Scale dependence of the power spectrum of the curvature perturbation determined using a numerical method in slow-roll inflation

TL;DR

This paper compares a new numerical method to the traditional Taylor expansion approach for analyzing the scale dependence of the curvature perturbation power spectrum in slow-roll inflation, revealing model-dependent differences.

Contribution

It introduces an alternative numerical method to study the $k$ dependence of the power spectrum, highlighting differences across inflation models.

Findings

1. 1.4% difference in power spectrum at k=1 Mpc between methods.

2. Nearly 10 in $ ext{chi}^2$ difference for new inflation.

3. No significant difference observed in hybrid inflation.

Abstract

The Taylor expansion method has been used to investigate the scale dependence of the power spectrum of the curvature perturbation. In the present study, an alternative numerical method is used to clarify the $k$ dependence. Although there is thought to be no large difference between these two methods, some differences arise among various inflation models. For example, at $k$ = 1 Mpc, there is a 1.4 % difference in the power spectrum, and with respect to the angular power spectrum, the difference of the value of $\chi^2$ nearly 10 occur in new inflation. However, in hybrid inflation, these differences do not occur. The time dependence of the inflationary and cosmological parameters is investigated, and differences among inflation models are clarified.