On the Hamilton-Jacobi approach to inflation beyond slow roll

2025/04/08 by Artigas, Danilo, Frion, Emmanuel, Miranda, Tays +2 · 3 citations
#Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.2504.05937

Abstract

The Hamilton-Jacobi approach is a powerful tool to describe super-Hubble dynamics during cosmological inflation in a non-linear way. A key assumption of this framework is to neglect anisotropic perturbations on large scales. We show that neglecting the anisotropic sector in the momentum constraint corresponds to discarding the non-adiabatic mode of scalar-field perturbations at large scales. Consequently, the Hamilton-Jacobi approach cannot be used to describe the evolution of large-scale perturbations during inflation beyond slow roll, when non-adiabatic fluctuations play an important role on super-Hubble scales due to the absence of an attractor trajectory. As an example, we analyse the case of cosmological perturbations during a phase of ultra-slow-roll inflation.

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• Inflaton perturbations through an Ultra-Slow Roll transition and Hamilton-Jacobi attractors

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