2020/01/31 by David Fajman, Gernot Heißel, Maciej Maliborski
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conjecture #Cosmology and Gravitation Theories #Field (mathematics) #Logarithm #Metric (unit) #Noncommutative and Quantum Gravity Theories #Nonlinear system #Scalar (mathematics) #Scalar field #Spacetime #Type (biology) #gr-qc #math-ph #math.MP
paper · pdf · doi:10.1088/1361-6382/ab8c97
25 pages, 6 figures. To be published in Classical and Qunatum Gravity - IOP. The new version includes small changes motivated by the helpful comments of the referees. In particular, we now give more information on the asymptotics of the scalar field
openalex created_date 2020/01/10 · arxiv created 2020/04/06 · openalex publication_date 2020/04/23 · arxiv updated 2020/08/26 · openalex updated_date 2026/08/06
Abstract We analyse spatially homogenous cosmological models of locally rotationally symmetric Bianchi type III with a massive scalar field as matter model. Our main result concerns the future asymptotics of these spacetimes and gives the dominant time behaviour of the metric and the scalar field for all solutions for late times. This metric is forever expanding in all directions, however, in one spatial direction only at a logarithmic rate, while at a power-law rate in the other two. Although the energy density goes to zero, it is matter dominated in the sense that the metric components differ qualitatively from the corresponding vacuum future asymptotics. Our results rely on a conjecture for which we give strong analytical and numerical support. For this we apply methods from the theory of averaging in nonlinear dynamical systems. This allows us to control the oscillations entering the system through the scalar field by the Klein–Gordon equation in a perturbative approach.