Quantization of the massive gravitino on FRW spacetimes

TL;DR

This paper investigates the quantization and causal behavior of a massive spin 3/2 field in FRW spacetimes, demonstrating causal propagation and constructing a positive inner product for the field solutions.

Contribution

It introduces a quantization scheme for the massive gravitino on FRW backgrounds and analyzes the causal structure of its degrees of freedom.

Findings

The inner product for solutions is positive definite.

Transversal and longitudinal modes decouple and follow Dirac-type equations.

Longitudinal propagation remains causal in relevant cosmological models.

Abstract

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.