Generalized Friedman equations on the bundle with the Lie group SU(2) and the cosmological constant
DOI:
https://doi.org/10.32603/2071-2340-2026-2-5-19Keywords:
Kaluza--Klein cosmology, Supernova Ia, MathematicaAbstract
In this paper, we consider the spacetime to be a direct product M4 × SU(2) of the Friedmann— Lemaitre— Robertson— Walker space M4 and the Lie group SU(2) (3-sphere) equipped with a bi-invariant metric. In this spacetime, the Riemannian curvature of the Lie group SU(2) gives a nonzero contribution to the scalar curvature of the manifold M4×SU(2) and this contribution exactly corresponds to the cosmological constant Λ. The generalized Friedmann equations for this spacetime are reduced in the present work to a form suitable for numerical integration. The computer algebra system Mathematica was used to solve these differential equations. The behavior of these solutions is examined depending on cosmological parameters such as matter density, dark energy density (cosmological constant), and curvature. Cosmological parameters were estimated by means of a nonlinear regression problem based on Type Ia supernova data. The derived constraints on the model parameters are compatible with the standard cosmological model. Nevertheless, non-zero spatial curvature is necessary to account for the "early galaxies" phenomenon.
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Copyright (c) 2026 Victor Krym
This work is licensed under a Creative Commons Attribution 4.0 International License.
This work is licensed under a Creative Commons Attribution 4.0 International License.
