Hidden Symmetries of Power-Law Inflation

Takeshi Chiba; Tsuyoshi Houri

Hidden Symmetries of Power-Law Inflation

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arxiv 2404.19162 v2 pith:66CDUNQH submitted 2024-04-29 gr-qc hep-th

Takeshi Chiba , Tsuyoshi Houri This is my paper · ORCID

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keywords fieldexponentialinflationsystembeenhiddenintegrabilitypotential

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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
gr-qc 2026-07 conditional novelty 6.0 of 10

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.

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