Decoherence, Correlation, and Unstable Quantum States in Semiclassical Cosmology

TL;DR

This paper explores how complex poles in quantum field theory in curved spacetime lead to damping and growth effects, expanding the initial conditions under which entropy growth, decoherence, and correlations occur in cosmology.

Contribution

It introduces a rigorous formalism using rigged Hilbert spaces to analyze complex eigenvalues, showing they can significantly influence cosmological phenomena.

Findings

Complex poles in S-matrix induce damping and growth effects.

Rigged Hilbert space formalism provides a rigorous foundation.

Damping factors expand initial conditions for entropy and decoherence.

Abstract

It is demonstrated that almost any S-matrix of quantum field theory in curved spaces posses an infinite set of complex poles (or branch cuts). These poles can be transformed into complex eigenvalues, the corresponding eigenvectors being Gamow vectors. All 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. It is known that the growth of entropy, decoherence, and the appearance of correlations, occur in the universe evolution, but only under a restricted set of initial conditions. It is proved that the damping factors allow to enlarge this set up to almost any initial conditions.