Numerical Techniques in Loop Quantum Cosmology

TL;DR

This paper reviews numerical methods used to solve the quantum Hamiltonian constraint in loop quantum cosmology, focusing on difference equations, stability, semi-classical limits, and lattice refinement.

Contribution

It provides a comprehensive overview of numerical techniques and key issues in solving LQC constraint equations, highlighting differences from classical approaches.

Findings

Difference equations replace differential equations in LQC

Stability and semi-classical limits are critical for solutions

Lattice refinement impacts the behavior of quantum cosmological models

Abstract

In this article, we review the use of numerical techniques to obtain solutions for the quantum Hamiltonian constraint in loop quantum cosmology (LQC). First, we summarize the basic features of LQC, and describe features of the constraint equations to solve - generically, these are difference (rather than differential) equations. Important issues such as differing quantization methods, stability of the solutions, the semi-classical limit, and the relevance of lattice refinement in the difference equations are discussed. Finally, the cosmological models already considered in the literature are listed, along with typical features in these models and open issues.