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One loop to rule them all: Perturbativity in the presence of ultra slow-roll dynamics
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We discuss the issue of perturbativity in single-field inflationary models with a phase of ultra slow-roll (USR) tailor suited to generate an order-one abundance of primordial black holes (PBHs). More in detail, we impose the condition that loop corrections made up of short-wavelength modes enhanced by the USR dynamics do not alter the tree-level power spectrum of curvature perturbations. In our analysis, the USR phase is preceded and followed by two stages of ordinary slow-roll (SR), and we model the resulting SR/USR/SR dynamics using both instantaneous and smooth transitions. Focusing on scales relevant for CMB observations, we find that it is not possible, with these arguments, to rule out the scenario of PBH formation via USR, not even in the limit of instantaneous transition. However, we also find that loop corrections of short modes on the power spectrum of long modes, even though not large enough to violate perturbativity requirements, remain appreciable and, most importantly, are not tamed in realistic realisations of smooth SR/USR/SR transitions. This makes perturbativity a powerful theoretical tool to constrain USR dynamics. We extend the analysis at any scale beyond those relevant for CMB observations. We find that loop corrections of short modes remain within the few percent if compared to the tree-level power spectrum. However, we also find one notable exception of phenomenological relevance: we show that the so-called dip in the power spectrum of curvature perturbation is an artifact of the tree-level computation.
Forward citations
Cited by 9 Pith papers
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UV artefacts in ultra-slow-roll models of inflation
Hubble-flow models of ultra-slow-roll inflation introduce spurious UV artefacts in the potential that Fourier filtering removes, restoring Wands duality.
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Gravitational Waves from Black Hole Reheating: The Scalar-Induced Component
Accounting for the minimal mass spread of primordial black holes from gravitational collapse suppresses the Poltergeist GW background to the level of generic scalar-induced signals and reopens ultra-light PBH parameter space.
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Background-independent one-loop renormalization of tensor and scalar primordial spectra
UV divergences of one-loop primordial tensor and scalar spectra are absorbed by covariant and tadpole counterterms using only the universal WKB expansion of internal modes, yielding finite model-independent renormaliz...
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Constant-Roll Inflation: Analytical Formulae for Power Spectrum and Implications for Induced Gravitational Waves
Analytical formulae for power spectrum peaks in constant-roll inflation enable parameter reconstruction from peak features and smoothed approximations for induced gravitational wave estimates.
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Hamiltonians to all Orders in Perturbation Theory and Higher Loop Corrections in Single Field Inflation with PBHs Formation
Derives all-order Hamiltonians via EFT of inflation for USR models and shows L-loop corrections to CMB-scale perturbations scale as (ΔN P_e L)^L, exiting perturbative control at L=4 for typical ΔN≈2.5.
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Non-Perturbative Hamiltonian and Higher Loop Corrections in USR Inflation
In USR inflation with an idealized instantaneous sharp transition to slow-roll, higher loop corrections to curvature perturbations on CMB scales grow rapidly with loop order L and may exit perturbative control.
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Cancellation of one-loop time dependence in superhorizon curvature perturbations from all scales
One-loop time dependence in superhorizon curvature perturbations cancels when all-scale contributions and boundary terms are included consistently via the δN formalism.
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Fixing the Renormalization of Inflationary Loops via Ward Identities
Ward identities from large gauge symmetry impose model-independent constraints on renormalizing inflationary loops and non-perturbatively govern the infrared power spectrum evolution.
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Ward Identity Constraints on Loop Corrections in Non-Attractor Inflation
Ward identities derived from perturbation-theory symmetries enforce non-perturbative constraints on the infrared power spectrum and guarantee conservation of super-horizon modes in non-attractor inflation.
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