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Dynamics of tilted Bianchi models of types III, IV, V in presence of diffusion

We investigate the three types of class B Bianchi cosmologies filled with a tilted perfect fluid undergoing velocity diffusion in a scalar field background. We consider the two most importantcases: dust and radiation. A complete numerical integration of the Einstein field equations coupled with the diffusion equations is done to demonstrate how the presence of diffusion can affect the dynamics of cosmological evolution, where the most attention is paid to changes to the late-time behaviour. We show that aside from quantitative effects, diffusion can result in significant qualitative differences. For example, the cosmologies may recollapse if diffusion is sufficiently strong, or evolve towards the de Sitter state otherwise. In constrast to the diffusionless case, radiation isotropizes in presence of diffusion, and the tilt decreases exponentially at later times: $V\sim e^{-0.25τ}$; also, we determine the decay rates of energy density, which become slower when the diffusion term is non-zero.