  By means of the Green's function method, we computed the spectral indices up
to third order in the slow-roll approximation for a general scalar-tensor
theory in both the Einstein and Jordan frames. Using quantities which are
invariant under the conformal rescaling of the metric and transform as scalar
functions under the reparametrization of the scalar field, we showed that the
frames are equivalent up to this order due to the underlying assumptions.
Nevertheless, care must be taken when defining the number of $e$-folds.
