On the duality in constant-roll inflation

There is a duality in the observables nₛ, r and the inflaton potential between large and small ηH for the constant-roll inflation if the slow-roll parameter εH is negligible. In general, the duality between ηH and η̄H does not hold for the background evolution of the inflation. For some particular solutions for the constant-roll inflation with ηH 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 ηH changes to η̄H=3-ηH. If the scalar field is small and the contribution of εH is negligible, we find that there exists the logarithmic duality and the duality between large and small ηH for the primordial curvature perturbation in inflationary models with the quadratic potential.