Numerical solutions to lattice-refined models in loop quantum cosmology

TL;DR

This paper introduces a numerical method for solving quantum evolution equations in lattice-refined loop quantum cosmology models, demonstrating its effectiveness through analysis of a Schwarzschild interior geometry model.

Contribution

The paper presents a new efficient numerical technique for lattice-refined models in loop quantum cosmology, enabling accurate and robust solutions.

Findings

Numerical solutions align with von Neumann stability analysis

Method is accurate and robust for complex models

Applied successfully to Schwarzschild interior geometry

Abstract

In this article, we develop an intuitive and efficient, numerical technique to solve the quantum evolution equation of generic lattice-refined models in loop quantum cosmology. As an application of this method, we extensively study the solutions of the recently introduced, lattice-refined anisotropic model of the Schwarzschild interior geometry. Our calculations suggest that the results obtained from the approach are accurate, robust and are in complete agreement with the expectations from the von Neumann stability analysis of the model.