EXPANSION OF EFFECTIVE ACTION IN CURVED SPACETIME WITH LARGE ANISOTROPY

A simple perturbative method is used to evaluate the renormalized effe ctive action of a free scalar field in the Bianchi type I spacetime wi th large anisotropy. With the help of the zeta function regularization method the action is expanded to the second order in the Schwinger pe rturbative formula. We apply the method of iterative reduction to redu ce the generalized Einstein equation to a second-order equation to obt ain the self-consistent solution of the semiclassical gravity theory. The reduced equation shows that the space anisotropy, which will be sm oothed out during the evolution of Universe, may play an important rol e in the dynamics of early Universe. We thus quantize the correspondin g minisuperspace model to investigate the behavior of space anisotropy in the early Universe. From the wavefunction of the Wheeler-De Witt e quation we see that the state probability of the Bianchi type I spacet ime with large anisotropy is less than that with a small anisotropy. ( C) 1998 Elsevier Science B.V. All rights reserved.