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

• Published in: The journal of high energy physics Vol. 2021; no. 11; pp. 1 - 26
• Main Authors: Ng, Kin-Wang, Wu, Yi-Peng
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 11.11.2021; Springer Nature B.V; Springer; SpringerOpen
• Subjects: Adiabatic conditions; Astrophysics; Black holes; Classical and Quantum Gravitation; Conformal Field Theory; Cosmology of Theories beyond the SM; Elementary Particles; Exact solutions; Gravitational waves; High energy physics; High Energy Physics - Phenomenology; High Energy Physics - Theory; Mathematical analysis; Perturbation; Phases; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Space-Time Symmetries; Spacetime; String Theory; Conformal Field Theory; Space-Time Symmetries; Cosmology of Theories beyond the SM; power spectrum; symmetry: de Sitter; black hole: formation; critical phenomena; invariance: scale; horizon: crossing; inflaton: potential; field theory: conformal; black hole: primordial; scaling: dimension; boundary condition; vacuum state; space-time: de Sitter; symmetry: dilation; inflation: model; field theory: scalar: massless; Hubble constant; curvature: perturbation; background: de Sitter; dark matter; correlation function; non-Gaussianity; slow-roll approximation: violation
• ISSN: 1029-8479; 1126-6708; 1029-8479
• DOI: 10.1007/JHEP11(2021)076

A bstract 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.