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First of all, I'm a layman to cosmology. So please excuse the possibly oversimplified picture I have in mind.

I was wondering how we could know that the observable universe is only a fraction of the overall universe. If we imagine the universe like the surface of a balloon we could be seeing only a small part of the balloon

or we could be seeing around the whole balloon

so that one of the apparently distant galaxies is actually our own.

In the example with the balloon one could measure the curvature of spacetime to estimate the size of the overall universe, but one could also think about something like a cube with periodic boundary conditions.

Is it possible to tell the size of the overall universe?

Artistic image of the observable universe by Pablo Carlos Budassi.
A. P.
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    Hello! I have reduced the size of your images to improve readability (in my opinion). Feel free to rollback if you wish! – jng224 Mar 14 '21 at 21:22
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    @Jonas Thanks, that improved the readability indeed. I just changed it to HTML tags, so the high resolution version is linked, but the images are still displayed smaller. – A. P. Mar 14 '21 at 21:33
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    People have actually checked the "wrap-around universe" theory (which is what you'd expect for a universe with positive curvature and simple topology) by looking for repeated patterns, but the results were negative. So either the curvature isn't positive, or it's so small that the repetitions are too far away. Or the topology isn't simple. – PM 2Ring Mar 14 '21 at 22:02
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    If the universe is only 14 billion years old, how can it be 92 billion light years wide? – mmesser314 Mar 15 '21 at 00:26
  • VTC. Perhaps I'm in the wrong here, but I fail to see the difference between this "repeat pattern" universe, and, say, cold fusion. – Dmitry Grigoryev Mar 15 '21 at 13:50
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    @DmitryGrigoryev Sorry, but I fail to see the connection between my question and cold fusion. Could you elaborate more? – A. P. Mar 15 '21 at 13:57
  • @A.P. See https://physics.meta.stackexchange.com/q/4538/83721 – Dmitry Grigoryev Mar 15 '21 at 13:57
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    @DmitryGrigoryev Ah, I see. In that sense my question is about mainstream physics, because it asks whether mainstream physics provides a way to differentiate between the different models in my question. And the fact that serious research was done to clarify this (like the paper in benrg's answer) shows that this is a serious topic. – A. P. Mar 15 '21 at 14:04
  • That's what I don't understand. There were also serious research groups (e.g Caltech) which tried to replicate cold fusion as well (unsuccessful of course), so where is the line between a wrong theory and "non-mainstream physics"? – Dmitry Grigoryev Mar 15 '21 at 14:11
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    @DmitryGrigoryev The accepted answer to that meta question literally says "For example, a question that proposes a new concept or paradigm, but asks for evaluation of that concept within the framework of current (mainstream) physics is OK.", which is exactly what this question is about. – TooTea Mar 15 '21 at 14:13
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    @DmitryGrigoryev The meta article leaves quite some room for interpretation, but I think a reasonable line could be set between (A) questions which start by assuming a disproved theory is right and build up their crazy ideas or (B) questions which ask how to disprove certain theories. – A. P. Mar 15 '21 at 14:16
  • @A.P. That article disproves a particular topology which would let you see the same object more than once, which is not the same as the topology in your question ("cube with periodic boundary conditions"). I don't see how you could have arrived to this cube topology at all using mainstream physics. – Dmitry Grigoryev Mar 15 '21 at 14:35
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    @DmitryGrigoryev As far as I understand the article the cube with periodic boundary conditions is explicitly mentioned on page 1 as "For example, Euclidean space can be tiled by cubes, resulting in a three-torus topology. Assuming that light has sufficient time to cross the fundamental cell, an observer would see multiple copies of a single astronomical object." – A. P. Mar 15 '21 at 14:40
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    related https://physics.stackexchange.com/questions/10127/size-of-the-universe – Mithoron Mar 17 '21 at 20:20
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    https://physics.stackexchange.com/questions/407244/how-small-could-the-universe-be – Mithoron Mar 17 '21 at 20:36
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    @PM2Ring - Would patterns even be visible, over the timescale that it would take light to "loop the universe"? – IronEagle Mar 18 '21 at 00:24
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    @IronEagle Maybe not, but bear in mind that the space scale has increased by ~1100 times since the era when the CMB was emitted. – PM 2Ring Mar 18 '21 at 05:33
  • I believe that the cosmological model most compatible with the interesting possibility that the OP has raised may be Nikodem Poplawski's torsion-based model of closed universes formed in a past- and future-eternal process, described in 2010-2021 papers whose preprints can be found by his name on Cornell University's Arxiv site. – Edouard Mar 20 '21 at 00:06

