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

Constant-rate inflation, including ultra-slow-roll inflation as a special case, has been widely applied to the formation of primordial black holes with a 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 the slow-roll to the constant-rate phases.

Automated summary

The study focuses on the impact of constant-rate inflation on the formation of primordial black holes, deriving analytic solutions for curvature perturbations related to conformal weights and emphasizing the continuity of conformal weights between different rolling phases protected by the adiabatic condition of the inflaton perturbation. The temporal excitation of subleading states triggering the steepest growth of the power spectrum is attributed to entropy production in the transition from slow-roll to constant-rate phases.