  In this work we calculate the tensor power spectrum and the tensor-to-scalar
ratio r within the frame of the Starobinsky inflationary model using the
improved uniform approximation method and the third-order phase-integral
method. We compare our results with those obtained with numerical integration
and the slow-roll approximation to second order. We have obtained consistent
values of r using the different approximations, and r is inside the interval
reported by observations.
