Primordial perturbations in Type III hilltop inflation models

We analytically compute the power spectrum of primordial curvature perturbations in Type III hilltop inflation models under the slow-roll approximation. The model parameters are constrained using current Cosmic Microwave Background (CMB) data. The curvature perturbations that exit the horizon at small scales show sufficiently large amplitudes to produce primordial black holes (PBHs). We then consider the quantum one-loop corrections in these models from both the self-interaction of the inflaton and its interaction with the waterfall field. We show the loop corrections in both cases for 60 e-folds of inflation are negligible, ensuring the tree-level results are reliable within the chosen parameter regime.