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We describe embeddings of $n$-dimensional Lorentzian manifolds, includingFriedmann-Lema\^itre-Robertson-Walker spaces, in $\mathbb{R}^{n+2}$ such thatthe metrics of the submanifolds are inherited by a restriction from that of$\mathbb{R}^{n+2}$, and the action of the linear group SO$(2, n)$ of theambient space reduces to conformal transformations on the submanifolds.

SO$(2,n)$-compatible embeddings of conformally flat $n$-dimensional submanifolds in $\mathbb{R}^{n+2}$