On the constant-roll inflation

TL;DR

This paper examines the limitations of the Bessel function approximation in calculating primordial power spectra during constant-roll inflation, highlighting the need for more accurate methods when the slow-roll parameter is not small.

Contribution

It compares numerical and analytical methods for power spectrum calculation in constant-roll inflation, emphasizing the inaccuracies of the Bessel approximation in certain regimes.

Findings

Bessel approximation can significantly differ from numerical results on super-horizon scales.

The discrepancy is notable when the slow-roll parameter $ta_H$ is not small.

More precise calculation methods are necessary for accurate primordial spectrum estimation.

Abstract

The primordial power spectra of scalar and tensor perturbations during slow-roll inflation are usually calculated with the method of Bessel function approximation. For constant-roll or ultra slow-roll inflation, the method of Bessel function approximation may be invalid. We compare the numerical results with the analytical results derived from the Bessel function approximation, and we find that they differ significantly on super-horizon scales if the constant slow-roll parameter $\eta_H$ is not small. More accurate method is needed for calculating the primordial power spectrum for constant-roll inflation.