Study of scalar and tensor power spectra in the generalized Starobinsky inflationary model using semiclassical methods

TL;DR

This paper analyzes scalar and tensor power spectra in a generalized Starobinsky inflation model using semiclassical approximation methods, comparing results with numerical solutions to validate accuracy.

Contribution

It applies improved semiclassical methods to derive inflationary perturbation spectra in a generalized model, demonstrating their effectiveness compared to numerical integration.

Findings

Semiclassical methods accurately reproduce power spectra and spectral indices.

Results are consistent with numerical integration.

Presented in the (n_S, r) parameter space.

Abstract

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.