On the oscillations and future asymptotics of locally rotationally symmetric Bianchi type III cosmologies with a massive scalar field

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.

arXiv comment25 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

References in corpus (13)

• The Einstein-Vlasov System/Kinetic Theory
• Asymptotic self-similarity breaking at late times in cosmology
• Cosmological models and centre manifold theory
• The global nonlinear stability of Minkowski space for self-gravitating massive fields. The wave-Klein-Gordon model
• Dynamics of spatially homogeneous locally rotationally symmetric solutions of the Einstein-Vlasov equations
• Global dynamics and inflationary center manifold and slow-roll approximants
• Bianchi Cosmologies with Anisotropic Matter: Locally Rotationally Symmetric Models
• Late-time asymptotic dynamics of Bianchi VIII cosmologies
• Non-tilted Bianchi VII_0 models - the radiation fluid
• Future stability of the $1+3$ Milne model for Einstein-Klein-Gordon system
• Global dynamics of Yang-Mills field and perfect-fluid Robertson-Walker cosmologies
• Isotropization of Slowly Expanding Spacetimes
• Kantowski-Sachs cosmology with Vlasov matter

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• Averaging Generalized Scalar Field Cosmologies I: Locally Rotationally Symmetric Bianchi III and open Friedmann-Lemaître-Robertson-Walker models
• Averaging Generalized Scalar Field Cosmologies II: Locally Rotationally Symmetric Bianchi I and flat Friedmann-Lemaître-Robertson-Walker models
• Scalar field evolution at background and perturbation levels for a broad class of potentials
• Future attractors of Bianchi types II and V cosmologies with massless Vlasov matter
• Averaging method and coherence applied to Rabi oscillations in a two-level system