Semiclassical gravitation and quantization for the Bianchi type-I universe with large anisotropy

We use a perturbative method to evaluate the effective action of a free scalar field propagating in Bianchi type-I spacetime with large space anisotropy. The zeta-function regularization method is used to evaluate the action to second order in the Schwinger perturbative formula. As the quantum corrections contain a fourth derivative in the metric we apply the method of iterative reduction to reduce it to second-order form to obtain a self-consistent solution of the semiclassical gravity theory. The reduced Einstein equation shows that the space anisotropy, which will be smoothed out during the evolution of universe, may play an important role in the dynamics of early universe. We quantize the corresponding minisuperspace model to investigate the behavior of the space anisotropy in the initial epoch. From the wave function of the Wheeler-DeWitt equation we see that the probability for the Bianchi type-I spacetime with large anisotropy is less than that with small anisotropy.