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The effect of the initial condition of inflation on the power spectra ofscalar and tensor perturbations is estimated assuming a slow-roll inflationmodel. By defining a more general initial state in inflation particularproperties of the power spectrum such as oscillation can be revealed. Thebehavior of the power spectrum is shown to exhibit a step-like variation withrespect to finite inflation length in cases of both radiation- and scalarmatter-dominated pre-inflation. The power spectrum is shown to oscillate in theradiation-dominated case. The effects of such a power spectrum on the TT and TEpower spectra are examined for three typical slow-roll inflation models; asmall-field model, a large field model, and a hybrid model, considering bothpre-inflation models. It is found that the discrepancies between WMAP3 data andthe Lambda CDM model, such as suppression of the spectrum at l=2, may beexplained to a certain extent by the finite length of inflation for inflationof close to 60 e-folds. The small-field inflation model with scalarmatter-dominated pre-inflation provides the best fit to the WMAP3 data amongthe models considered. Relatively large changes in the angular TT powerspectrum occur in response to small changes in inflation length in theradiation-dominated pre-inflation models, and half cases do not fit well withthe observed data. This behavior is considered to be attributable to theoscillatory behavior of the power spectrum. The scalar matter-dominated case isthus preferred to the radiation-dominated case of pre-inflation, independent ofthe length of inflation.

Effect of initial condition of inflation on power and angular power spectra in finite slow-roll inflation