The spectrum of gravitational wave perturbations in the one-bubble open inflationary universe

We give the initial spectrum of quantized gravitational waves in the context of the one-bubble open inflationary universe scenario. In determining the quantum state after the bubble nucleation, we adopt the prescription to require the analyticity of positive frequency functions in half of the Euclidian extension of the background O(3, 1)-symmetric spacetime. We find the spectrum is well behaved at the infrared limit and there appears no supercurvature mode. In the thin wall approximation, the explicit form of the spectrum of gravitational wave perturbations is calculated.