Quantization of semiclassical gravitation theory in anisotropic spacetime

The renormalized effective action of a free scalar field propagating in the Bianchi type I spacetime is examined. As it contains higher-order derivatives of the metric the Hamiltonian structure of the theory will be changed. Thus, to obtain the self-consistent solution of the semiclassical gravity theory the method of iterative reduction is used to reduce it to a second-order equation. We solve the reduced equation and see that the space anisotropy, which will be smoothed out during the evolution of Universe, may play important role in the dynamics of early Universe. To investigate the behavior of space anisotropy in the early Universe we then quantize the corresponding minisuperspace. The associated Wheeler-DeWitt equation is solved in the WKB approximation and, from the solution, it is seen that the most probable state of the Bianchi type I spacetime is that with a small anisotropy.