Lattice Refining LQC and the Matter Hamiltonian

TL;DR

This paper investigates how different lattice refinement models in loop quantum cosmology constrain matter content by analyzing the Hamiltonian constraint with various operator properties.

Contribution

It introduces a parametrization of lattice refinement and matter Hamiltonian, analyzing their effects on wave-function solutions in loop quantum cosmology.

Findings

Constraints on parameter space (A, δ) restrict matter content.

Solutions depend on self-adjointness of Hamiltonian.

Physical restrictions limit supported matter types.

Abstract

In the context of loop quantum cosmology, we parametrise the lattice refinement by a parameter, $A$, and the matter Hamiltonian by a parameter, $\delta$. We then solve the Hamiltonian constraint for both a self-adjoint, and a non-self-adjoint Hamiltonian operator. Demanding that the solutions for the wave-functions obey certain physical restrictions, we impose constraints on the two-dimensional, $(A,\delta)$, parameter space, thereby restricting the types of matter content that can be supported by a particular lattice refinement model.