# Quantization of the massive gravitino on FRW spacetimes

September 14, 2011

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 = w rho and w
in (-1,1] the light cones of the effective metric are more narrow than the
standard cones, which are recovered for the de Sitter case w=-1. In particular,
this shows that the propagation of the longitudinal part, although non-standard
for w different from -1, is completely causal in cosmological constant, dust
and radiation dominated universes.

Keywords:

Rarita-Schwinger field, gravitino, QFT on curved spacetimes