Effective action and decoherence by fermions in quantum cosmology

TL;DR

This paper develops a formalism to analyze how fermions influence quantum cosmology, specifically focusing on the effective action and decoherence, and introduces a regularization method ensuring a consistent density matrix.

Contribution

It introduces a novel formalism for the one-loop no-boundary state with fermions and proposes a nonlocal Bogoliubov transformation for regularization.

Findings

Fermionic decoherence is less than bosonic decoherence.

Dimensional regularisation leads to inconsistencies in the density matrix.

A nonlocal Bogoliubov transformation ensures a consistent density matrix.

Abstract

We develop the formalism for the one-loop no-boundary state in a cosmological model with fermions. We use it to calculate the reduced density matrix for an inflaton field by tracing out the fermionic degrees of freedom, yielding both the fermionic effective action and the standard decoherence factor. We show that dimensional regularisation of ultraviolet divergences would lead to an inconsistent density matrix. Suppression of these divergences to zero is instead performed through a nonlocal Bogoliubov transformation of the fermionic variables, which leads to a consistent density matrix. The resulting degree of decoherence is less than in the case of bosonic fields.