5 Answers5

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Yes, it's possible in principle that we see the same galaxy more than once due to light circling the universe. It wouldn't necessarily be easy to tell because each image would be from a different time in the galaxy's evolution.

There is a way to test for this. The cosmic microwave background that we see is a 2D spherical part of the 3D plasma that filled the universe just before it became transparent. If there has been time for light to wrap around the universe since it became transparent, then that sphere intersects itself in one or more circles. Each circle appears in more than one place in the sky, and the images have the same pattern of light and dark patches. There have been searches for correlated circles in the CMB pattern (e.g. Cornish et al 2004), and none have been found.

benrg
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    Intersecting in circles seems to assume a spherical topology, which isnt a given. Moreover it assumes the becoming transparent was a rather fast and uniform event, which one might also question. – Eelco Hoogendoorn Mar 15 '21 at 07:40
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    @EelcoHoogendoorn The argument depends on the spatial curvature being constant, but it works regardless of the sign of the curvature. If the space isn't simply connected you can take the universal cover and imagine it to contain copies of Earth, which must all see the same thing. The paper I linked discusses this starting at the end of page 1. You're right that the last scattering surface has to be thin for this to work. I'm almost sure it is thin enough, though there may be some blurring. This paper is relevant. – benrg Mar 15 '21 at 08:16
  • Thank you for this nice and clear answer. Did I understand it correctly that the CMB maps used for example in the Cornish paper are created by imaging the surface of last scattering? So basically by focusing the radio telescopes onto a distance of 42 billion lightyears? – A. P. Mar 15 '21 at 10:42
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    @benrg I see how it would work for a curvature that has any sort of symmetry - but couldn't it be more... say, like a (randomly) crumpled paper, than a sphere? It would be hard to see any interference patterns from a non-symmetric interference. It would present as noise. – Stian Mar 15 '21 at 13:57
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    @StianYttervik It's always a sphere "modulo" the spatial wrap-around. If the universe is much smaller than the (apparently) visible universe then the sphere will intersect itself a large number of times. I think that would be easy to detect: if the spatial slices were positively curved, then the spatial curvature would be bounded well away from zero by the model fitting, and if they were flat or hyperbolic but not simply connected, then there would be obvious violations of isotropy. – benrg Mar 15 '21 at 20:08
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    @StianYttervik : Crumpled paper would have obvious physical consequences everywhere. For instance, space would be filled with cosmic strings along every fold of the crumple. We don't see any cosmic strings, so any crumpling must have been (and be) very sparse. The cosmic gravitational background would contain a lot of energy from the folds and over the last several years, we are starting to be able to try to measure that using pulsar timing arrays. – Eric Towers Mar 16 '21 at 08:29
  • It takes an awful lot of time for light to travel a full lap around the balloon, implying a large red shift (in a now deleted question I got $z\approx 500$, but that was using a wrong model). Does that red shift not ruin all the light/dark patches? – Jyrki Lahtonen Mar 17 '21 at 03:44
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    To answer my own question in a previous comment (and for all optics people who might ask themselves the same question): Yes, the CMB maps used in the Cornish paper are created by imaging the last scattering surface. But unlike in microscopy one doesn't focus on the object, because it's so far away and the numerical aperture of the parabolic mirror is so small. Instead, one uses infinity focus, as it would be called in photography. – A. P. Mar 17 '21 at 10:08
  • @JyrkiLahtonen I don't think that the red-shift would ruin the image. One can still detect spots with higher or lower intensity or different polarizations. The brightness and polarization are given by the source, and that is what is imaged. Of course we could achieve a higher resolution if the wavelength was less red-shifted. – A. P. Mar 17 '21 at 10:13
  • @JyrkiLahtonen The last scattering surface is (almost exactly) the same time-away in every direction, hence the same distance-away (c is constant!), and (barring some extremely warped cosmologies) experiences the same red-shift in every direction. Things that violate these assumptions (scattering surface didn't happen at the same time-away in different directions, cosmology is extremely warped, etc) would leave evidence elsewhere that is not in evidence. – Yakk Mar 17 '21 at 13:59
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    @Yakk Thanks. But I have the impression that for the purposes of identifying "full laps around the balloon" we would be comparing patches from two different laps. When one would necesssarily be much older. My wrong toy model where the radius of the balloon is exactly the age of the universe lead to the estimated expansion factor $z\approx 500$ per lap, which should be enough red-shift to make comparison between two images meaningless. May be I have misunderstood what is being searched from the CMB images? – Jyrki Lahtonen Mar 17 '21 at 17:47
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    @JyrkiLahtonen Everything that is being compared has the same redshift, that of the CMB (about 1100). What is being compared is light that circled the universe in different directions, not different numbers of times. – benrg Mar 17 '21 at 19:49
  • Thanks @benrg. That makes more sense. As hopefully does my earlier query, now. – Jyrki Lahtonen Mar 17 '21 at 20:06
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Another possibility (to complement the existing answers) is that space could be finite in some directions but infinite in others, like a cylinder.

