Lattice loop quantum cosmology: scalar perturbations

TL;DR

This paper develops a lattice-based approach to scalar perturbations in loop quantum cosmology, ensuring anomaly-free quantum constraints and deriving effective equations consistent with prior holonomy corrections.

Contribution

It introduces a lattice framework for scalar perturbations in loop quantum cosmology with anomaly-free constraints and derives effective equations matching previous results.

Findings

Quantum theory is anomaly-free with commuting constraints.

Effective equations incorporate leading quantum gravity corrections.

Lattice approach reproduces known holonomy-corrected dynamics.

Abstract

We study the scalar modes of linear perturbations in loop quantum cosmology. This is done on a lattice where each cell is taken to be homogeneous and isotropic and can be quantized via standard homogeneous loop quantum cosmology techniques. The appropriate interactions between nearby cells are included in the Hamiltonian in order to obtain the correct physics. It is shown that the quantum theory is anomaly-free: the scalar and diffeomorphism constraint operators weakly commute with the Hamiltonian. Finally, the effective theory encoding the leading order quantum gravity corrections is derived and is shown to give the same holonomy-corrected effective equations that have been obtained in previous studies.