Pseudo-Nambu-Goldstone inflation with ZN symmetric waterfall fields

A bstract We propose a hybrid inflation model where a pseudo-Nambu-Goldstone boson inflaton couples to N waterfall scalar fields respecting a Z N symmetry. We identify the phases for the inflation and the consequent waterfall transition, concretely, in Z 2 , Z 3 and Z 4 cases. From the Coleman-Weinberg potential for the inflaton, we show that the quadratically divergent corrections coming from the waterfall sector are cancelled due to the Z N symmetry, while the logarithmically divergent corrections are absent only for N > 2, ensuring the radiative stability of the inflaton potential. We show the parameter space for a successful inflation with the loop-corrected inflaton potential in each model and compare the results between different discrete symmetries. We further analyze the vacuum structure of the models and the reheating process due to the Z N -invariant Higgs-portal couplings for the waterfall fields. We find that the maximum temperature can be smaller than the mass of the waterfall field condensate such that the Z N symmetry is not restored after reheating and there is no domain wall problem in the models. We also comment on the possibility of multi-component dark matter from the Z N partners of the waterfall field condensate.