On Divergence of Decoherence Factor in Quantum Cosmology

TL;DR

This paper investigates the divergence of the decoherence factor in quantum cosmology, analyzing conditions for convergence and implications for the quantum-to-classical transition in a universe model.

Contribution

It provides a detailed analysis of the divergence of the decoherence factor and establishes constraints for its convergence in quantum cosmology.

Findings

Decoherence factor can diverge, indicating perfect decoherence and failure of classical correlation.

Constraints for the convergence of the decoherence factor are derived.

The divergence depends on the system/environment splitting arbitrariness.

Abstract

To discuss the quantum to classical transition in quantum cosmology, we study the decoherence factor and the peak of the Wigner function, which respectively represent the degree of decoherence and the degree to which the classical motion of the Universe is defined, in a Robertson-Walker universe model coupled with a scalar field. It is known that the decoherence factor is divergent in some cases. This implies that perfect decoherence occurs, and classical correlation criterion fails. In this paper we discuss the divergence of the decoherence factor in some detail and obtain the constraints for decoherence factor to be convergent, making use of the arbitrariness defining the reduced density matrix. The result is discussed in connection with the arbitrariness of {\it system/environment} splitting.