  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 continuous momentum scaling generically occurs at the
transition across different conformal dimensionalities. The temporal excitation
of subleading states (with the next-to-lowest conformal weights) is recorded as
the "steepest growth" of the power spectrum in the transition from slow-roll to
constant-rate phases.
