2002/12/31 by Marek Szydlowski, Marek Szydłowski, Adam Krawiec
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Curvature #De Sitter universe #Flatness (cosmology) #Galaxies: Formation, Evolution, Phenomena #Geometry #Hamiltonian (control theory) #Initial singularity #Isotropy #Mathematical analysis #Mathematical physics #Mathematics #Phase space #Physics #Quantum mechanics #Singularity #Speed of light (cellular automaton) #Universe #gr-qc
paper · pdf · doi:10.1103/physrevd.68.063511
published as Phys.Rev. D68 (2003) 063511 · 18 pages, 5 figures, RevTeX4; final version to appear in PRD
arxiv created 2003/07/23 · openalex publication_date 2003/09/26 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The methods of dynamical systems have been used to study homogeneous and isotropic cosmological models with a varying speed of light (VSL). We propose two methods for the reduction of the dynamics to the form of planar Hamiltonian dynamical systems for models with a time dependent equation of state. The solutions are analyzed on two-dimensional phase space in the variables (x,\mathrmx\ifmmode \else \.\fi) where x is a function of a scale factor a. Then we show how the horizon problem may be solved on some evolutional paths. It is shown that the models with a negative curvature overcome the horizon and flatness problems. The presented method of reduction can be adapted to the analysis of the dynamics of the Universe with the general form of the equation of state p=\ensuremathγ(a)\ensuremathε. This is demonstrated using as an example the dynamics of VSL models filled with a noninteracting fluid. We demonstrate a new type of evolution near the initial singularity caused by a varying speed of light. Singularity-free oscillating universes are also admitted for a positive cosmological constant. We consider a quantum VSL Friedmann-Robertson-Walker closed model with radiation and show that the highest tunneling rate occurs for a constant velocity of light if c(a)\ensuremath∝an and \ensuremath-1<n<~0. It is also proved that the class of models considered is structurally unstable for the case of n<0.