  By using the newtonian gauge, we re-confirm that, as in the minimal case, the
re-scaled Mukhanov-Sasaki variable is conserved leading to a constraint
equation for the Newtonian potential. However, conversely to the minimal case,
in Horndeski theories, the super-horizon Newtonian potential can potentially
grow to very large values after inflation exit. If that happens, inflationary
predictability is lost during the oscillating period. When this does not
happen, the perturbations generated during inflation can be standardly related
to the CMB, if the theory chosen is minimal at low energies. As a concrete
example, we analytically and numerically discuss the new Higgs inflationary
case. There, the Inflaton is the Higgs boson that is non-minimally kinetically
coupled to gravity. During the high-energy part of the post-inflationary
oscillations, the system is anisotropic and the Newtonian potential is largely
amplified. Thanks to the smallness of today's amplitude of curvature
perturbations, however, the system stays in the linear regime, so that
inflationary predictions are not lost. At low energies, when the system relaxes
to the minimal case, the anisotropies disappear and the Newtonian potential
converges to a constant value. We show that the constant value to which the
Newtonian potential converges is related to the frozen part of curvature
perturbations during inflation, precisely like in the minimal case.
