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We analyse spatially homogenous cosmological models of locally rotationallysymmetric Bianchi type III with a massive scalar field as matter model. Ourmain result concerns the future asymptotics of these spacetimes and gives thedominant time behaviour of the metric and the scalar field for all solutionsfor late times. This metric is forever expanding in all directions, however inone spatial direction only at a logarithmic rate, while at a power-law rate inthe other two. Although the energy density goes to zero, it is matter dominatedin the sense that the metric components differ qualitatively from thecorresponding vacuum future asymptotics.  Our results rely on a conjecture for which we give strong analytical andnumerical support. For this we apply methods from the theory of averaging innonlinear dynamical systems. This allows us to control the oscillationsentering the system through the scalar field by the Klein-Gordon equation in aperturbative approach.

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