References, for a theoretical approach:

  • Lachieze-Rey & Luminet (1995), "Cosmic topology". This is an 80-page review
  • Ellis (1971), "Topology and cosmology".
Colin MacLaurin
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    FWIW, we have an old question discussing SR (specifically, the twin paradox) in a cylindrical universe. https://physics.stackexchange.com/q/361/123208 – PM 2Ring Mar 17 '21 at 05:41
  • Wouldn't this break isotropy of space in an almost certainly observable way? I mean it's easy to miss periodicity of space if it looks everywhere the same, but if it's different in one direction, there should be patterns that are already visible at large scale, wouldn't it? – oliver Apr 03 '21 at 08:32
  • Indeed one might see "ghost images" in a multiply-connected universe, as Lachieze-Rey & Luminet section 10 calls them. However if the curled-up direction(s) were larger than an appropriate horizon (e.g. the observable universe, or particle horizon, or something) then we wouldn't see them. – Colin MacLaurin Apr 05 '21 at 02:10
  • The paper also distinguishes between "local isotropy", which still holds, and global isotropy, which is broken in most multiply-connected models. Curiously, section 9.3 states: "It is worthy to note that globally anisotropic models do not contradict observations, since the homogeneity of space and the local isotropy ensure the complete isotropy of the Cosmic Microwave Background, and the statistical isotropy of the distribution of discrete sources". – Colin MacLaurin Apr 05 '21 at 02:12
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  1. "I was wondering how we could know that the observable universe is only a fraction of the overall universe."
  2. "Is it possible to tell the size of the overall universe?"

The first step in knowing (1) and/or (2) is to know whether the universe is infinite of finite. At the present time this is not known with any high level of confidence. In a few decades I think it is likely cosmologists will know with a reasonable level of confidence.

If the universe is infinite then it is clear that it is bigger than the observable universe which is finite.

If it becomes known that the universe is probably finite it is likely it will also be known that the value of the curvature density (represented by $\Omega_k$) will be known to be in a range of values with a confidence level like 95%. If the entire 95% range has all values < 0, say between -a and -b. then it will be known with a reasonably accurate probability distribution that the radius of curvature will have a positive value within a corresponding range of some billions of light years.

