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

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. *The authors acknowledge support of the Austrian Science Fund (FWF) through the Project Geometric transport equations and the non-vacuum Einstein flow (P 29900-N27). The second author also thanks the Hausdorff Research Institute for Mathematics for funding and hospitality in the Junior Trimester Program 'Kinetic Theory' during the final research and write up phase of this project. Finally, we are grateful to the referees for their detailed and helpful comments and suggestions.