  The one-loop renormalized effective potentials for the massive $\phi^4$
theory on the spatially homogeneous models of Bianchi type I and
Kantowski-Sachs type are evaluated. It is used to see how the quantum field
affects the cosmological phase transition in the anisotropic spacetimes. For
reasons of the mathematical technique it is assumed that the spacetimes are
slowly varying or have specially metric forms. We obtain the analytic results
and present detailed discussions about the quantum field corrections to the
symmetry breaking or symmetry restoration in the model spacetimes.

General Relativity and Quantum Cosmology;High Energy Physics - Theory