Quantum cosmology as a lattice in a box

TL;DR

This paper explores how different lattice discretizations in quantum cosmology influence effective equations, showing that a bounce at Planck density uniquely determines the volume lattice, aligning with loop quantum cosmology results.

Contribution

It introduces a lattice-based quantization scheme for scalar field cosmology, demonstrating the unique selection of the volume lattice that reproduces loop quantum cosmology equations.

Findings

A bounce at Planck density selects the volume lattice.

Effective equations match those of loop quantum cosmology.

Conditions for the validity of the effective equations are established.

Abstract

We describe quantization schemes for scalar field cosmology in the metric variables with fundamental discreteness imposed with a lattice. The variables chosen for quantization determine the lattice, and each lattice produces distinct effective equations derived from semiclassical states. We show that requiring a bounce at the Planck density uniquely selects the volume lattice and gives the same effective Friedmann equation as that obtained in loop quantum cosmology. We also present conditions for the validity of the effective equations.