On the Constant-Roll Inflation with Large and Small ηH

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.