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Constant-rate inflation, including ultra-slow-roll as a special case, hasbeen widely applied to the formation of primordial black holes with significantdeviation from the standard slow-roll conditions at both the growing anddecaying phases of the power spectrum. We derive analytic solutions for thecurvature perturbations with respect to the late-time scaling dimensions(conformal weights) constrained by the dilatation symmetry of the de Sitterbackground and show that the continuity of conformal weights across differentrolling phases is protected by the adiabatic condition of the inflatonperturbation. The temporal excitation of subleading states (with thenext-to-lowest conformal weights), recorded as the "steepest growth" of thepower spectrum, is triggered by the entropy production in the transition fromslow-roll to constant-rate phases.

Constant-rate inflation: primordial black holes from conformal weight transitions