Is the universe expanding around a 4-dimensional point? This is not a duplicate to the many questions asking where the universe is expanding from; it is a follow-up to the answers to those questions.
The universe's expansion is described as comparable to dots on the surface of a balloon that is being blown up. There is no "center" of expansion from the perspective of someone on the surface; the whole space is growing larger everywhere. But in the balloon analogy, there is a center of expansion — the center of the balloon, in 3-dimensional space compared to the 2-dimensional space on the surface of the balloon. So is the universe a 3D surface on a 4D space we cannot see, and expanding from the center of that space? Or does the analogy oversimplify things?
 A: The balloon analogy, while it's a lot less wrong than even simpler models, is kind of unfortunate since it has two defects:


*

*you can immediately visualise the balloon as a two-dimensional object embedded in three-dimensional space and thus you get the question you are asking;

*the balloon is finite, and its surface is curved (intrinsically curved I mean).


Here's a model which is less easy to visualise but gets away from both of these problems.
Consider an infinite two-dimensional plane (pretty much $\mathbb{R}^2$), with a regular rectangular grid inscribed upon it (a coordinate system, if you will).  Over time this plane is expanding in the same way that the balloon is expanding, so the spacing of the grid increases over time, or equivalently any two points you were to mark on this plane would get further apart over time.
Now this model is harder to visualise than the balloon because of the whole infinite thing: how do you even think about an infinite object expanding?  And it has properties which are hard to understand: for instance two points on the plane have recession velocities proportional to their separation, and since there is no upper bound to the possible separations between points (the plane is infinite) there is also no upper bound to the recession velocities of two points.  In particular, this means (if the speed of light is finite) that the plane has a horizon: you can't see points on it further away than a certain distance because they are receding from you faster than $c$ (the universe does have such a horizon in fact).  And finally, it's also not completely right as a model because it's possible to imagine such a plane as existing into the arbitrary past, which is not the case for the universe.
But it gets away from two of the problems of the balloon analogy: there clearly is no notion of a 'centre' of this thing about which it is expanding, and neither is the plane intrinsically curved.
A: I believe the balloon analogy refers to the increase in separation of the dots across the surface of the balloon, not the increase in separation across the interior of the balloon. If you view the expansion in this sense, there is no point at the center of the expansion.
This analogy is actually a 2D representation of the expansion, where each of the dots on the balloon are existing on a curved plane that is expanding, not on the outside of a 3D volume.
A: The balloon analogy is quantumly oversimplified for the simple observation that relativity illustrates that any point cannot be defined except from another point/s, so, expansion is relative to how many points are considered and the medium.
Would you measure distance by the number of molecules between two points or the time it takes to traverse from one point to another?
In a perfect vacuum , by this standard, there is no distance between points, but on a star the "distance" is very minute, and, the same measure could encompass any amount of time.
Arguably the balloon expansion analogy has many points of reference and the variation of expansion due to pressures, materials thicknesses, densities, and heat, is a decent place to start, but what happens to it when you stick the balloon to the wall using static electrical charge? It betrays the electrical universe.
