On the duality in constant-roll inflation

Abstract

There is a duality in the observables $n_s$, $r$ and the inflaton potential between large and small $η_H$ for the constant-roll inflation if the slow-roll parameter $ε_H$ is negligible. In general, the duality between $η_H$ and $\barη_H$ does not hold for the background evolution of the inflation. For some particular solutions for the constant-roll inflation with $η_H$ being a constant, we find that in the small field approximation, the potential takes the quadratic form and it remains the same when the parameter $η_H$ changes to $\barη_H=3-η_H$. If the scalar field is small and the contribution of $ε_H$ is negligible, we find that there exists the logarithmic duality and the duality between large and small $η_H$ for the primordial curvature perturbation in inflationary models with the quadratic potential.