Hamiltonian formalism and gauge invariance for linear perturbations in inflation

A Hamiltonian treatment of gauge-invariant cosmological perturbations is presented. In this framework the gauge-invariant perturbations as well as their evolution equations are obtained with minimal work, thanks to the use of a Hamilton--Jacobi technique which takes advantage of the gauge invariance of general relativity. This formalism is applied to perturbations around spatially flat and closed Friedmann--Robertson--Walker universes with the matter being given by a scalar field, both for the gauge-invariant `scalar' perturbations and gravitational waves.