Curvature Perturbations and non-Gaussianities from Waterfall Phase Transition during Inflation

We consider a variant of hybrid inflation where the waterfall phase transition happens during inflation. By adjusting the parameters associated with the mass of the waterfall field we arrange that the phase transition is not sharp so inflation can proceed for about 50-60 e-folds after the waterfall phase transition. We show that one can work in the limit where the quantum back-reactions are subdominant compared to the classical back-reactions. It is shown that significant amount of large scale curvature perturbations are induced from the entropy perturbations. The curvature perturbations spectral index is either blue or red depending on whether the mode of interest leaves the horizon before the phase transition or after the phase transition. This can have interesting observational consequences on CMB. The non-Gaussianity parameter $f_{NL}$ is calculated to be $\lesssim 1$ but much bigger than the slow-roll parameters.