Scalaron from R2-gravity as a heavy field

We study a model of inflation in which a scalar field chi is non-minimally coupled to Starobinsky's R-2 gravity. After transforming it to the Einstein frame, a new scalar field, the scalaron phi, will appear and couple to chi with a nontrivial field metric, while chi acquires a positive mass via the non-minimal coupling. Initially inflation occurs along the phi direction with chi trapped near its origin by this induced mass. After phi crosses a critical value, it starts rolling down rapidly and proceeds to damped oscillations around an effective local minimum determined by the value of chi, while inflation still continues, driven by the chi field at this second stage where the effect of the non-minimal coupling becomes negligible. The presence of the damped oscillations during the transition from the first to second stage of inflation causes enhancement and oscillation features in the power spectrum of the curvature perturbation. Assuming that the oscillations may be treated perturbatively, we calculate these features by using the delta N formalism, and discuss its observational implications to large scale CMB anomalies or primordial black hole formation, depending on the scale of the features.