Abstract
The one-loop effective potential for a massive, quartically self-interacting scalar field nonminimally coupled to gravity is calculated in a Bianchi type-I universe with a small anisotropy. The kernel of a Schr\odinger-like equation is found, and its coincidence limit used to obtain the determinant of the Klein-Gordon operator. The effects of the anisotropy on symmetry breaking and the viability of new inflation are considered, with the value of the coupling to gravity $\ensuremath{\xi}$ found to play a crucial role. Classically, a positive $\ensuremath{\xi}$ restores symmetry and helps inflation, while the opposite effects are found for negative coupling. Quantum effects depend on the value of $\ensuremath{\xi}$ relative to the conformal value ⅙. For small coupling, the quantum term may dominate, which tends to restore symmetry and aid inflation. A comparison to previous work is made, and differences discussed.
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