Is the universe round or flat?

[GeorgeDishman]

Does the universe's flatness mean that non Euclidean geometry isn't important in physics?

It is flat on average over very large scales. Locally it has curvature, we call that gravity and without it the Earth wouldn't orbit the Sun so yes, non-Euclidean geometry remains important.

 

[urodoc]

flat or round, spherical or trumpet - does the universe have a thickness ?
is it centrally thicker like 2 cymbals placed together ? how do we know if it is symmetrical ? is it getting thinner in the centre as it expands peripherally? why should it be symmetrical - was the singularity that preceded the big bang spinning in order to give it such symmetry ?

 

[Mark M]

flat or round, spherical or trumpet - does the universe have a thickness ?
is it centrally thicker like 2 cymbals placed together ? how do we know if it is symmetrical ? is it getting thinner in the centre as it expands peripherally? why should it be symmetrical - was the singularity that preceded the big bang spinning in order to give it such symmetry ?

Urodoc, when people speak of the shape of the universe, they are speaking of a natural curvature that spacetime has over large distances. The universe doesn't have a 'shape' in the literal since, as it has no boundary.

Keep in mind that the expansion of the universe occurs everywhere at once. There is no center or boundary. Also, the universe is symmetrical because it underwent a period called 'inflation' in it's very early history. Inflation was an enormous expansion, of unimaginable magnitudes. It essentially functioned to 'iron out' any inhomogeneities in the early universe.

 

[George Jones]

It is flat on average over very large scales. Locally it has curvature, we call that gravity and without it the Earth wouldn't orbit the Sun so yes, non-Euclidean geometry remains important.

when people speak of the shape of the universe, they are speaking of a natural curvature that spacetime has over large distances.

When people talk about the curvature of the universe, they mean the curvature of space, not the curvature of spacetime. For example, in a flat FRW universe, space is Euclidean and flat, while spacetime is neither flat nor Euclidean.