Evolution of cosmological perturbations in the universe dominated by multiple scalar fields

By the effort of several researchers, it has been recently established that the dynamical behavior of the cosmological perturbation on superhorizon scales is well approximated by that of the long wavelength limit, and that the latter can be constructed from the evolution of corresponding exactly homogeneous universe. Using these facts, we investigate the evolution of the cosmological perturbation on superhorizon scales in the universe dominated by oscillating multiple scalar fields which are generally interacting with each other, and the ratio of whose masses is incommensurable. Since the scalar fields oscillate rapidly around the local minimum of the potential, we use the action angle variables. We find that this problem can be formulated as the canonical perturbation theory in which the perturbed part appearing as the result of the expansion of the universe and the interaction of the scalar fields is bounded by the negative power of time. We show that by constructing the canonical transformations properly, the transformed Hamiltonian becomes simple enough to be solved. As a result of the investigation using the long wavelength limit and the canonical perturbation theory, under sufficiently general conditions we prove that for the adiabatic growing mode the Bardeen parameter stays constant and that for all the other modes the Bardeen parameter decays. From the viewpoint of the ergodic theory, it is discussed that, for the Bardeen parameter, the singularities appear probabilistically. This analysis serves the understanding of the evolution of the cosmological perturbations on superhorizon scales during reheating