Gauge invariance in Loop Quantum Cosmology : Hamilton-Jacobi and   Mukhanov-Sasaki equations for scalar perturbations
  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. 
Thomas Cailleteau, Aurelien Barrau
gr-qc astro-ph.CO hep-th