Symmetry behavior in the Einstein universe: effect of spacetime curvature and arbitrary field coupling
For the investigation of the effect of spacetime curvature and arbitrary field coupling on symmetry restoration, we have computed by zeta-function regularization the one-loop effective potential for a self-interacting scalar field arbitrarily coupled to a static Robertson-Walker universe. The classical contribution of curvature can restore broken symmetries for a wide range of parameters from conformal to near-minimal couplings whereas the quantum contribution is important only for a small range of values near the minimal coupling point. The symmetry behavior of the two extremes is found to be very different.
D. J. O'Connor, B. L. Hu, and T. C. Shen, "Symmetry behavior in the Einstein universe: effect of spacetime curvature and arbitrary field coupling," Phys. Lett. 130B, 31 (1983).