1995/03/10 by U. Bleyer, BLEYER, U., M. Rainer +1
Biochemistry, Genetics and Molecular Biology · Earth and Planetary Sciences · Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geological Studies and Exploration #Geomagnetism and Paleomagnetism Studies
paper · pdf · doi:10.48550/arxiv.gr-qc/9503019
openalex publication_date 1995/03/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We consider a multidimensional model of the universe given as a D-dimensional geometry, represented by a Riemannian manifold (M,g) with arbitrary signature of g, M= \R× M1× ⋯ × Mn, where the Mi of dimension di are Einstein spaces, compact for i>1. For Lagrangian models L(R,ϕ) on M which depend only on the Ricci curvature R and a scalar field ϕ, there exists a conformal equivalence with minimal coupling models. For certain nonminimal models we study classical solutions and their relation to solutions in the equivalent minimal coupling model. The domains of equivalence are separated by certain critical values of the scalar field ϕ. Furthermore, the coupling constant ξ of the coupling between ϕ and R is critical at both, the minimal value ξ=0 and the conformal value ξc=(D-2)/(4(D-1)). In different noncritical regions of ξ the solutions behave qualitatively different. Instability can occure only in certain ranges of ξ. This paper is dedicated to Prof. D. D. Ivanenko.