Recursive Stochastic Effects in Valley Hybrid Inflation

Hybrid Inflation is a two-field model where inflation ends by a tachyonic instability, the duration of which is determined by stochastic effects and has important observational implications. Making use of the recursive approach to the stochastic formalism presented in Ref. [1], these effects are consistently computed. Through an analysis of back-reaction, this method is shown to converge in the valley but points toward an (expected) instability in the waterfall. It is further shown that quasi-stationarity of the auxiliary field distribution breaks down in the case of a short-lived waterfall. It is found that the typical dispersion of the waterfall field at the critical point is then diminished, thus increasing the duration of the waterfall phase and jeopardizing the possibility of a short transition. Finally, it is found that stochastic effects worsen the blue tilt of the curvature perturbations by an order one factor when compared with the usual slow-roll contribution.