If the universe is 'flat', what shape is it? [duplicate]

Question

As in the title, If the universe is considered to be 'flat', what shape is it?

Is it a disc, elliptical, square, rectangle?

Or is this still unknown as we can only study a small segment of the entire universe, known as the observable universe?

---

EDIT

This previous related question did ask the same thing. However the OP was also asking about if the universe had a centre and if everything (galaxies, dust, stuff etc...) was evenly spread out only along the outer edges.

As far as I understand it, the Big Bang that started everything off isn't a typical 'explosion' with a central point. Shapley noted that it appeared as if galaxies are moving away from the Milky Way. We now realise that it is the space between galaxies that is expanding (and that we are not the centre of the universe). in 1998, Hubble then found that the far distant galaxies appear to be moving faster than closer galaxies. This means that the rate of expansion is accelerating. This acceleration rate is known as the Hubble constant.

---

---

I feel as if the answers focussed more on his sub questions. I found the comments to be more helpful than the answers.

Can I assume that the answer is still as summarized in the related questions comments?

'We don't know?'

Astromax commented on the question,

Well, it is indeed flat, meaning Euclidean geometry can be used. Since light travels at a finite rate and the universe is not infinitely old, our 'bubble' of observable stuff within the universe would be in the shape of a sphere centered on us. However, the center of the sphere would change if you decided to move to a different part of the universe. Is the universe infinite? This is not known, since we cannot see passed our observational horizon

---

---

Accepted Answer

To be honest I didn't understand the first half of the accepted answer, and having attempted to read through the Planck paper that was linked, I can tell you that I don't know much about astronomy! I kept getting lost in all the new (to me) astonomical terms being thrown about.

I read the second half of the accepted answer to be explaining that the universe has no centre.

Gerald commented on the OP's question about the shape 'shortly' after the big bang,

Something else: Roughly resembling the 3-dimensional surface of 4-dimensional sphere, but not quite symmetrical. The precise shape is not exactly known, but probably not too much distorted, like a torus, a cube or a dodecahedron. This is still under investigation; more precise results are expected within a few years, when polarization of the CMB will be analysed

and went further to clarify the linked Planck paper

Neither the circles-in-the-sky search nor the likelihood method find evidence for a multiply-connected topology" of the Planck paper, section 6.1 means it's not a torus-like or more complex object with holes.

---

Second Answer

The more popular second answer, definitely focussed more on answering the 'does the universe have a centre?' question.

Helpful comments to my focus, Astromax commented

Also, that the universe is "infinite" is not something anyone can prove. The expansion of space-time seems to occur everywhere, but that does not mean that the universe is infinite.

Stan Lou commented

Being infinite doesn't imply having no boundary (not by itself, at least).

and ended with

Yes, a flat 3-torus is a possible geometry, but the geometry does not have to be "repetitive" in the sense of wrapping around on itself. It doesn't have to be a torus. Beyond the horizon could be a Euclidean space instead of a flat torus. Or there could be pink unicorns. Or anything else. The point of the horizon is that we don't know what's beyond it. (But if one assumes that the universe is globally isotropic, then it can't be a torus.)

And the OP summarised it by saying

So it seems like it boils down to this: It's probably flat, probably 3D. It might be edge-less, or not, we don't know. If yes, might be hypertorus and we could eventually do a round trip and came to starting point. If not, might be a ball, or anything else. We don't know, and can't imagine because of our limited scope. Is this at least remotely aligned with today's theories or are there still some gapping holes?

The comments then end, as they moved the discussion to chat.

Can I assume that the answer is still as summarized. 'We don't know?'

Answer 1

Let me clear this up first. Shape of the Universe means the curvature of the Universe. The meaning of "shape" is not the same as in "what is the shape of this object I'm holding". It doesn't mean that the Universe necessarily has a boundary or is finite in shape — it just describes its space.

The idea that the Universe is flat means that the Pythagorean theorem holds up for spatial coordinates. If you've studied non-Euclidean geometry, you'll know that a triangle can have more or less than 180°, depending on the surface its drawn on.

If the Universe is flat, we could draw a triangle between spatial coordinates, and the angles would add up to 180°. If the Universe is negatively curved, the angles would add up to less than 180°; if it were positively curved, the angles would be more than 180°.

In general relativity, mass, energy, momentum and a bunch of other properties of matter curve spacetime. Thus, most astronomers assume the curvature of space to be very close to zero, although they are not certain of its sign, meaning it may be slightly positive or negative.

So we still don't know the exact curvature of the Universe. However, most astronomers postulate that the Universe is infinite in size. This means there is no boundary or "triangular, rectangular, etc." shape. It cannot be viewed from the outside because the Universe is infinite — there's no shape for something that extends infinitely in all directions.