State refinements and coarse graining in a full theory embedding of loop quantum cosmology

TL;DR

This paper explores how to refine and coarse grain quantum states in loop quantum cosmology, ensuring the effective dynamics remain consistent, using symmetry assumptions and a simplified model to bridge different quantum descriptions.

Contribution

It demonstrates how to perform state refinements and coarse graining in a full theory embedding of loop quantum cosmology under symmetry assumptions, ensuring dynamic invariance.

Findings

States can be refined and coarse grained while preserving dynamics

A scaling property of quantum states is necessary for invariance

Solutions extend to the full theory in a specific approximation

Abstract

Bridging between descriptions involving few large and many small quantum numbers is the main open problem in loop quantum gravity. In other words, one would like to be able to represent the same physical system in terms of a few "coarse"' quantum numbers, while the effective dynamics at the coarse level should agree with the one induced by a description involving many small quantum numbers. Efforts to understand this relationship face the problem of the enormous computational complexity involved in evolving a generic state containing many quanta. In a cosmological context however, certain symmetry assumptions on the quantum states allow to simplify the problem. In this paper, we will show how quantum states describing a spatially flat homogeneous and isotropic universe can be refined and coarse grained. Invariance of the dynamics of the coarse observables is shown to require a certain scaling property (familiar from loop quantum cosmology) of the quantum states if no running of parameters is taken into account. The involved states are solutions to the Hamiltonian constraint when terms coming from spatial derivatives are neglected, i.e. one works in the approximation of non-interacting FRW patches. The technical means to arrive at this result are a version of loop quantum gravity based on variables inspired by loop quantum cosmology, as well as an exact solution to the quantum dynamics of loop quantum cosmology which extends to the full theory in the chosen approximation.