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Inflaton perturbations through an Ultra-Slow Roll transition and Hamilton-Jacobi attractors
Tomislav Prokopec, Gerasimos Rigopoulos
https://arxiv.org/abs/2507.04114

Inflaton perturbations through an Ultra-Slow Roll transition and Hamilton-Jacobi attractors
We examine the behaviour of the gauge invariant scalar field perturbations in an analytic inflationary model that transitions from slow roll to an ultra-slow roll (USR) phase. We find that the numerical solution of the Mukhanov-Sasaki equation is well described by Hamilton-Jacobi (HJ) theory, as long as the appropriate branches of the Hamilton-Jacobi solutions are invoked: Modes that exit the horizon during the slow roll phase evolve into the USR as described by the first HJ branch, up to a sub…

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