  The one-loop effective potential for $\phi ^4$ theory on a Bianchi type-I
universe is evaluated in the adiabatic approximation. It is used to see the
quantum-field effects on symmetry breaking and restoration in anisotropic
spacetimes. The results show that the fate of symmetry will not be changed in
the cases of conformal coupling or a vanishing scale curvature, and only for
some suitable values of scalar-gravitational coupling could the symmetry be
radiatively broken or restored.
