Slow and Safe Gravitinos

TL;DR

This paper investigates conditions under which supergravity inflation models with zero sound speed avoid excessive gravitino production, highlighting the roles of various constraints and potential issues like higher derivatives and superluminal speeds.

Contribution

It clarifies how different superfield constraints influence gravitino production and identifies potential problems in models with multiple constraints or higher derivative operators.

Findings

Unconstrained superfields prevent uncontrolled gravitino production.

Models with a nilpotent field also avoid overproduction.

Constraints from UV Lagrangians may introduce pathologies.

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 ${\bf S^2} =0$, i.e. sgoldstino-less models. Models with a second orthogonal constraint, ${\bf S(\Phi-\bar{\Phi})} =0$, where $\bf{\Phi}$ 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.