  Generalizing a previous work concerning cosmological linear tensor
perturbations, we show that the lagrangians and hamiltonians of cosmological
linear scalar and vector perturbations can be put in simple form through the
implementation of canonical transformations and redefinitions of the lapse
function, without ever using the background classical equations of motion. In
particular, if the matter content of the Universe is a perfect fluid, the
hamiltonian of scalar perturbations can be reduced, as usual, to a hamiltonian
of a scalar field with variable mass depending on background functions,
independently of the fact that these functions satisfy the background
Einstein's classical equations. These simple lagrangians and hamiltonians can
then be used in situations where the background metric is also quantized, hence
providing a substantial simplification over the direct approach originally
developed by Halliwell and Hawking.
