Slow and Safe Gravitinos

Abstract

It has been argued that supergravity models of inflation with vanishing sound speeds, $c_s$, lead to an unbounded growth in the production rate of gravitinos. We consider several models of inflation to delineate the conditions for which $c_s=0$. In models with unconstrained superfields, we argue that the mixing of the goldstino and inflatino in a time-varying background prevents the uncontrolled production of the longitudinal modes. This conclusion is unchanged if there is a nilpotent field associated with supersymmetry breaking with constraint ${\mathbf{S}}^2=0$, i.e. sgoldstino-less models. Models with a second orthogonal constraint, $\mathbf{S}(\mathbf{\Phi }-\bar{\mathbf{\Phi }})=0$, where $\mathbf{\Phi }$ is the inflaton superfield, which eliminates the inflatino, may suffer from the over-production of gravitinos. However, we point out that these models may be problematic if this constraint originates from a UV Lagrangian, as this may require using higher derivative operators. These models may also exhibit other pathologies such as $c_s>1$, which are absent in theories with the single constraint or unconstrained fields.

12 pages