Numerical solutions of the Mukhanov-Sasaki equation for inflaton perturbations across a slow-roll to ultra-slow-roll transition are well described by Hamilton-Jacobi theory when appropriate solution branches and a parameter shift are used for modes exiting in each phase.
and Bond, J.R
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Updated Planck CMB measurements give ns = 0.9649 ± 0.0042, r < 0.056, confirm flatness at 0.4 percent, and show no evidence for scale-dependent features or non-slow-roll dynamics in the inflaton potential.
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Inflaton perturbations through an Ultra-Slow Roll transition and Hamilton-Jacobi attractors
Numerical solutions of the Mukhanov-Sasaki equation for inflaton perturbations across a slow-roll to ultra-slow-roll transition are well described by Hamilton-Jacobi theory when appropriate solution branches and a parameter shift are used for modes exiting in each phase.
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Planck 2018 results. X. Constraints on inflation
Updated Planck CMB measurements give ns = 0.9649 ± 0.0042, r < 0.056, confirm flatness at 0.4 percent, and show no evidence for scale-dependent features or non-slow-roll dynamics in the inflaton potential.