Time dependence of cosmological and inflationary parameters in slow-roll inflation

TL;DR

This paper investigates how cosmological and inflationary parameters evolve over time during the last 60 e-folds of slow-roll inflation, using numerical methods to improve accuracy over traditional approximations.

Contribution

It introduces a numerical approach to analyze the time dependence of inflationary parameters, providing more precise results than traditional analytical approximations.

Findings

Hubble parameter and spectral index decrease during the last 60 e-folds

Numerical power spectrum differs from traditional methods in overall amplitude

Numerical, Bessel, and Taylor methods show consistent k-dependent spectra

Abstract

The dependence of cosmological and inflationary parameters on time during the last 60 e-folds in inflation is investigated using a slow-roll inflation model. The time dependence of the inflaton field is calculated for the case of chaotic inflation by a numerical method rather than the familiar approximations. It is found that the Hubble parameter and the spectral index decrease in the last 60 e-folds. The dependence of the power spectrum of the curvature perturbation on the size perturbation k is calculated numerically, and it is shown that the overall constant value of the power spectrum thus determined differs from that given by the familiar method. However, the k-dependent spectra of the numerical calculation, the Bessel function approximation, and the familiar Taylor expansion are all found to be consistent.