Talk:Shape of the universe

message: 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)
replies: text:  Working on this now --Eddie 21:50, 4 Jan 2005 (UTC)
replies: text:  Done.  Please improve and be bold.  Old text commented out in this page. --Eddie 23:10, 12 Jan 2005 (UTC)
thread_title: Tone of article

message: 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)
replies: text: 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)
thread_title:  A typo in Local geometries 

message: 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)
replies: text: 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)
thread_title:  Open Universe 

message: 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)
thread_title:  Multiple images in different age 

message: 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 π-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)
thread_title: stuff removed

message: 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 π-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)
thread_title:  Connectedness of the global manifold 

message: 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)
thread_title: Rewrite

message: 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.
* 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:
 === Non-Simply Connected Universe ===
 This is the case of a multiply-connected, or more generally 
 non-simply   connected, topology.
Boud 19:41, 10 July 2006 (UTC)
thread_title:  correcting several errors 

message: 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)
thread_title:  various 

message: I may be wrong, or there's a small geometry mistake here.
202.27.54.3 00:02, 15 March 2007 (UTC)
replies: text: Agreed. Boud (talk) 14:57, 11 February 2008 (UTC)
thread_title:  indeed, a great circle on a sphere has circumference only twice its diameter... 

message: 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)
thread_title:  Hyperbolic Universe Consistent with 1998 Measurements? 

message: 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)
replies: text: 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)
thread_title:  Curvature of the Universe? 

message: 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)
replies: text: 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)
thread_title:  CMB Analysis Shows Shape is Flat 

message: 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)
replies: text: 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)
replies: text: 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)
replies: text: 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:  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)
thread_title:  And the answer is.....? 

message: 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)
thread_title: Comment re Thurston geometries seems misleading

message: 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)
thread_title: Confusing definition of density parameter Ω

message: 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)
thread_title: Don't explain true physics with false math

message: 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)
replies: text: It's already in the final section, properly weighted. ScienceApologist (talk) 16:37, 14 June 2010 (UTC)
replies: text: 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)
thread_title:  no mention of dodecahrdron multiverse 

message: 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)
thread_title:  TODO: T^3 models by Aurich et al. 

message: 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)
replies: text: 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)
thread_title:  Why infinite? 

message: 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)
thread_title:  Spherical Expanding Universe 

message: 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)
thread_title:  More examples, less theory 

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

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

message: An RfC has been commenced at MOSCAPS Request for comment - Capitalise universe.
Cinderella157 (talk) 03:23, 22 March 2015 (UTC)
thread_title:  Notification of request for comment 

message: The introductory section includes the following passage:
"The shape of the global universe can be broken into three categories:
#   Finite or infinite
#   Flat (no curvature), open (negative curvature) or closed (positive curvature)
#   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)
replies: text: 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)

text: "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)
thread_title:  Ridiculous premise 

message: 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)
thread_title:  Inaccuracy in lead 

message: 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)
thread_title:  The flatness of the Universe isn't a result, but the cause of everything on it 

message: 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)
thread_title:  New paper shows evidence for a closed universe 

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

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

message: “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)
replies: text: (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 (4π steradians) directions. Boud (talk) 11:14, 16 May 2024 (UTC)
replies: text: 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)
replies: text: 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)
replies: text: 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)
thread_title:  Self contradictory statement