An observer's position at the center of the universe isn't substantiated by the CMB or quasars, no.

Wherever you look from is as good as the center, and if you care for details, it's self-substantiating.

I think the flaw here is assuming the universe is spherical like the earth, which it very probably isn't.

Beyond the surface of the "sphere" is unknown and unknowable. It can never be known. Sorry.

Honestly, we have no conception of the shape of the universe, and we're all seriously putting the cart before the horse.

But if it were a ball, and we were inside the ball, we'd be so small no one would ever find us in infinite years, except by chance. We are virtually invisible.

It is generally assumed that it is not meaningful to talk about the center of the universe because all locations could equally claim to be the center, like any location on the surface of a sphere. — TheArchitectOfTheGods

The reason for saying that there is no center of the universe is the observation/assumption of symmetry, or homogeneity of cosmos. If, on a large scale, the universe everywhere has the same properties, then there is no reason to single out any place as the "center." For this to be the case the topology does not need to be spherical. Think of a blank sheet, for instance, extended infinitely in all directions. It is featureless, and therefore does not have an obvious center.

As for a "hall of mirrors" universe, that is indeed a live hypothesis, which astronomers are trying to test, but so far there is no definitive evidence either way. This has nothing to do with the Galilean principle, but rather with the fact that we simply don't know what the topology of space is, other than that it is pretty flat around where we are. So we try to find whatever clues we can.

I have a horse. You got a cart? :]

We're certainly not invisible. We're just.. an island.

Maybe my original post was a little clumsy, but I was not actually suggesting that the topology of the universe could be spherical. Rather, that in order for the universe to be infinite, its topology would likely be closed.

It is difficult for me to imagine an infinite white sheet. But it is easy to imagine infinity on a closed surface. This infinity is not real infinity, but is caused by recursiveness, meaning if I travel long enough in one direction, I will eventually come back to the same point that I started from. Therefore I made an analogy to the 2-dimensional surface of a sphere.

Now of course we cannot visualize a closed topography that has a 3-dimensional 'surface', but for me recursiveness would in absence of better theories be the best explanation for the finiteness vs. infiniteness problem of the universe.

I don't think that our esthetic preferences, habits of thought or limits of imagination should dictate what we believe about the world. On the other hand, evidence for a closed universe may be easier to discover, and if so then we should certainly go for the low-hanging fruit first.

Most of the time, when weighing competing cosmological theories against each other, we have to settle for the one that accounts for the available evidence as well as any other and has the practical advantage of being simpler than the rest - which is why, when pressed to make a choice, cosmologists pick the flat, infinite universe as their default.

No doubt, finding the cosmic equivalent of an image of the back of your head out in the distance would be a smoking-gun evidence that we can usually only dream of. The evidence in favor of a closed universe that has been put forward so far is much more subtle and controversial.

So far as I can recall astronomers have searched for the same object they see in one part of the sky in the opposite part of the sky, but have not found any corresponding object.

Certainly the analogy of a finite universe as the surface of a sphere is a good one, with the actual space of the universe being a 3 dimensional surface in a 4 dimensional hyperspace.

If I am just briefly allowed to continue the analogy, the flat earth problem was of course a tremendous puzzle to our ancestors. A flat earth theory lacked aesthetics, it is 'ugly' to have to conceptualize either 'edges of the world' or an infinite flat surface, because it poses more questions than it gives answers, it is an incomplete theory. Although the theory corresponded to the world it as it was perceived, to prove the apparent obvious that earth was indeed flat was practically impossible. Since the theory was false, it could never be empirically confirmed by experiment or observation, and was eventually disproven by observation of another kind.

Whereas the explanation of the sphere effortlessly and beautifully explained the problem even before it was shown to be true and the flat earth theory was disproven. So the model that turned out to correspond to reality was not the more simple, but the more aesthetically appealing, and it was also the only of the two that ever had a chance of practical scientific confirmation.

So far goes the analogy, whether it is valid to extrapolate this reasoning to another dimension, can of course be debated, and I trust that science will eventually provide better explanations to the topology of the universe than we have currently.

Whereas the explanation of the sphere effortlessly and beautifully explained the problem even before it was shown to be true and the flat earth theory was disproven. — TheArchitectOfTheGods

Ancient cosmogonies were not overly constrained by empirical observations, the way (we like to think) our modern cosmology is; ancient people gave a lot of leeway to their metaphysical and religious imaginations. If people back then were really more comfortable with the concept of a spherical earth, what would have stopped them from conceiving it that way? And yet all the ancient cosmogonies that we know about posited a more-or-less flat earth, sometimes surrounded by water (not all ancient cultures thought this out all the way through, and some didn't bother with cosmogony at all). Spherical earth theory, at least as it developed in ancient Greece, was on the contrary prompted by empirical observations that did not sit well with a flat earth, such as the phenomenon of the receding horizon.

But this is not to say that present day cosmology is guided strictly by empirical considerations. Even setting aside the fact that what we think of as modern scientific empiricism is a philosophy in itself, science edges beyond empiricism when it comes to theory selection at its more speculative reaches. The principle of "naturalness" in particle physics and cosmology is a prime example of that.

I am not an expert, but I don't have the impression that the shape of the universe is a particularly common issue on which to make a philosophical stand. Check out Stoeger, Ellis and Kirchner's Multiverses and Cosmology: Philosophical Issues though, where they do just that, arguing (unpersuasively, IMHO) for a finite universe.

By the way, to confound things even more, the universe doesn't even have to be a hypersphere to have a closed topology. It can have zero intrinsic curvature everywhere, just like a flat sheet, and yet have a closed, finite topology of a hypertorus, or something even more exotic.

Thanks for the paper recommendation, I will check that out! Appreciated

To anyone who is interested, I found this great programme which goes really quite deep into the subject matter of discussing possible geometries of the cosmos
https://www.youtube.com/watch?v=tJevBNQsKtU