Computation of inflationary cosmological perturbations in chaotic inflationary scenarios using the phase-integral method

TL;DR

This paper applies the phase-integral approximation to compute scalar and tensor power spectra in chaotic inflation, demonstrating high accuracy and efficiency compared to numerical and traditional methods.

Contribution

It extends the phase-integral method to inflationary perturbations, providing explicit formulas up to fifth order and validating its effectiveness against other approaches.

Findings

Phase-integral approximation closely matches numerical results.

High accuracy in shape and spectral indices of power spectra.

Outperforms slow-roll and uniform approximation methods.

Abstract

The phase-integral approximation devised by Fr\"oman and Fr\"oman, is used for computing cosmological perturbations in the quadratic chaotic inflationary model. The phase-integral formulas for the scalar and tensor power spectra are explicitly obtained up to fifth order of the phase-integral approximation. We show that, the phase integral gives a very good approximation for the shape of the power spectra associated with scalar and tensor perturbations as well as the spectral indices. We find that the accuracy of the phase-integral approximation compares favorably with the numerical results and those obtained using the slow-roll and uniform approximation methods.