Bianchi type I universe with viscous fluid and a ΛΛ term: A qualitative analysis

The nature of cosmological solutions for a homogeneous, anisotropic Universe given by a Bianchi type-I (BI) model in the presence of a cosmological constant ΛΛ is investigated by taking into account dissipative process due to viscosity. The system in question is thoroughly studied both analytically and numerically. It is shown that the viscosity, as well as the ΛΛ term, exhibit essential influence on the nature of the solutions. In particular a positive ΛΛ gives rise to an ever-expanding Universe, whereas a suitable choice of initial conditions plus a negative ΛΛ can result in a singularity-free oscillatory mode of expansion. For some special cases it is possible to obtain oscillations in the exponential mode of expansion of the BI model even with a positive ΛΛ, where oscillations arise by virtue of viscosity.