Gauge invariance in Loop Quantum Cosmology : Hamilton-Jacobi and Mukhanov-Sasaki equations for scalar perturbations

TL;DR

This paper explores gauge invariance and the equations of motion for scalar perturbations in Loop Quantum Cosmology, extending Hamilton-Jacobi methods and analyzing corrections to better understand early universe dynamics.

Contribution

It develops a detailed Hamilton-Jacobi framework for gauge-invariant scalar perturbations in Loop Quantum Cosmology, including holonomy and inverse-volume corrections.

Findings

Gauge-invariant observables are constructed and their equations of motion are derived.

The approach clarifies the role of quantum corrections in scalar perturbations.

The methods unify Hamiltonian and Lagrangian perspectives.

Abstract

Gauge invariance of scalar perturbations is studied together with the associated equations of motion. Extending methods developed in the framework of hamiltonian General Relativity, the Hamilton-Jacobi equation is investigated into the details in Loop Quantum Cosmology. The gauge-invariant observables are built and their equations of motions are reviewed both in Hamiltonian and Lagrangian approaches. This method is applied to scalar perturbations with either holonomy or inverse-volume corrections.