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.
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