Regarding the title question, if the radius of curvature is R, and the radius of the observable universe (OU) is r, then the most distant point from an observer is $\pi$ R. If r = $\pi$ R, then you are seeing a point as far away as any exists. If r > $\pi$ R, then you are seeing the same point that is closer to you in the opposite direction. If what you are seeing is the CMB, you will only be able to see a point in it which is closer than the same point in an opposite direction. However, if r is sufficiently less than $\pi$ R, no point in the observable universe would be old enough to be the CMB emitting surface. This would then make it clear to the observer that r > $\pi$ R.

Buzz
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Another answer has explained the evidence that the observable universe does not wrap around and meet itself on the other side, in that the telltale signs do not appear to be there. However that answer only addressed a curved Universe, see below.

But how can we be confident that there is not an exact match, or that we cannot see almost all of it?

One argument is based on the assumption that there is nothing special about the present moment. The horizon of the observable universe arises because of the limited time its light has had to reach us. As time passes, more light from beyond the horizon will finally make it here and the horizon will recede accordingly. Assuming that this process is ongoing, there is no reason to suppose that we are, as yet, any where near the end of it.

Another argument is touched on in yet another answer, which hinges on the curvature of space. It is less than our ability to detect, or to put it another way, it is so nearly flat that we cannot tell the difference. If we could see almost all the universe, and it was a simple 3-sphere the way your pictured balloon is a 2-sphere, then it would be noticeably curved. But it is wrong to take the 3-sphere as the only possible shape. If you inflate a donut-shaped balloon, such as a plastic life preserver, its intrinsic (overall or average) curvature is always zero. A donut universe would always have zero curvature, no matter how much of it we could or could not see. But the topology of space (i.e. the correct solution to the equations of General Relativity) is unknown. We have no reason whatsoever to choose the sphere over the donut, indeed some models point to a hyperbolic space - which must be either infinite or with multiple "handles" like a higher-dimensional pretzel. So, despite many popular claims to the contrary, the apparent near-flatness of the Universe actually tells us very little.

In a simple toroidal Universe, geodesics are straight lines. If it were smaller than the observable scale then such lines would appear to repeat the distribution of mass/energy endlessly with a period of one Universal span. We would see the Universe beginning to repeat itself, like a stack of identical cubes. This was searched for many years ago and was found lacking, however our ability to observe great distances was limited by the technology of the day.

Since then we have mapped the CMB. But this does not help immediately, as the source of the CMB is just a 2-sphere (i.e. not a geodesic) at an arbitrary (time-dependent) and expanding distance away. Its apparent size is the boundary of the observable universe at that moment. The problem of relating such a busily-expanding sphere to the scale of a toroidal Universe is neatly illustrated in this video. (Note that the apparent reflections at the edge are an illusion, they are actually the other side coming across from the neighboring cube.) As far as I know, nobody has searched for such subtleties since that decades-old optical search (I'd love to hear if they have!).

And there are many other candidate shapes besides infinity, spheres and donuts. Each has its signature pattern of geodesics. For a good introduction see Jeffrey R. Weeks; The Shape of Space, CRC, 2002.

