I've tried to reword it to avoid this confusion. To answer your point more directly, the "observable universe" is "where the observer can potentially receive information from", so it depends on the observer in question. Our observable universe is a ball around us, if there is an observer at the edge of it, their observable universe ("what they can observe") would be a ball around them. And it doesn't matter whether there is matter there, it's about the location and whether a signal could travel here from there, not whether there is something there to emit that signal (if there's no matter, it would be just an observable void). And we have no good reason to suspect that matter ends at some point anyway. Neither that there is a center to our universe. L3erdnik (talk) 15:33, 25 May 2024 (UTC)
 * Good point about "any observer" - I missed the ambiguity. The correction looks fair enough at this level of description. Boud (talk) 00:19, 26 May 2024 (UTC)