Isotropization by scalar field driven inflation and the cosmological quantum boundary

We derive the Wheeler-de Witt equation for the scalar field of mass m > 0 in a Bianchi-type I universe. We argue that classical trajectories become possible at h² ⩽ αt_p^-2, h being the mean Hubble value and t_p the Planck time. We feel justified to set the numerical constant α ≈︁ 1. We discuss this condition in geometrically invariant quantities and compare it with ⩽t_p^-4. The proposed quantum boundary of classical trajectories represents a 3-dimensional sphere in the 4-space of the dynamical system. Equipartition of the initial energy over field (m < m_p) and shear variables at the quantum boundary will cause inflation with a probability p of the order p = 1 - m/m_p thus, p = 1 - 10^-4 for m taken from GUT. In the course of the inflationary stage the initially arbitrarily large shear-anisotropy exponentially decays.     

Shear-free homogeneous cosmological model with heat flux

We present the condition of vanishing shear in a spatially homogeneous spacetime in terms of the Ricci rotation co-efficients corresponding to an orthonormal tetrad (ν ^α. _A η ^α) (whereν ^α is the unit vector along the time axis and _A η ^α are the three independent reciprocal group vectors). Assuming that the velocity vector can be expanded in the direction ofν ^α and any one of the _A η ^α’s it is shown that shear-free motion is possible only in case of some special Bianchi types, and these cases are studied assuming the velocity vector to be geodetic and that there may be a nonvanishing heat flux term.