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.
