While it is clear that the earth is sort of round, rather like a baseball that has absorbed too many home runs, to the best of our understanding, the universe is flat.
By flat, we do not mean that you could walk to the edge and fall off, like pre Columbian notions of the earth. Rather, we mean that despite all of Mr. Einstein’s distortions of spacetime, at the largest scales we can manage, the universe follows the geometry of Euclid drawn flat in the sand.
If the old Greek guys had done their geometry on a sphere or a saddle (ignoring the impracticality of sand on these shapes for the sake of argument), the sum of angles in a triangle would not be 180 degrees. The same is true for any surface not perfectly flat.
Astronomers measure the distances to stars and such and can calculate the angles of triangles connecting them. Always 180 degrees.
This seems as peculiar as energy being a function of the speed of light squared.
Nevertheless, the flatness of the universe has become as embedded in our cosmology as pre Columbian notions of the earth. The critical density to achieve flatness is the cornerstone of many equations.
If you could fall off the edge of the universe, would you have found the multiverse?