Difference between open and closed Universes?

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A closed universe features positive Gaussian curvature (K = +1) and can be visualized as a sphere, while an open universe has negative Gaussian curvature (K = -1) and resembles a saddle shape. The current understanding of our universe suggests it is very close to flat, with a curvature of K = 0. The geometry of the universe is influenced by its energy and matter content, with closed universes being overdense, open universes underdense, and flat universes at critical density. Einstein's General Relativity provides the framework for understanding these geometric properties. For further details, resources like Wikipedia can offer additional insights into the shape of the universe.
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What is the difference between a closed Universe and an open Universe? Please explain in layman's terms and describe what type our Universe is.
 
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Geometrically, an open universe has a negative Gaussian curvature, K = -1. One way to visualize this geometry is as the 2D surface of a saddle in 3D space. A closed universe has positive Gaussian curvature, K = +1. A closed universe is readily visualized as a sphere. It is not currently known what the global geometry of the universe is; however, the observable universe is very close to flat, K = 0.

Einstein's General Relativity shows us that the geometry of space is determined by its energy/matter content, and so each of the above geometries also has a characteristic energy density: closed universes are overdense, open are underdense, and flat are at critical density -- they're "just right".

Wikipedia has a good discussion of these ideas: http://en.wikipedia.org/wiki/Shape_of_the_Universe

I'd recommend looking there for general questions like this first, then come to PF with more specific questions.
 

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