# Critical Insight into the Cosmological Sector of Loop Quantum Gravity

## TL;DR

This paper critically examines Quantum Reduced Loop Gravity, identifying its inconsistencies and proposing alternative symmetry-reduction methods that better connect full Loop Quantum Gravity with Loop Quantum Cosmology.

## Contribution

It reveals flaws in previous reduction procedures and introduces improved methods for deriving cosmological models from Loop Quantum Gravity.

## Key findings

- Previous reduction methods were inconsistent, leading to overconstrained dynamics.
- Alternative symmetry-reduction procedures avoid these issues.
- New approaches better connect full theory with Loop Quantum Cosmology.

## Abstract

This article sheds new light on the problem of cosmological reduction in Loop Quantum Gravity. We critically analyze Quantum Reduced Loop Gravity -- an attempt to extract the cosmological sector of the full theory. We reconsider the reduction procedure applied to the states of the kinematical Hilbert space, developing a comparative analysis with previous efforts in the literature. We show that the constraints of the model were formerly instantiated in an inconsistent fashion, leading to an overconstrained dynamics and an ill-defined Hilbert space. We then scrutinize alternative implementations of symmetry-reduction. While remaining unaffected by the shortcomings encountered in Quantum Reduced Loop Gravity, these latter procedures bridge the gap between the full theory and former endeavors in Loop Quantum Cosmology.