Salvage of Too Slow Gravitinos

TL;DR

This paper investigates gravitino behavior in cosmological models with spontaneously broken supersymmetry and Lorentz symmetry, showing that their longitudinal modes can avoid divergent production by maintaining relativistic dispersion relations.

Contribution

It demonstrates that in certain supersymmetric cosmological models, gravitino longitudinal modes have relativistic dispersion, preventing catastrophic production when sound speed vanishes.

Findings

Gravitino longitudinal modes can have relativistic dispersion relations.

Catastrophic gravitino production can be avoided in specific models.

Explicit examples show the stability of gravitino propagation.

Abstract

Gravitinos can inherit a non-relativistic dispersion relation while propagating in a background breaking both supersymmetry and Lorentz symmetry spontaneously. This is because the longitudinal mode velocity is controlled by the sound speed in the background. It was pointed out recently by Kolb, Long and McDonough that the production of gravitinos might diverge when this sound speed vanishes. We argue that in the framework of cosmological models with linearly spontaneously broken realised supersymmetry, where the physical fermions are combinations of the vacuum goldstino and the inflatino, the gravitino longitudinal mode has a relativistic dispersion relation and therefore avoids the catastrophic production. We illustrate this in some explicit examples.