Abstract

The effective gravitational equations induced by quantum effects of a scalar field in the Bianchi type IX space-time are derived in the present work. The curvature tensor components and their combinations are calculated in the Bianchi type IX spaces. To estimate a one-loop effective action, the asymptotic Schwinger-DeWitt perturbative formula with consideration of terms up to the second order is used. Quantum corrections involve the fourth-order derivative of the metric; as a consequence, the background gravitational action also includes terms up to the fourth-order derivatives of the metric.

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