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Assuming that the effects of trans-Planckian physics are encoded in the choice of initial conditions, mode by mode, for vacuum states at the time when its wavelength becomes equal to the scale of new physics (Plancks scale for example), we calculate the spectrum of energy densities of total relic gravitational waves from de Sitter inflation to the matter dominated universe. Our results show that the spectrum acquires corrections due to the consideration of trans-Planckian physics and these corrections depend sensitively on the vacuum state that was actually realized at the beginning of the inflation.