  In this work we study the scalar power spectrum and the spectral index for
the Starobinsky inflationary model using the phase integral method up-to
third-order of approximation. We show that the semiclassical methods reproduce
the scalar power spectrum for the Starobinsky model with a good accuracy, and
the value of the spectral index compares favorably with observations. Also, we
compare the results with the uniform approximation method and the second-order
slow-roll approximation.
