Decoherence, correlation, and unstable quantum states in semiclassical cosmology

As almost any S-matrix of quantum theory possesses a set of complex poles (or branch cuts), it is shown using one example that this is the case in quantum field theory in curved space-time. These poles can be transformed into complex eigenvalues, the corresponding eigenvectors being Gamow vectors. This formalism, which is heuristic in ordinary Hilbert space, becomes a rigorous one within the framework of a properly chosen rigged Hilbert space. Then complex eigenvalues produce damping or growing factors and a typical two semigroups structure. It is known that the growth of entropy, decoherence, and the appearance of correlations, occur in the universe evolution, but this fact is demonstrated only under a restricted set of initial conditions. It is proved that the damping factors are mathematical tools that allow one to enlarge the set.