An Inhomogeneous Space-Time Patching Model Based on a Nonlocal and Nonlinear Schrodinger Equation

TL;DR

This paper models inhomogeneous space-time patching in loop quantum cosmology using an integrable nonlocal nonlinear Schrödinger equation, exploring exact solutions and potential links to cosmological consistency conditions.

Contribution

It introduces a novel application of the nonlocal nonlinear Schrödinger equation to inhomogeneous LQC, analyzing its solutions and integrability properties.

Findings

Exact solutions of the NNSE are reviewed and characterized.

The integrability of the NNSE may relate to LQC consistency conditions.

The model provides a new framework for understanding inhomogeneous space-time patching.

Abstract

We consider an integrable, nonlocal and nonlinear, Schr\"odinger equation (NNSE) as a model for building space-time patchings in inhomogeneous loop quantum cosmology (LQC). We briefly review exact solutions of the NNSE, specially those obtained through "geometric equivalence" methods. Furthemore, we argue that the integrability of the NNSE could be linked to consistency conditions derived from LQC, under the assumption that the patchwork dynamics behaves as an integrable many-body system.