International Journal of Theoretical Physics

, Volume 9, Issue 2, pp 117-127

First online:

Geometry of the de-Sitter universe

  • Eric A. LordAffiliated withDepartment of Applied Mathematics, Indian Institute of Science

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By making use of the fact that the de-Sitter metric corresponds to a hyperquadric in a five-dimensional flat space, it is shown that the three Robertson-Walker metrics for empty spacetime and positive cosmological constant, corresponding to 3-space of positive, negative and zero curvative, are geometrically equivalent. The 3-spaces correspond to intersections of the hyperquadric by hyperplanes, and the time-like geodesics perpendicular to them correspond to intersections by planes, in all three cases.