On the Constant-Roll Inflation with Large and Small ηH

Qing Gao,Yungui Gong,Zhu Yi

doi:10.3390/universe5110215

Qing Gao, Yungui Gong + Show 1 more

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https://doi.org/10.3390/universe5110215

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Abstract

We study the apparent duality between large and small η H for the constant-roll inflation with the second slow-roll parameter η H being a constant. In the previous studies, only the constant-roll inflationary models with small η H are found to be consistent with the observations. The apparent duality suggests that the constant-roll inflationary models with large η H may be also consistent with the observations. We find that the duality between the constant-roll inflation with large and small η H does not exist, because both the background and scalar perturbation evolutions are very different. By fitting the constant-roll inflationary models to the observations, we get − 0.016 ≤ η H ≤ − 0.0078 at the 95% C.L if we take N = 60 for the models with increasing ϵ H , in which inflation ends when ϵ H = 1 . For the models with decreasing ϵ H , we obtain 3.0135 ≤ η H ≤ 3.021 at the 68% C.L. and 3.0115 ≤ η H ≤ 3.024 at the 95% C.L.

Highlights

Inflation explains the flatness and horizon problems in standard cosmology [1,2,3,4], and the quantum fluctuations of the inflaton seed the large scale structure of the Universe and leave imprints on the cosmic microwave background radiation [5,6,7,8]
We extend the discussion of the duality between the ultra-slow-roll inflation and the slow-roll inflation with constant η H to include the effect of e H
E H is usually not negligible for the slow-roll inflation, whereas it may be negligible for the ultra-slow-roll inflation, the amplitudes (29) and (32) for both the scalar and tensor spectra will be different when the effect of e H is included, so there is no duality in the constant-roll inflation with large η H ≈ 3 and small η H ≈ 0

Summary

Introduction

Inflation explains the flatness and horizon problems in standard cosmology [1,2,3,4], and the quantum fluctuations of the inflaton seed the large scale structure of the Universe and leave imprints on the cosmic microwave background radiation [5,6,7,8] To solve problems such as the flatness, horizon, and monopole problems, the number of e-folds remaining before the end of inflation must be large enough, and it is usually taken to be N = 50 − 60 due to the uncertainties in reheating physics. We extend the discussion of the duality between the ultra-slow-roll inflation and the slow-roll inflation with constant η H to include the effect of e H.

The Constant-Roll Inflation

The Constant-Roll Models

The Duality between the Slow-Roll and the Ultra Slow-Roll Inflation

The Observational Constraints

Conclusions