# 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. Jan 4 '14 at 13:01
• OK, if it is shaped like "standard Euclidian 3-space", what kind of shape would it have?
– Ska
Jan 4 '14 at 16:12
• 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. Jan 4 '14 at 16:52
• .. Nor can we travel sufficiently far away to test this, I should add. Jan 4 '14 at 16:58
• Possible duplicate of What is in the center of the universe? Jul 29 '16 at 8:01

Ok, maybe you have some misconceptions.

The Universe has no center at all. It looks the same from avaery point, to wherever you look to. It is approximatedly as follows:

This image represents a very large scale box on our universe on current time (not on perceived time, based on received light). Of course, it is just a computer simulation. Each dot represents a cluster of galaxies.

So you need to imagine an infinite tridimensional space filled with filament-like structures like these. And infinite means it has no bounds, so it has no "external" shape. No ball, rugby-ball nor cone there. Also not irregular external shape, just infinite. Any of these shapes have a 2D boundary on a 3D space, but the universe has no boundary.

• Where is this simulation from and where in it would be a Milky Way approximately? From this model it looks very much like cube-like shape, not infinite at all, not at this point in time at least. Maybe it can be considered infinite based on the speed of inflation: curious.astro.cornell.edu/question.php?number=575, but at any one given frozen point it is not. And although from the outside there is no spacetime, so no shape, we still "know" that galaxies put together, no matter how huge, are put together in a certain pattern, forming a certain "shape".
– Ska
Jan 4 '14 at 0:54
• Being infinite doesn't imply having no boundary (not by itself, at least). @Ska: if you were looking for the distribution of galaxies, you should have asked for that directly. Jan 4 '14 at 13:16
• By the way, this box that people use to run simulations in is periodic (particles which go off one side appear on the other). @Ska The fact that they've chosen a cube to represent a chunk of the universe which they care to learn about is irrelevant. Also, that the universe is "infinite" is not something anyone can prove. The expansion of space-time seems to occur everywhere, but that does not mean that the universe is infinite. Jan 4 '14 at 16:57
• @Ska: your assumption is mistaken; space does not have and never had a boundary in any cosmological model consistent with what we know of gravity (the caveat is that our knowledge of gravity in the very early universe is completely uncertain). However, there was (and is) a horizon that defines the limit of possible observation, as astromax said above. But there's nothing physically special there; every point in space has its own horizon. Jan 4 '14 at 20:07
• @Ska: Yes, a flat $3$-torus is a possible geometry, but the geometry does not have to be "repetitive" in the sense of wrapping around on itself. It doesn't have to be a torus. Beyond the horizon could be a Euclidean space instead of a flat torus. Or there could be pink unicorns. Or anything else. The point of the horizon is that we don't know what's beyond it. (But if one assumes that the universe is globally isotropic, then it can't be a torus.) Jan 4 '14 at 22:03

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?
– Ska
Jan 8 '14 at 22:45
• 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. Jan 8 '14 at 23:37
• "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. Jan 8 '14 at 23:49
• Explanation of simply-connected spaces: en.wikipedia.org/wiki/Simply_connected_space. Jan 9 '14 at 0:41
• ...should have started; the American version still works for me: youtube.com/embed/6cpTEPT5i0A?list=PL3C690048E1531DC7 Jan 11 '14 at 1:01