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.
A dynamic correspondence between Bose-Einstein condensates and Friedmann-Lema\^itre-Robertson-Walker and Bianchi I cosmology with a cosmological constant
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abstract
In some interesting work of James Lidsey, the dynamics of Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmology with positive curvature and a perfect fluid matter source is shown to be modeled in terms of a time-dependent, harmonically trapped Bose-Einstein condensate. In the present work, we extend this dynamic correspondence to both FLRW and Bianchi I cosmologies in arbitrary dimension, especially when a cosmological constant is present.
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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.