An Isotropization Mechanism in Bianchi I Model

We ask whether the problem on the initial conditions in Cosmology can be solved if an efficient elimination mechanism of the anisotropy was present at earlier epochs. We explore the consequences of the existence of an epoch in which the material content of the Universe was represented by an stress-energy tensor possessing anisotropic pressure which depends nonlinearly on the expansion parameter. We show that for selected candidate behaviors the associated shear pass through a maximum and vanishes asymptotically. We use the Hamiltonian formalism to define a constant of motion which enables us to classify the cosmological world-models