On FLRW reductions of N=1 supergravity

TL;DR

This work addresses the difficulty of obtaining a supersymmetric FLRW background in $N=1$ supergravity by applying the quadratic Killing framework to the superspace metric generalization $ψ_m^{\ α} ψ_{n α}$. By reducing the gravitino sector to a single spinor $φ^α$ and treating $a(t)$ and $N(t)$ as a supermultiplet, the authors derive isometry-preserving transformations for both flat and closed FLRW geometries and show that the conformal time gauge $N=a$ emerges naturally. They further extend the construction to allow arbitrary time gauge while preserving a consistent FLRW-type multiplet, including a complex geometry generalization, thereby broadening the space of supersymmetric quantum cosmology backgrounds. The results provide a principled route to embedding FLRW cosmologies in $N=1$ supergravity with a background spinor, which is potentially relevant for supersymmetric cosmology and early-universe phenomenology.

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 $ψ_m^{\ α} ψ_{n α}$ arising from a particular superspace generalization of the metric tensor. Imposing the FLRW form on this object reduces $ψ_m^{\ α}$ to a single 2-component spinor $φ^α$, 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 $N, ψ_0^{\ α}$. We determine the allowed supergravity transformations that preserve the resulting FLRW supermultiplets.