Slow Roll during the Waterfall Regime: The Small Coupling Window for SUSY Hybrid Inflation

TL;DR

This paper explores how significant inflation can occur during the waterfall phase of SUSY hybrid inflation under specific conditions, affecting the spectral index and observational predictions.

Contribution

It derives conditions under which the waterfall regime produces many e-folds and analyzes the resulting spectral index in SUSY hybrid inflation models.

Findings

Large waterfall e-folds possible when kappa << M^2/M_P^2

Spectral index n_s=1-4/N_e during waterfall inflation

Lower bound on symmetry breaking scale from power spectrum normalization

Abstract

It has recently been pointed out that a substantial amount of e-folds can occur during the waterfall regime of hybrid inflation. Moreover, Kodama et.al. have derived analytic approximations for the trajectories of the inflaton and of the waterfall fields. Based on these, we derive here the consequences for F- and D-term SUSY hybrid inflation: A substantial amount of e-folds may occur in the waterfall regime, provided kappa << M^2/M_P^2, where kappa is the superpotential coupling, M the scale of symmetry breaking and M_P the reduced Planck mass. When this condition is amply fulfilled, a number of e-folds much larger than N_e\approx60 can occur in the waterfall regime and the scalar spectral index is then given by the expression found by Kodama et.al. n_s=1-4/N_e. This value may be increased up to unity, if only about N_e e-folds occur during the waterfall regime, such that the largest observable scale leaves the horizon close to the critical point of hybrid inflation, what can be achieved for kappa\approx10^(-13) and M\approx5x10^(12) GeV in F-term inflation. Imposing the normalization of the power spectrum leads to a lower bound on the scale of symmetry breaking.