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.
Hidden Symmetries of Power-Law Inflation
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A scalar field with an exponential potential has been proposed as a model of inflation (called power-law inflation). Although it admits an exact solution, the integrability of the system has not been shown.We uncover the hidden symmetries behind the system by utilising the Eisenhart lift of field theories. We find that a conformal Killing vector field in the field space exists only for a particular combination of exponential functions that includes a single exponential potential. This implies the existence of additional conserved quantity and explains the integrability of the system.
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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.