Internal symmetry in Bianchi type-I cosmologies

Using the one-parameter internal symmetry group in the Bianchi type-I spacetime for cosmological models with a perfect fluid, we show that a system of coordinates exists in the associated internal space where two scale factors become equal. We find the general solution for an anisotropic model containing a perfect fluid with constant baryotropic index and investigate the asymptotic regimes. We obtain exact solutions for a set of anisotropic fluids which includes an anisotropic stiff fluid.