Higgs Boson Decays into Light Gravitinos

We study decays of the neutral and charged Higgs bosons of the minimal supersymmetric standard model into a very light gravitino and a neutralino or chargino. Present experimental constraints already imply that the lighter scalar Higgs boson can only have a very small branching ratio into this mode. However, if the gravitino mass is below $\sim 0.5$ eV, the heavier neutral and charged Higgs boson decays into a gravitino can be important or even dominant. We discuss the resulting signature for associate production of the heavy CP-even and the CP-odd states at future $e^+ e^-$ colliders, and comment on Higgs boson production at hadron colliders.