Unitarity and ultraviolet regularity in cosmology

TL;DR

This paper investigates the unitarity of quantum field dynamics in curved, time-dependent spacetimes, proposing a generalized unitarity concept that ensures consistent quantum evolution in cosmological models.

Contribution

It introduces a generalized unitarity framework for quantum fields in curved spacetimes, extending the standard notion to include cosmological and more general globally hyperbolic models.

Findings

Standard unitarity does not hold in time-dependent spacetimes.

A generalized unitarity concept is established for quantum fields.

The approach enables consistent Schrödinger picture formulation in cosmology.

Abstract

Quantum field theory in curved space-times is a well developed area in mathematical physics which has had important phenomenological applications to the very early universe. However, it is not commonly appreciated that on time dependent space-times ---including the simplest cosmological models--- dynamics of quantum fields is not unitary in the standard sense. This issue is first explained with an explicit example and it is then shown that a generalized notion of unitarity does hold. The generalized notion allows one to correctly pass to the Schr\"odinger picture starting from the Heisenberg picture used in the textbook treatments. Finally, we indicate how these considerations can be extended from simple cosmological models to general globally hyperbolic space-times