Study of scalar and tensor power spectra in the generalized Starobinsky
  inflationary model using semiclassical methods
  In this work we solved the equation of scalar and tensor perturbations for
the generalized Starobinsky inflationary model using the improved uniform
approximation method and the phase-integral method up to third-order in
deviation. We compare our results with the numerical integration. We have
obtained that both semiclassical methods reproduce the scalar power spectra
$P_{S,T}$, the scalar spectral index $n_S$, and the tensor-to-scalar ratio $r$.
Also we present our results in the $(n_S,r)$ plane.
