Cosmology in Loop Quantum Gravity: symmetry reduction preserving gauge degrees of freedom

TL;DR

This paper introduces a gauge-invariant symmetry reduction method in Loop Quantum Cosmology that preserves SU(2) symmetry and some diffeomorphism invariance, connecting cosmological models more closely with Loop Quantum Gravity.

Contribution

It proposes a novel gauge-invariant reduction approach inspired by fiber bundle theory, maintaining SU(2) symmetry in cosmological models within Loop Quantum Gravity.

Findings

Preserves SU(2) gauge symmetry in cosmological sector

Identifies symmetry properties of cylindrical functions

Analyzes classical constraint algebra with symmetry considerations

Abstract

In this manuscript, we address the issue of the loss of SU(2) internal symmetry in Loop Quantum Cosmology and its relationship with Loop Quantum Gravity. Drawing inspiration from Yang-Mills theory and employing the framework of fiber bundle theory, we propose a new gauge-invariant symmetry-reduction approach. Using this method, we successfully identify a cosmological sector of General Relativity in terms of Ashtekar variables that preserves the SU(2) structure of the theory as well as part of the diffeomorphism gauge symmetry. Additionally, we analyze the properties of cylindrical functions and the classical constraint algebra, revealing that certain cylindrical functions exhibit distinctive symmetry features.