Early inflation, isotropization, and late time acceleration in a Bianchi type-I universe

A system of Einstein equations is solved for the Bianchi type-I metrics that describes a homogeneous and isotropic Universe. The system contains nonlinear differential equations of the second-order, which depend only on time. The method of solution is described, and the general form of the solution is found. Explicit analytical expressions are obtained in some particular cases. Numerical integration is used to describe possible solution types in the general case. The evolution of the Universe has been investigated in the presence of different types of sources, namely, a perfect fluid, a van der Waals fluid, the cosmological constant, quintessence, a Chaplygin gas, a modified quintessence, and a nonlinear spinor field. It is shown that the presence of a van der Waals fluid leads to inflation in the early stage of evolution, while the modified quintessence leads to a cyclic or oscillating Universe. It has been shown, that for some special choice of parameters the late time acceleration can be attributed to the influence of a nonlinear spinor field.