1995/01/12 by David Scialom, Philippe Jetzer · 3 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential equation #Einstein #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear system #Ordinary differential equation #Phase portrait #Physics #Pure mathematics #Quantum mechanics #Quartic function #Scalar (mathematics) #Scalar field #Universe #astro-ph #gr-qc
paper · pdf · doi:10.1103/physrevd.51.5698
published as Phys.Rev.D51:5698-5706,1995 · uuencoded, compressed tarfile containing a 15 pages Latex file and 2 postscipt figures. Accepted for publication on Phys. Rev. D
arxiv created 1995/01/12 · openalex publication_date 1995/05/15 · arxiv updated 2010/11/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the coupled Einstein-Klein-Gordon equations for a complex scalar field with and without a quartic self-interaction in a zero curvature Friedmann-Lemaitre universe. The equations can be written as a set of four coupled first-order nonlinear differential equations, for which we establish the phase portrait for the time evolution of the scalar field. For that purpose we find the singular points, including those lying at infinity, of the differential equations of the phase space and study the corresponding asymptotic behavior of the solutions. This knowledge is of relevance, since it provides the initial conditions needed to solve numerically the differential equations. For some singular points lying at infinity we recover the expected emergence of an inflationary stage.