Gauge invariant cosmological perturbations for the nonminimally coupled
  inflaton field
  We construct the gauge invariant free action for cosmological perturbations
for the nonminimally coupled inflaton field in the Jordan frame. For this the
phase space formalism is used, which keeps track of all the dynamical and
constraint fields. We perform explicit conformal transformations to demonstrate
the physical equivalence between the Jordan and Einstein frames at the level of
quadratic perturbations. We show how to generalize the formalism to the case of
a more complicated scalar sector with an internal symmetry, such as Higgs
inflation. This work represents a first step in developing gauge invariant
perturbation theory for nonminimally coupled inflationary models.