Guy Inchbald
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  • I don't see a donut-shaped universe discussed seriously anywhere, so I guess observations don't match that idea. In particular, a donut-shaped universe would have a positive curvature in one direction and a negative one in a perpendicular direction, and we'd see that. – user132372 Mar 16 '21 at 15:12
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    @user132372 No, the curvature of a donut is a property only of its immersion in a higher space. A familiar donut has a 2D surface immersed in 3D, and looks curved. A donut universe would be 3D and not immersed in anything. Within its intrinsic metric, the 3-donut space is everywhere flat. But other spaces are intrinsically curved. See for example Jeffrey R. Weeks; The Shape of Space, CRC, 2002. – Guy Inchbald Mar 16 '21 at 17:52
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    if the universe was a flat torus smaller than the observable universe in at least one direction, we would still see correlated circles in the CMB data, one pair for each closed spacelike geodesic shorter than the observable universe diameter. – John Dvorak Mar 16 '21 at 17:57
  • is there any other 3D manifold that's locally flat everywhere and of finite volume than a flat torus, R3 modulo a lattice? – John Dvorak Mar 16 '21 at 18:01
  • @JohnDvorak Yes, that's true about the circles. It is covered by my first paragraph. The curvature argument is a different one, and is the context in which I discuss the donut. – Guy Inchbald Mar 16 '21 at 18:03
  • @JohnDvorak Yes, there are several other flat 3-manifolds. Some are non-orientable (the Klein bottle is a flat, non-orientable 2-manifold). I recall a dodecahedral wrap-around Universe being proposed, not sure if it was flat, but it too lacked its circles in the sky. Perhaps somebody else knows? – Guy Inchbald Mar 16 '21 at 18:16
  • Good point about non-orientable surfaces. The weak force isn't preserved under parity inversion though. Charge-parity symmetry is also broken. CPT symmetry is preserved as of yet, but being able to reverse your arrow of time by going around the universe would have ... interesting consequences. You could try the double cover of a klein bottle, but that's just a torus, and a projective surface doubles into a sphere (and its flat version is just euclidean space plus infinity anyways). – John Dvorak Mar 16 '21 at 18:32
  • Orientability is perhaps a bit off-topic, but hey-ho. We have to bear in mind that a sub-space may be non-orientable, but the whole space orientable, as for example with the projective plane embedded in projective 3-space. It is mathematically possible that spacetime is orientable but 3-space is not. Guaranteed to hurt the head of your average cosmologist! – Guy Inchbald Mar 16 '21 at 19:17
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    @JohnDvorak CPT symmetry also means that going far enough and matter becomes antimatter (and mirrored, and going backward in time). Any "seam" between matter and antimatter dominant regions would be ... energetic. – Yakk Mar 17 '21 at 14:04
  • On reflection, I don't think the correlated geodesics in a flat donut would be circles. In T3 they are straight lines which appear to repeat the distribution of mass/energy endlessly with a period of one Universal span. If the Universe were smaller, we would simply see it beginning to repeat itself. This was searched for many years ago and was found lacking. – Guy Inchbald Apr 03 '21 at 07:24
  • I have updated my answer with some of the above. – Guy Inchbald Apr 03 '21 at 08:08
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We could discover that the actual universe is larger than the observable universe when there is a non-zero constant curvature everwhere. Then, this would be like standing upon the earth and seeing as far as the horizon. In the picture drawn above what we can observe would be limited by a kind of cosmological horizon.

Mozibur Ullah
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  • Hi @Mozibur Ullah: The thought you presented seems flawed: "We could discover that the actual universe is larger than the observable universe when there is a non-zero constant curvature everywhere." Can you describe a mechanism that would enable researchers to measure the universe curvature for either a small scale or a large scale. The only mechanism I can think of (not a practical one) is to chose three points in space at a distance from each other, and also adequately distant from any significant gravitation influence from matter. (More to follow.) – Buzz Jun 09 '22 at 20:38
  • The triangle formed by the three points would include the three lines which are at minimum distant between each pair of points. The sum of the angles at the three points will be greater than 180 degrees if the universe is a finite hyper-sphere. I confess my lack of confidence that such a measurement could ever be practically made. – Buzz Jun 09 '22 at 20:38
  • @Buzz: Well, I'm going on theoretic reasoning rather than practical reasoning. In practise, finding out whether the universe has constant curvature would be difficult but that doesn't negate the theoritical possibility. Despite the Planck scale being well out of reach for the forsseable future to experiment hasn't stopped string theorists investigating that scale. Also, Newton admitted the possibility of our universe being embedded in a larger one. You seem to think if you can't observe it, it must be wrong or not worth pursuing. – Mozibur Ullah Jun 22 '22 at 15:41