Frame-dependence of higher-order inflationary observables in
  scalar-tensor theories
  In the context of scalar-tensor theories of gravity we compute the
third-order corrected spectral indices in the slow-roll approximation. The
calculation is carried out by employing the Green's function method for scalar
and tensor perturbations in both the Einstein and Jordan frames. Then, using
the interrelations between the Hubble slow-roll parameters in the two frames we
find that the frames are equivalent up to third order. Since the Hubble
slow-roll parameters are related to the potential slow-roll parameters, we
express the observables in terms of the latter which are manifestly invariant.
Nevertheless, the same inflaton excursion leads to different predictions in the
two frames since the definition of the number of e-folds differs. To illustrate
this effect we consider a nonminimal inflationary model and find that the
difference in the predictions grows with the nonminimal coupling and it can
actually be larger than the difference between the first and third order
results for the observables. Finally, we demonstrate the effect of various
end-of-inflation conditions on the observables. These effects will become
important for the analyses of inflationary models in view of the improved
sensitivity of future experiments.
