Non-Gaussianities and Curvature Perturbations from Hybrid Inflation

Abstract

For the original hybrid inflation as well as the supersymmetric F-term and D-term hybrid models, we calculate the level of non-gaussianities and the power spectrum of curvature perturbations generated during the waterfall, taking into account the contribution of entropic modes. We focus on the regime of mild waterfall, in which inflation continues for more than about 60 e-folds N during the waterfall. We find that the associated f_nl parameter goes typically from f_nl \simeq -1 / N_exit in the regime with N >> 60, where N_exit is the number of e-folds between the time of Hubble exit of a pivot scale and the end of inflation, down to f_nl ~-0.3 when N \gtrsim 60, i.e. much smaller in magnitude than the current bound from Planck. Considering only the adiabatic perturbations, the power spectrum is red, with a spectral index n_s = 1 - 4 / N_exit, in the case N >> 60, whereas in the case N \gtrsim 60, it increases up to unity. Including the contribution of entropic modes does not change the observable predictions in the first case. However, in the second case, they are a relevant source for the power spectrum of curvature perturbations, of which the amplitude increases by several orders of magnitudes and can lead to black hole formation. We conclude that due to the important contribution of entropic modes, the parameter space leading to a mild waterfall phase is excluded by CMB observations for all the considered models.