### What is the physical, geometric shape of the universe?

• I'm not asking about theoretical ball, vs saddle, vs flat surface which is just a metaphor with 2D space.

It's hard to say as we see very little of it, and we see them in the past because light travels for so long. But what we do know is that it is inflating (not exploding as one might thing from the "big bang" naming).

How would the universe look like, if we were to freeze it in a moment, is it likely to be a ball, or rugby ball, a cone or a sort of an irregular shape?

Is it filled throughout with galaxies, dust, black-holes, or does it live on the edges of its 3D shape, and the central part is "empty"?

Does it have a giant black hole or a star in the middle around which everything revolves?

This question is confused, because it depends on some private notion of "geometric shape" that's not made clear. The geometric shape of the universe at any moment of cosmological time is *flat*, and that's **not** "just a metaphor with 2D space." Or rather, the bit of it we see is pretty flat, so if some version of the Copernican principle is assumed, then it is shaped like standard Euclidean \$3\$-space. If it's not assumed, then no answer to large-scale geometric shape can be given.

OK, if it is shaped like "standard Euclidian 3-space", what kind of shape would it have?

Well, it is indeed flat, meaning Euclidean geometry can be used. Since light travels at a finite rate and the universe is not infinitely old, our 'bubble' of observable stuff within the universe would be in the shape of a sphere centered on us. However, the center of the sphere would change if you decided to move to a different part of the universe. Is the universe infinite? This is not known, since we cannot see passed our observational horizon.

.. Nor can we travel sufficiently far away to test this, I should add.

So, it is the limitation of our observation preventing us to even imagine the entire universe, i.e. beyond observable universe? I totally understand that observable universe is 3D space centred on us because of expansion, and that we perceive it as spherical. But can't we draw any conclusions about how the entire thing would look like? At least if we do assume it's a 3D space that's expanding, we could maybe dream up some possible shapes, unless a 4th dimension is in order, no?

@Ska: of course we can imagine different things beyond the horizon, but none of them have, or even *could* have, observational evidence for regions beyond the horizon. All we really know is that the part that we see is close to flat on average. To conclude any particular geometry beyond the horizon requires some assumption, such as the aforementioned Copernican principle.

• Gerald Correct answer

9 years ago

The overall geometry and topology of the universe has been investigated by the Planck mission. Some results are described in this paper. Final results are not yet available.

An excerpt:

We have calculated the
Bayesian likelihood for speciﬁc topological models in universes
with locally ﬂat, hyperbolic and spherical geometries, all of
which ﬁnd no evidence for a multiply-connected topology with
a fundamental domain within the last scattering surface. After
calibration on simulations, direct searches for matching circles
resulting from the intersection of the fundamental topological
domain with the surface of last scattering also give a null result
at high conﬁdence
...
Future Planck
measurement of CMB polarization will allow us to further test
models of anisotropic geometries and non-trivial topologies and
may provide more deﬁnitive conclusions, for example allowing
us to moderately extend the sensitivity to large-scale topology.

The amount of anisotropy of the universe is going to be inferred from the cosmic microwave background (CMB).

Image Credit: European Space Agency, Planck Collaboration

Higher resolved images of the CMB can be found here

The universe is roughly a 4-dimensional spacetime with the big bang as a singularity. It has no edges in the 3d space when travelling. When looking to the past the border, if you like to call it like this, is the big bang. The big bang looks to us on Earth like being in a distance of 13.81 billion (13.81e9) light years in any direction. Or being 13.81 billion years in the past as light needed that time to travel to us. But we cannot travel to that boundary, because the universe expands faster than we (or light) can travel. We had to travel into the past or faster than light to get there, no matter in which spacial direction.

There is no black hole in the center of the universe, but the big bang, if you like to call it the center of a 4-d spacetime.

The universe, when looking to a fixed age of say 13.81 billion years is filled almost homogeneously with galaxies on the very large scale. Locally galaxies are grouped to clusters and superclusters. Superclusters form kind of a 3d-net. But there aren't totally void regions. There is always some gas or some dust or some plasma or some fast-travelling cosmic rays, neutrinos, etc.

If you could stop the expansion of the universe at a given cosmic time, you would see yourself in either direction in approximately the same distance, and in approximately the same past. (Such a structure is called a 3-sphere. The surface of a 4-ball is an example of a 3-sphere. This youtube video tries to visualize a rotating 3-sphere.)

Due to the fast expansion of spacetime, light cannot travel fast enough around the universe to make this possible. Therefore we can at best look back to the big bang, no matter which direction we look. The light needs more time to travel around the universe as the universe is existing after the big bang.

Ok, to simplify to the lowest point I can imagine. Universe inflated to the size of about a solar system at the end of inflationary period, somewhere at 10 -32 seconds. Was it more of a disk or a ball shape then, or something else?

Something else: Roughly resembling the 3-dimensional surface of 4-dimensional sphere, but not quite symmetrical. The precise shape is not exactly known, but probably not too much distorted, like a torus, a cube or a dodecahedron. This is still under investigation; more precise results are expected within a few years, when polarization of the CMB will be analysed.

"Neither the circles-in-the-sky search nor the likelihood method ﬁnd evidence for a multiply-connected topology" of the Planck paper, section 6.1 means it's not a torus-like or more complex object with holes.

Explanation of simply-connected spaces: http://en.wikipedia.org/wiki/Simply_connected_space.

"A 3-sphere can be constructed topologically by "gluing" together the boundaries of a pair of 3-balls. The boundary of a 3-ball is a 2-sphere, and these two 2-spheres are to be identified. That is, imagine a pair of 3-balls of the same size, then superpose them so that their 2-spherical boundaries match, and let matching pairs of points on the pair of 2-spheres be identically equivalent to each other. In analogy with the case of the 2-sphere (see below), the gluing surface is called an equatorial sphere.", see http://en.wikipedia.org/wiki/3-sphere

Take a 2d-hyperboloid (http://en.wikipedia.org/wiki/Hyperboloid), intersect it with a horizontal plane: you get a circle (1-sphere). Now try to imagine the same with two more dimensions: Adding one dimension returns the surface (2-sphere) of a usual ball in 3d. The next dimension returns a 3-sphere, roughly the shape of a the universe at a fixed cosmic time (http://en.wikipedia.org/wiki/Cosmic_time).

The answer in your first comment is the most precise I heard so far. Now I would like to dig even more :) I understand how 3-sphere "works", but *not* how it would look like as that "gluing" would lead to some heavy distortions of the "outer" sphere, which would heavily distort the objects inside (imagine a fish in connected spherical containers), but I do get the idea. Is this then 4D geometrical shape?

The snapshot is a non-Euclidean surface of a 4D geometrical shape. The gluing leads to distortions, if you try to do it in our everyday's 3D space. It's different in 4D. It can be symmetric there without ugly distortions.

It's the analogon to gluing two discs (2-balls) at the outer circle (1-spheres) to get a 2-sphere (surface of a 3-ball), just one dimension higher. The 2-sphere is ugly in 2D, but nice in 3D.

If you have a few more hours of sparetime, I can recommend the youtube lecture about 4D: http://www.dimensions-math.org/ In English it's staring here: http://www.dimensions-math.org/Dim_reg_E.htm

...should have started; the American version still works for me: http://www.youtube.com/embed/6cpTEPT5i0A?list=PL3C690048E1531DC7

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Content dated before 7/24/2021 11:53 AM

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