For flat FLRW with n free massless scalars, the physical symmetry algebra of the minisuperspace is conf(n,1), and the Schrödinger algebra seen in the Eisenhart-Duval lift is gauge-dependent except for the single-field case.
Rovelli,Quantum Gravity, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge (2004)
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Gauge vs (hidden) physical symmetries of FLRW cosmologies
For flat FLRW with n free massless scalars, the physical symmetry algebra of the minisuperspace is conf(n,1), and the Schrödinger algebra seen in the Eisenhart-Duval lift is gauge-dependent except for the single-field case.