  The effect of the initial conditions in inflation on scalar and tensor
perturbations is investigated. Formulae for the power spectra of gravitational
waves and curvature perturbations for any initial conditions in inflation are
derived, and the ratio of scalar to tensor perturbations and spectral index are
calculated. The formulation is applied to some simplified pre-inflationary
cosmological models, and the differences of the ratio and spectral index are
investigated with respect to two matching conditions. In addition, the present
power spectrum of gravitational waves is derived. The proposed formulation is
preliminarily shown to be a possible test of the appropriateness of a given
pre-inflationary model.
