# Shape of the known universe?

## Main Question or Discussion Point

Does anyone know what shape the universe is? I.e. a sphere, or an eliptical sphere? and is that the observed shape of the shape after relativity calculation?

The universe does not have a 3 dimensional shape per se. Rather it has a 4-dimensional topology. Depending on the value of the cosmological constant it may be flat or curved on very large scales (it is currently believed to be very very close to being flat due to inflation).

It doesn't seem like, from a topological perspective, we'd be able to differentiate a smooth, spherically shaped universe from a smooth, flat universe.

I understand the bit about the effect of the cosmological constant, but what perplexes me is why we think the universe is flat versus spherical (although I admit I have no idea what a beyond-3d sphere would look like), especially if there are long distance curves.

How is this different from a purely topologic view of the Earth - where it can be drawn either flat or on a globe, but the spherical globe is the actual shape?

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LURCH
The fourth dimension being time, a four-dimensionally spherical universe would keep coming back to the same point in time over and over (repeating its entire history). So, a 4-D sphere looks alot like a loping video.

"The fourth dimension being time, a four-dimensionally spherical universe would keep coming back to the same point in time over and over (repeating its entire history). So, a 4-D sphere looks alot like a loping video."

I don't see how this would be the case given a dynamic universe. If the universe is expanding, then it would be impossible for the universe to return to a previous time frame for the same reason that if I leave New York and fly around the world back to New York, it would not be the same place when I returned as when I left.

But stepping back from all of that, is it even correct to talk about the 4d universe having a shape? How can time have a particular shape? The time period from ancient Rome to the present day isn't in the form of a shape. Maybe I'm being too literal though. If the question "what is the shape of a 4d universe" is asked in the same way as "which direction is the arrow of time pointing" maybe shape is just a metaphor.

In that case though, we'd still be able to identify necessary components of a 4d universe, right?

It'd have to be roughly uniform - since the progression of universal time (whatever that is) moves in all directions equally. And if that is the case, the universe would have to have more "spherical" properties than linear ones, right - because the universe would be expanding from one point outward in all directions, thus negating any sort of right-to-left or left-to-right time progression from oldest to youngest.

But it seems reasonable that there is little but a semantic difference between an expanding "flat" universe and an expanding "spherical" universe.

jhe1984 said:
It doesn't seem like, from a topological perspective, we'd be able to differentiate a smooth, spherically shaped universe from a smooth, flat universe.

I understand the bit about the effect of the cosmological constant, but what perplexes me is why we think the universe is flat versus spherical (although I admit I have no idea what a beyond-3d sphere would look like), especially if there are long distance curves.

How is this different from a purely topologic view of the Earth - where it can be drawn either flat or on a globe, but the spherical globe is the actual shape?
I think you're mixing 4D and 3D here and it doesn't work. Its likely that in a 3D sense, the matter forms a sphere, assuming roughly uniform expansion in all directions. If the universe is topologically flat on large scales, this just means that if you head off in one direction, you keep going in that way, you don't wind up back where you started (anyone more familiar with differential geometry or topology can feel free to chime in and correct me if i'm mistaken).