B Geometries of the Universe: What are the Most Accepted Models?

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The most widely accepted geometries of the universe include Euclidean geometry, which describes flat space, and non-Euclidean geometries like elliptical (Riemann) geometry, which accounts for curved space. Current models suggest the universe is expanding with spatial slices of constant comoving time that are predominantly flat. However, measurements indicate a slight possibility that the universe could also exhibit a 3-sphere or open hyperbolic geometry, both with a very large radius of curvature. This means that while the universe appears flat, there is still room for alternative geometrical interpretations. Understanding these geometries is crucial for comprehending the overall structure and evolution of the universe.
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What are the most widely accepted geometries of the universe?
 
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Euclidean geometry (that's the one where we learn about area of shapes, sectors, etc.). Then you have the non-Euclidean geometries like elliptical geometry (Riemann geometry), which describes curved space.
 
Allen_Wolf said:
What are the most widely accepted geometries of the universe?

I'm not sure what you mean by this. We have one current best-fit model for the spacetime geometry of the universe: it's an expanding universe with spatial slices of constant comoving time that are flat (Euclidean). The error bars in measurements still allow a small chance that the spatial geometry of slices of constant comoving time is a 3-sphere or an open "3-hyperbolic" geometry, either way with an extremely large radius of curvature (i.e., very close to flat). Is that what you're asking about?
 

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