On the nonexistence of a Lobachevsky geometry model of an isotropic and homogeneous universe

Authors:
Michal Křížek;Jana Pradlová
Affiliations:
Mathematical Institute, Academy of Sciences, Zitná 25, CZ-115 67 Prague 1, Czech Republic;Department of Mathematics, Faculty of Applied Sciences, University of West Bohemia, Univerzitní 22, CZ-306 14 Pilsen, Czech Republic
Venue:
Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
Year:
2003

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Abstract

According to the Einstein cosmological principle, our universe is homogeneous and isotropic, i.e. its curvature is constant at any point and in any direction. On large scales, when all local irregularities are ignored, this assumption has been confirmed by astronomers. We show that there is no reasonable hyperbolic geometry model in R4 of a homogeneous and isotropic universe for a fixed time which would fit the cosmological principle. Hence, there does not exist any model in R4 of an isotropic universe which would be represented by a three-dimensional hypersurface with the Lobachevsky geometry.