# Is there a center of the Universe if the Universe is finite?

Ok, let me make myself clear. I saw all the other questions related to the question, but none of them actually asks the question the way I would put it and therefore no one answers it the way I want it answered, so here it is, I'll try to formulate it.

I perfectly understand that every single point in the Universe may be taken as the "location of the Big Bang", as it happened, because everything was in the very same place - the singularity (zero volume and infinite mass), in terms of 3-dimensional space.

As far as I understand, once all this energy was released and the Big Bang occurred, it created and started expanding what we now perceive as the 3-dimensional space of our Universe. And as far as I understand it was expanding (and still is) equally in all directions. In Wikipedia the model given is that of a bread muffin, so that we see that all reference points expand equally, given a relative center, no matter where you are in the Universe. However, this is not true if you are close to the outer surface of the muffin, and the muffin has finite size and has an edge, where the Universe ends. Given the example with the muffin, with finite Universe, there is a single point that never formed a vector of movement, ever since the Big Bang took place. And this is the center of the muffin. That would be the center of the Universe, given the possibility that it is finite.

However, if the Universe has no edge and no boundaries and is infinite in terms of 3-dimensional space, there would be no center in that space and I would be perfectly happy :) But if it is finite, as I described above, it would have a center. Or am I wrong?

Please do not mark my question as duplicate, since no one puts it that way in the other questions, I've made my research :)

• I guess the question could also be, "Does the universe have a barycenter"? – ja72 Dec 23 '13 at 16:41
• @ja72 you mean in four dimensional space – anna v Dec 23 '13 at 16:44
• martin, the thickness of the muffin is misleading. Take a perfect sphere, its surface is two dimensional and has no depth in the third dimension ( along r, the radius of the sphere). Similarly there is no width to the three dimensional universe considered in four dimensions. – anna v Dec 23 '13 at 16:46
• We don't live in a 3D world, we live in a 4D world (that is, the surface of a 3-sphere) – Kyle Kanos Dec 23 '13 at 16:47
• @annav so basically you're saying that the Universe is infinite in the 3-dimensional space? – Martin Asenov Dec 23 '13 at 16:54

You are right that a finite universe, if flat, would necessarily have a center.

However, an infinite universe has no center. An infinite muffin in 3D has a divergent volume at any point in its history, and so any point you choose will have equal (equally infinite, speaking loosely) amounts of stuff in every direction from it. All we can say is that the universe has expanded by some factor between time $t_1$ and time $t_2$.

Alternatively, a finite universe can also have no center if it is curved. In particular, if it has positive curvature1 everywhere, it loops back on itself. The analogy here is of the surface of a balloon. This is a finite 2D surface, and it has a perfectly well defined area. Still, all points are equal and none can be said to be the center. Even if the balloon is expanding, the "center" is not a part of the "universe" in this model.

The balloon analogy is used a lot in explaining cosmology, but in fact the infinite muffin describes our actual universe better. As best we can tell, our actual universe is flat and infinite.

1 Uniform positive curvature is characteristic of a (hyper)sphere. Uniform negative curvature in 2D yields a saddle.

• In principle, can't even a space with positive curvature have a barycenter? For instance, imagine the universe as the surface of a sphere and the universe is empty save for a 2D muffin. Wouldn't the center of mass of the muffin be the universe's barycenter? I agree with your conclusion if mass is uniformly distributed, but what if the localization of mass in the universe is small compared to the scale of the (finite, positive curvature) universe? – Geoffrey Dec 23 '13 at 17:24
• @ChrisWhite doesn't a finite curved Universe make an infinite Universe? :) In such a Universe, we are linearly linked to ourselves (with a 3D line), so with a fast enough ship we can depart from here in a straight line and be able to come back. In this scenario, I guess we'll be able to see the Milky Way on the sky and also we'd be able to detect patterns of repeating and/or equal portions of distributions of galaxies on the sky. But it looks like this is not the case. I guess this leads more to the conclusion that the Universe is infinite and flat, as you said. – Martin Asenov Dec 23 '13 at 17:29
• @ChrisWhite it would mean that the Universe does have a center, but it is in a perhaps 4-dimensional space... – Martin Asenov Dec 23 '13 at 17:31
• @Geoffrey Indeed - I'm implicitly assuming homogeneity. I suppose arbitrary (but paracompact) manifolds can always have a nonzero mass distribution with finite integral. – user10851 Dec 23 '13 at 20:41
• @MartinAsenov if the entire universe is sufficiently large then even if it closed, photons do not have enough time given current age of universe to lap it and produce ghost images. In other words a sufficiently large open or closed universe may appear flat in the local perspective,e.g. Spherical earth appears flat for short distances – gregsan Dec 23 '13 at 22:14

Yes you are correct Sophia. This is a major component of the standard model itself, which concludes the opposite (that space is expanding in an infinite cosmos), but the only reason a conclusion like that comes about, is because what we observe is indistinguishable from being at the centre of a finite universe that races away from precisely us, uniformly in all directions. If the absolute edge was the edge of our light cone that's exactly what would be true.

The universe is finite but doesn't have a center. It is also 2 dimensional, like riding the skin of a balloon. It doesn't have a shape. Space is curved due to gravity. There isn't any space that isn't curved. There isn't any edge to the universe. One cannot view the universe from the outside because an outside doesn't exist. Anywhere in the universe can be considered as the center. If the Big Bang happened as a typical explosion, galaxies wouldn't be moving the way they do. They would be moving the way matter would move away from a center.

• The main point I'd quibble about in this answer is that the Universe is not 2 dimensional, it's 3 (+ 1 time) dimensional. Just because the balloon inflation analogy makes use of the 2D surface of a balloon, it does not mean that inflation requires 2D space. Also, we really don't know if the Universe is finite or not. The visible universe is though. – Brandon Enright Jul 9 '14 at 18:38