Hidden Symmetries of Power-Law Inflation

TL;DR

This paper reveals hidden symmetries in power-law inflation models with exponential potentials, explaining their integrability through the Eisenhart lift and conserved quantities.

Contribution

It uncovers hidden symmetries in power-law inflation models using Eisenhart lift, demonstrating the conditions for integrability in these systems.

Findings

Existence of a conformal Killing vector field only for specific exponential potentials

Identification of an additional conserved quantity in the system

Explanation of the system's integrability through hidden symmetries

Abstract

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.