A Nonlinear Model of a Quantum Minisuperspace System with Back Reaction

TL;DR

This paper models quantum evolution in a simplified minisuperspace system and compares it to a more complex system to develop criteria for when simplified models provide useful insights into the full quantum dynamics, with implications for quantum gravity.

Contribution

It introduces a comparison framework between simplified and extended minisuperspace models to assess their validity in quantum gravity research.

Findings

Develops criteria for the usefulness of minisuperspace models

Demonstrates the comparison approach with a λφ^4 theory

Provides insights into quantum gravity modeling

Abstract

We consider the quantum evolution of the space-independent mode of a $\lambda {\phi}^4$ theory as a minisuperspace in the space of all $\phi$. The motion of the wave packet in the minisuperspace is then compared to the motion of a wave packet in a larger minisuperspace consisting of the original minisuperspace plus one space-dependent mode. By comparing the motion of the two packets we develop criteria that tell us when the quantum evolution in the space-independent minisuperspace gives us useful information about the true evolution in the larger minisuperspace. These criteria serve as a toy model for similar(but much more complex) criteria that will tell us whether or when quantized gravitational minisuperspaces can possibly give any useful information about quantum gravity.