Is there a center of the Universe if the Universe is finite?
Solution 1
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 curvature^{1} 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.
Solution 2
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.
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Martin Asenov
Updated on March 11, 2020Comments

Martin Asenov over 3 years
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 3dimensional 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 3dimensional 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 3dimensional 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 :)

John Alexiou almost 10 yearsI guess the question could also be, "Does the universe have a barycenter"?

anna v almost 10 years@ja72 you mean in four dimensional space

anna v almost 10 yearsmartin, 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.

Kyle Kanos almost 10 yearsWe don't live in a 3D world, we live in a 4D world (that is, the surface of a 3sphere)

Martin Asenov almost 10 years@annav so basically you're saying that the Universe is infinite in the 3dimensional space?

Qmechanic almost 10 yearsRelated: physics.stackexchange.com/q/2378/2451 , physics.stackexchange.com/q/16074/2451 , physics.stackexchange.com/q/25591/2451 , and links therein.

Martin Asenov almost 10 years@Qmechanic I read all of these posts and none of them answers it in terms of what I ask. Thank you!

Admin almost 10 years@MartinAsenov Though it's good practice to provide the links yourself and explain where they fall short. And welcome to Physics.SE!

Andy aka almost 10 yearsI don't understand the muffin analogy. I'm in England and I think there may be some translation difficulties en.wikipedia.org/wiki/English_muffin

Martin Asenov almost 10 years@Andyaka just look at the Wikipedia reference I've given, at midpage and you'll understand... Yes, it is about muffins! P.S. well actually this very article talks about raisin bread, but I've seen the muffin example numerous times.


Geoffrey almost 10 yearsIn 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?

Martin Asenov almost 10 years@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 almost 10 years@ChrisWhite it would mean that the Universe does have a center, but it is in a perhaps 4dimensional space...

Admin almost 10 years@Geoffrey Indeed  I'm implicitly assuming homogeneity. I suppose arbitrary (but paracompact) manifolds can always have a nonzero mass distribution with finite integral.

Admin almost 10 years@MartinAsenov "Infinite" here means total volume (3D), surface area (2D), or length (1D). You wouldn't say a circle has infinite circumference ;) The notion you're talking about  flying off in one direction forever  is related to the universe being boundaryless. As for having a center in a higherdimensional space, there is a theorem that says you can always find such a space with at most double the number of dimensions, but GR is all about intrinsic geometry without reference to something external like that.

gregsan almost 10 years@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

Brandon Enright over 9 yearsThe 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.