Quantization of the massive gravitino on FRW spacetimes

In this article we study the quantization and causal properties of a massive spin 3/2 Rarita-Schwinger field on spatially flat Friedmann-Robertson- Walker (FRW) spacetimes. We construct Zuckerman's universal conserved current and prove that it leads to a positive definite inner product on solutions of the field equation. Based on this inner product, we quantize the Rarita-Schwinger field in terms of a CAR-algebra. The transversal and longitudinal parts constituting the independent on-shell degrees of freedom decouple. We find a Dirac-type equation for the transversal polarizations, ensuring a causal propagation. The equation of motion for the longitudinal part is also of Dirac-type, but with respect to an "effective metric". We obtain that for all four-dimensional FRW solutions with a matter equation of state p=ωρ and ω(-1,1] the light cones of the effective metric are more narrow than the standard cones, which are recovered for the de Sitter case ω=-1. In particular, this shows that the propagation of the longitudinal part, although nonstandard for ω -1, is completely causal in cosmological constant, dust and radiation dominated universes. © 2012 American Physical Society.