2008/12/04 by Genly Leon · 2 citations
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Coupling (piping) #Dark energy #Dynamical systems theory #Einstein #Invariant (physics) #Scalar (mathematics) #Scalar field #Scaling #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/26/3/035008
published as Class.Quant.Grav.26:035008,2009 · 38 pages, 2 figures, accepted for publication in CQG
arxiv created 2008/12/04 · openalex publication_date 2009/01/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We apply dynamical system techniques to investigate cosmological models inspired in scalar–tensor theories written in the Einstein frame. We prove that if the potential and the coupling function are sufficiently smooth functions, the scalar field almost always diverges into the past. The dynamics of two important invariant sets are investigated in some detail. By assuming some regularity conditions for the potential and the coupling function, a dynamical system is constructed, well suited to investigating the dynamics where the scalar field diverges, i.e. near the initial singularity. The critical points therein are investigated and the cosmological solutions associated with them are characterized. We find that our system admits scaling solutions. Some examples are taken from the bibliography to illustrate the major results. Also we present asymptotic expansions for the cosmological solutions near the initial spacetime singularity, which extend, in a way, the previous results of other researchers.