  In previous works, it was shown that the Lagrangians and Hamiltonians of
cosmological linear scalar, vector and tensor perturbations of homogeneous and
isotropic space-times with flat spatial sections containing a perfect fluid can
be put in a simple form through the implementation of canonical transformations
and redefinitions of the lapse function, without ever using the background
classical equations of motion. In this paper, we generalize this result to
general fluids, which includes entropy perturbations, and to arbitrary
spacelike hyper-surfaces through a new method together with the Faddeev-Jackiw
procedure for the constraint reduction. A simple second order Hamiltonian
involving the Mukhanov-Sasaki variable is obtained, again without ever using
the background equations of motion.
