# Cosmological principle: can there be a center of the universe "outside" the universe?

I've been watching youtube videos about the cosmological principle. I understand that the expansion of the universe is not concentric (around a specific point in space). The balloon example helped me understand this better: if the universe were the surface of an inflating balloon, every point on the surface could be expanding without any "center" of expansion on the balloon surface.

However, we as a 3-dimensional observer could see that there is an actual center of the balloon which doesn't reside on the surface but rather inside it, and from which everything is expanding out uniformly (It's a little hard for me to define the true center of the balloon, but I hope you get the intuition).

Now I'm thinking, maybe there is such a true center of the universe which resides not on the universe itself, but on some higher-dimensional space, of which the universe is a subspace.

I know there must be bulks of research about this but I can't seem to find the right keywords to search for it. So I'd appreciate any explanations/resources on this idea!

This kind of confusion arises when you take the visualizations too seriously. By definition, the universe is all there is, so there can't be anything outside it.

Now, let's come to your balloon example. The problem here is, that in order to visualize a curved 2-dimensional space (for example a sphere), we have to embed it into a three-dimensional space. But this is only done for visualization! Mathematically, only the surface of the balloon exists, not the space around it. You can define a curved space, without defining any higher-dimensional space into which it is curved.

Only the surface exists, so there is no such thing as a center.

Now, you could imagine a theory where what we call the universe is actually just a part of a higher-dimensional space. People are doing that. String Theory is such an example. So let's imagine that our universe is actually a sphere inside a higher-dimensional space. Now, the sphere really does have a center. Would this violate the cosmological principle? No, because the cosmological principle only applies to our universe, which by definition is only the surface of the sphere.

Another thing: There are actually 3 possible shapes the universe can have that satisfy the cosmological principle. A closed sphere (the one you mentioned), a flat space or an open hyperboloid. And all current data that we have suggests that it is actually flat.

• Thanks so much for the explanation! Yes, I do tend to take the analogies too seriously sometimes, unfortunately! But when I heard the balloon example, I couldn't help wondering about this idea and to what extent one can push it forward. You already referred to string theory and now I have a thread to follow: string cosmology! Could you kindly give me some other examples or keywords of the researches in cosmology that take into account this idea of the universe as a subspace of a higher-dimensional space? Commented May 23, 2023 at 15:50
• A balanced and perfect answer by Lenard Kesselmann, which leads to biased conclusion by aminak. This example speaks to the awkward situation when experts and amateurs try to communicate. Commented May 23, 2023 at 17:42
• @MadMax I can see your criticism (and was expecting it tbh) as I'm not even an amateur in the field and am just pursuing this subject out of curiosity. Thanks for the input! Commented May 23, 2023 at 19:25
• I (weak on formalism) may be relying excessively on visualizations (the eyes being extensions of the brain, etc.), but my own impression from various cosmological models (mostly relativistic) has been that the flatness of space seems reliably extant only because of limitations on the energy available to magnify the visibility of its particulate contents (whose motions reflect wavelike effects) without collapsing the "particles" into black holes whose interiors remain inherently (and perhaps permanently) unobservable. This would remain unverifiable, but consistent with an infinite spacetime. Commented May 24, 2023 at 3:17
• @aminak Relevant keywords would be "brane" or "brane cosmology". It's short for membrane and denotes this concept of a "universe" inside a higher-dimensional space. Branes arise quite naturally in String Theory. The idea is explained beautifully in the book "The science of Interstellar" by Kip Thorne. Commented May 24, 2023 at 15:29