Anisotropy damping through quantum effects in the early universe

We consider a quantized field in a Bianchi type-I anisotropically expanding universe. A suitable expectation value of the renormalized energy-momentum tensor acts as the source of the metric in the Einstein equations. The coupled set of differential equations is numerically integrated, with the help of several approximations, in the case when the quantized field is the massless conformal scalar field. Boundary conditions are imposed at an initial time $t_0$ of the order of the Planck time, with the initial expansion rates varying over a wide range consistent with the constraints. It is found that the expansion rates tend toward isotropy and approach a radiation-filled Friedmann expansion in an interval of less than ${10}^3$ Planck times, for the full range of initial expansion rates considered.