The relation between the size of the universe and its curvature

Details The relation between the size of the universe and its curvature The relation between the size of the universe and its curvature

Nov 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980zhetf..79.1617b&link_type=abstract

Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki, vol. 79, Nov. 1980, p. 1617-1628. In Russian.

Mathematics

Logic

3

Astronomical Models, Cosmology, Riemann Manifold, Universe, Curvature, Diameters, Dimensional Analysis, Relativity, Universal Time

Scientific paper

Closed three-dimensional Riemann spaces with a curvature that is the same in all directions are examined. It is such that the topological structure of any such space uniquely determines the sign of its curvature H and also the limitations of its size. Let R be the radius of curvature and D the diameter of the space, i.e., the distance between the two farthest points. Then for H greater than 0, D is greater than 0.326 R; for H less than 0, D is greater than 1.128 of the absolute value of R; for H = 0, the value of D is arbitrary. A model of a plane world is proposed which is closed and has the shape of a three-dimensional torus, all the parameters of which (size, rate of expansion, mean density of matter, etc.) can be expressed in terms of atomic constants and universal time.

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