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A scalar field with an exponential potential in FLRW universe admits the exact solution. 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 which includes a single exponential potential. This implies the existence of additional conserved quantity and explains the integrability of the system.
Chiba et al. (Mon,) studied this question.
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