On FLRW reductions of $$N=1$$ supergravity

An FLRW reduction of $$N=1$$ 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 nα 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 ψ m α to a single 2-component spinor φ ^α ϕ α , which becomes the superpartner of both the scale factor a and lapse N , thus inducing the conformal time gauge, $$N=a$$ 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 N , ψ 0 α . We determine the allowed supergravity transformations that preserve the resulting FLRW supermultiplets.