Coleman-Weinberg Symmetry Breaking in a Bianchi I Universe

The one-loop eeective potential for a massive, quartically self-interacting scalar eld nonminimally coupled to gravity is calculated in a Bianchi I universe with small anisotropy. The kernel of a Schrr odinger-like equation is found, and its coincidence limit used to obtain the determinant of the Klein-Gordon operator. The eeects of the anisotropy on symmetry breaking and the viability of new innation are considered, with the value of the coupling to gravity found to play a crucial role. Classically, a positive restores symmetry and helps innation, while opposite eeects are found for negative coupling. Quantum eeects depend on the value of relative to the conformal value 1/6. For small coupling, the quantum term may dominate, which tends to restore symmetry and aid innation.