  We have considered the perturbation equations governing the growth of
fluctuations in generalized scalar tensor theory during inflation. we have
found that the scalar metric perturbations at very early times are negligible
compared with the scalar field perturbation, just like general relativity. At
sufficiently early times, when $q/a\gg H$, we have obtained the metric and
scalar field perturbation in the form of WKB solutions up to an undetermined
coefficient. Then we have quantized the scalar fluctuations and expanded the
metric and the scalar field perturbations with the help of annihilation and
creation operators of the scalar field perturbation. The standard commutation
relations of annihilation and creation operators fix the unknown coefficient.
Going over to the gauge invariant quantities which are conserved beyond the
horizon, we have obtained the initial condition of the generalized
Mukhanov-Sasaki equation. And a similar procedure is performed for the case of
tensor metric perturbation.
