Coleman-Weinberg symmetry breaking in an anisotropic spacetime

The Coleman-Weinberg mechanism of symmetry breaking in a Bianchi type-I universe is investigated. The one-loop effective potential for a ${\phi }^4$ theory and for scalar electrodynamics is calculated by the $\zeta$-function method. The result indicates that the symmetry of the theory will be restored in the highly anisotropic, cold, early universe, irrespective of the coupling between the scalar field and the spacetime curvature scalar. This mechanism of the phase transition explains the isotropy of our universe.