Relativity and Cosmology

    

On the Shape of the Universe

Authors: Warren D. Smith

This is the second of a 3-part series of papers on "the shape of the universe." Bright objects such as quasars are observed to be uniformly distributed on the sky-sphere. We prove a theorem that if this is true for almost every observer-location (i.e. the location of the Earth is not special in this respect) then the universe must be a "harmonic manifold." We also argue that the universe must be an orientable 3-manifold not containing any closed geodesic whose traversal causes "twist." We also discuss incompletely-convincing evidence that the universe contains a nonzero finite number of short closed geodesics passing through the Earth. If that is genuine, we prove our assumptions winnow down the possible topologies for the universe to only 3 possibilities: "flat 3-torus" and its degenerate versions with some paralelipiped sidelengths infinite.

Comments: 10 Pages. Paper on internet since 2003, now uplaoded to VIXRA for archival purposes.

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[v1] 2026-07-11 03:07:44

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