Non-Gaussianities and curvature perturbations from hybrid inflation

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) similar or equal to -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) similar to -0.3 when N greater than or similar to 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 greater than or similar to 60, it increases up to unity. Including the contribution of entropic modes does not change observable predictions in the first case, and the spectral index is too low for this regime to be viable. In the second case, entropic modes are a relevant source for the power spectrum of curvature perturbations, of which the amplitude increases by several orders of magnitude. When spectral index values are consistent with observational constraints, the primordial spectrum amplitude is much larger than the observed value and can even 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 cosmic microwave background observations for all the considered models.