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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.
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    $\begingroup$ Hello! I have reduced the size of your images to improve readability (in my opinion). Feel free to rollback if you wish! $\endgroup$
    – Jonas
    Mar 14, 2021 at 21:22
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    $\begingroup$ 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. $\endgroup$
    – PM 2Ring
    Mar 14, 2021 at 22:02
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    $\begingroup$ If the universe is only 14 billion years old, how can it be 92 billion light years wide? $\endgroup$
    – mmesser314
    Mar 15, 2021 at 0:26
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    $\begingroup$ @DmitryGrigoryev Sorry, but I fail to see the connection between my question and cold fusion. Could you elaborate more? $\endgroup$
    – A. P.
    Mar 15, 2021 at 13:57
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    $\begingroup$ @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. $\endgroup$
    – A. P.
    Mar 15, 2021 at 14:04

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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.

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    $\begingroup$ 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. $\endgroup$
    – Eelco Hoogendoorn
    Mar 15, 2021 at 7:40
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    $\begingroup$ @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. $\endgroup$
    – benrg
    Mar 15, 2021 at 8:16
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    $\begingroup$ @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. $\endgroup$
    – Stian
    Mar 15, 2021 at 13:57
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    $\begingroup$ @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. $\endgroup$
    – benrg
    Mar 15, 2021 at 20:08
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    $\begingroup$ @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. $\endgroup$
    – benrg
    Mar 17, 2021 at 19:49
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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".
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    $\begingroup$ FWIW, we have an old question discussing SR (specifically, the twin paradox) in a cylindrical universe. physics.stackexchange.com/q/361/123208 $\endgroup$
    – PM 2Ring
    Mar 17, 2021 at 5:41
  • $\begingroup$ 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? $\endgroup$
    – oliver
    Apr 3, 2021 at 8:32
  • $\begingroup$ 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. $\endgroup$
    – Colin MacLaurin
    Apr 5, 2021 at 2:10
  • $\begingroup$ 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". $\endgroup$
    – Colin MacLaurin
    Apr 5, 2021 at 2:12
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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.

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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.

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  • $\begingroup$ 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. $\endgroup$
    – user132372
    Mar 16, 2021 at 15:12
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    $\begingroup$ @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. $\endgroup$
    – Guy Inchbald
    Mar 16, 2021 at 17:52
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    $\begingroup$ 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. $\endgroup$
    – John Dvorak
    Mar 16, 2021 at 17:57
  • $\begingroup$ is there any other 3D manifold that's locally flat everywhere and of finite volume than a flat torus, R3 modulo a lattice? $\endgroup$
    – John Dvorak
    Mar 16, 2021 at 18:01
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    $\begingroup$ @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. $\endgroup$
    – Yakk
    Mar 17, 2021 at 14:04
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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.

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  • $\begingroup$ 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.) $\endgroup$
    – Buzz
    Jun 9, 2022 at 20:38
  • $\begingroup$ 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. $\endgroup$
    – Buzz
    Jun 9, 2022 at 20:38
  • $\begingroup$ @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. $\endgroup$
    – Mozibur Ullah
    Jun 22, 2022 at 15:41

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