Constant-rate inflation: primordial black holes from conformal weight
  transitions
  Constant-rate inflation, including ultra-slow-roll as a special case, has
been widely applied to the formation of primordial black holes with significant
deviation from the standard slow-roll conditions at both the growing and
decaying phases of the power spectrum. We derive analytic solutions for the
curvature perturbations with respect to the late-time scaling dimensions
(conformal weights) constrained by the dilatation symmetry of the de Sitter
background and show that the continuity of conformal weights across different
rolling phases is protected by the adiabatic condition of the inflaton
perturbation. The temporal excitation of subleading states (with the
next-to-lowest conformal weights), recorded as the "steepest growth" of the
power spectrum, is triggered by the entropy production in the transition from
slow-roll to constant-rate phases.
