On the constant-roll inflation with large and small $\eta_H$

Understand

We study the seemingly duality between large and small $\eta_H$ for the constant-roll inflation with the second slow-roll parameter $\eta_H$ being a constant.

• In the previous studies, only the constant-roll inflationary models with small $\eta_H$ are found to be consistent with the observations.
• The seemingly duality suggests that the constant-roll inflationary models with large $\eta_H$ may be also consistent with the observations.
• We find that the duality between the constant-roll inflation with large and small $\eta_H$ does not exist because both the background and scalar perturbation evolutions are very different.