On FLRW reductions of N=1 supergravity

TL;DR

This paper explores the challenges of applying FLRW reductions to N=1 supergravity, proposing a novel approach involving a specific quadratic form to maintain supersymmetry and gauge invariance.

Contribution

It introduces a new method using a quadratic form of the Rarita-Schwinger field to achieve FLRW reduction while preserving supersymmetry and gauge invariance.

Findings

Reduction of the Rarita-Schwinger field to a single spinor  simplifies FLRW supergravity models.

Restoration of time-reparametrization invariance through gauge field deviations.

Identification of supergravity transformations compatible with FLRW supermultiplets.

Abstract

An FLRW reduction of N=1 supergravity is troublesome since spatial isotropy prohibits a non-vanishing Rarita-Schwinger field. In view of this, we consider the quadratic form $\psi_m^{\ \alpha} \psi_{n \alpha}$ arising from a particular superspace generalization of the metric tensor. Imposing the FLRW form on this object reduces $\psi_m^{\ \alpha}$ to a single 2-component spinor $\phi^\alpha$, which becomes the superpartner of both the scale factor $a$ and lapse $N$, thus inducing the conformal time gauge, $N=a$. Time-reparametrization invariance is restored if we allow for deviations of FLRW form that are proportional to the gauge fields $N, \psi_0^{\ \alpha}$. We determine the allowed supergravity transformations that preserve the resulting FLRW supermultiplets.