This Quanta Magazine article (below) is a helpful visual recap of whether the cosmos is “flat” or not. Does the cosmic landscape of stars and galaxies extend / expand in all directions like an endless piece of paper? Or another “flat” geometry – “by cutting a chunk out of Euclidean space and gluing it together.”
Or does space curve in some way in higher dimensions? (“By gluing up a suitable chunk” of a 3-sphere, for example.)
What’s the evidence against a flat universe? The paths of “straight” lines and angles in triangles might tell.
• Quanta Magazine > “What Is the Geometry of the Universe?” by Erica Klarreich (March 16, 2020)
There was a time, after all, when everyone thought the Earth was flat, because our planet’s curvature was too subtle to detect and a spherical Earth was unfathomable.
We can ask two separate but interrelated questions about the shape of the universe. One is about its geometry: the fine-grained local measurements of things like angles and areas. The other is about its topology: how these local pieces are stitched together into an overarching shape.