The gravitino is the hypothetical supersymmetric partner of the graviton, as predicted by theories combining general relativity and supersymmetry, i.e. supergravity theories. If it exists it is a fermion of spin 3/2, therefore obeys Rarita-Schwinger equation.

Light Gravitino

If the gravitino is the lightest supersymmetric particle and R-parity is conserved (or nearly so), many or all supersymmetric particles can decay into their superpartner and a gravitino which yields the following effects:

1) The gravitino could make up most of the dark matter in the universe.

2) The decays might be detected at future particle accelerators. This can be done if either a neutral supersymmetric particle decays within the detector (only for very short lifetimes) or if a charged supersymmetric particle is stopped outside the detector (possible for longer lifetimes, too).

The other leading candidate for the lightest supersymmetric particle is the neutralino.

Fermions | Quantum gravity

Gravitiino | גרביטינו