Feasibility of a Unitary Quantum Dynamics in the Gowdy $T^3$ Cosmological Model

TL;DR

This paper investigates the fundamental reasons behind the failure of unitarity in the quantum dynamics of polarized Gowdy T^3 cosmologies and explores how close the model can be approximated by unitary transformations.

Contribution

It provides a detailed analysis of the roots of non-unitarity in Gowdy T^3 models and shows how modifications to the Hamiltonian affect unitarity, offering insights into potential approximations.

Findings

Unitarity fails due to specific sensitivities in the Hamiltonian.

Modifications can bring the model arbitrarily close to unitarity.

The failure of unitarity is highly sensitive to the Hamiltonian's form.

Abstract

It has been pointed out that it is impossible to obtain a unitary implementation of the dynamics for the polarized Gowdy $T^{3}$ cosmologies in an otherwise satisfactory, nonperturbative canonical quantization proposed for these spacetimes. By introducing suitable techniques to deal with deparametrized models in cosmology that possess an explicit time dependence (as it is the case for the toroidal Gowdy model), we present in this paper a detailed analysis about the roots of this failure of unitarity. We investigate the impediments to a unitary implementation of the evolution by considering modifications to the dynamics. These modifications may be regarded as perturbations. We show in a precise manner why and where unitary implementability fails in our system, and prove that the obstructions are extremely sensitive to modifications in the Hamiltonian that dictates the time evolution of the symmetry-reduced model. We are able to characterize to a certain extent how far the model is from unitarity. Moreover, we demonstrate that the dynamics can actually be approximated as much as one wants by means of unitary transformations.