On the Hamilton-Jacobi approach to inflation beyond slow roll
arXiv:2504.05937 · doi:10.1088/1475-7516/2025/08/032
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.
Matches published version in JCAP. Details added to Sec. 5.3. References added. Conclusion unchanged
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