Hamiltonian approach to 2nd order gauge invariant cosmological
  perturbations
  In view of growing interest in tensor modes and their possible detection, we
clarify the definition of tensor modes up to 2nd order in perturbation theory
within the Hamiltonian formalism. Like in gauge theory, in cosmology the
Hamiltonian is a suitable and consistent approach to reduce the gauge degrees
of freedom. In this paper we employ the Faddeev-Jackiw method of Hamiltonian
reduction. An appropriate set of gauge invariant variables that describe the
dynamical degrees of freedom may be obtained by suitable canonical
transformations in the phase space. We derive a set of gauge invariant
variables up to 2nd order in perturbation expansion and for the first time we
reduce the 3rd order action without adding gauge fixing terms. In particular,
we are able to show the relation between the uniform-$\phi$ and Newtonian
slicings, and study the difference in the definition of tensor modes in these
two slicings.
