what does it mean when people say the universe is flat?
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Gravity is curvature in space-time, so when physicists talk about the “shape” of the universe, they’re talking about how much gravity there is.
In a “closed”/”elliptic” universe, there’s enough gravity that all the matter and energy will eventually end up in the same place: the universe that began with a Big Bang will end in a Big Crunch. In terms of curvature, what this means is that if you shine two locally-parallel laser beams out into space, their paths will get gradually closer together and eventually cross (like two locally-parallel lines on the surface of a sphere).
In an “open”/”hyperbolic” universe, there’s so little gravity that the universe will expand faster and faster over time: the universe that began with a Big Bang will end in a Big Rip. In terms of curvature, what this means is that if you shine two locally-parallel laser beams out into space, their paths will get gradually further and further apart from one another (like two locally-parallel lines on the surface of a saddle).
A flat/”Euclidian” universe is one perfectly balanced between these two possibilities: there’s enough gravity to eventually bring the expansion of the universe arbitrarily close to a stop, but not enough to actually reverse that expansion. In terms of curvature, what this means is that if you shine two locally-parallel laser beams out into space, they will remain at a constant distance from one another indefinitely (like two parallel lines on a flat sheet of paper).
Here’s a Wikipedia picture that might help: [link](https://upload.wikimedia.org/wikipedia/commons/4/44/Comparison_of_geometries.svg) .
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