  The method of a conformal transformation is applied to a general class of
single field inflation models with non-minimal coupling to gravity and
non-standard kinetic terms, in order to reduce the cosmological perturbative
calculation to the conventional minimal coupling case to all orders in
perturbation theory. Our analysis is made simple by the fact that all
perturbation variables in the comoving gauge are conformally invariant to all
orders. The structure of the vacuum, on which cosmological correlation
functions are evaluated, is also discussed. We show how quantization in the
Jordan frame for non-minimally coupled inflation models can be equivalently
implemented in the Einstein frame. It is thereafter argued that the general
N-point cosmological correlation functions (of the curvature perturbation) are
independent of the conformal frame.
