Ermakov-Lewis invariant in single field inflation

2026/07/17 by Seoktae Koh
#hep-th

paper · pdf

Abstract

We investigate the dynamical symmetry of the Sasaki-Mukhanov equation, which governs the evolution of primordial perturbations during inflation. By mapping the Sasaki-Mukhanov equation to a constant-frequency harmonic oscillator via an auxiliary Ermakov field satisfying the Ermakov-Pinney equation, we construct the associated sl(2, R) generators and derive the Ermakov-Lewis invariant. We apply this framework to de Sitter space and slow-roll inflation, demonstrating that the Bunch-Davies vacuum gives I_EL = 1/2, conserved non-perturbatively at all orders in slow-roll.

Citations

• Quantized Fields and Particle Creation in Expanding Universes. I

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