Computation of the Power Spectrum in Chaotic $1/4 \lambda \phi^4$ Inflation

TL;DR

This paper applies the phase-integral approximation to compute the scalar power spectrum in quartic chaotic inflation, demonstrating high accuracy compared to numerical and other analytical methods.

Contribution

It explicitly derives the phase-integral formulas up to fifth order for the power spectrum in this inflationary model, enhancing analytical precision.

Findings

Phase-integral approximation matches numerical results closely.

Fifth-order formulas improve accuracy over lower orders.

Method outperforms slow-roll and uniform approximations.

Abstract

The phase-integral approximation devised by Fr\"oman and Fr\"oman, is used for computing cosmological perturbations in the quartic chaotic inflationary model. The phase-integral formulas for the scalar power spectrum are explicitly obtained up to fifth order of the phase-integral approximation. As in previous reports [1-3], we point out 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.