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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Horizon crossing and inflation with large \eta
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abstract
I examine the standard formalism of calculating curvature perturbations in inflation at horizon crossing, and derive a general relation which must be satisfied for the horizon crossing formalism to be valid. This relation is satisfied for the usual cases of power-law and slow roll inflation. I then consider a model for which the relation is strongly violated, and the curvature perturbation evolves rapidly on superhorizon scales. This model has Hubble slow roll parameter $\eta = 3$, but predicts a scale-invariant spectrum of density perturbations. I consider the case of hybrid inflation with large $\eta$, and show that such solutions do not solve the ``$\eta$ problem'' in supergravity. These solutions correspond to field evolution which has not yet relaxed to the inflationary attractor solution, and may make possible new, more natural models on the string landscape.
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representative citing papers
Vector modes from primordial magnetic fields remain constant in a kination epoch and source second-order curvature perturbations scaling as P_R(k) ∝ k^{-5}, sufficient for PBH dark matter abundance in a Ratra-type magnetogenesis model.
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 renormalized expressions.
Hybrid inflation's waterfall tachyonic instability grows isocurvature modes that convert to curvature perturbations at the field-space turn, yielding a k^{3}-peaked spectrum with always-positive f_NL that enhances PBH formation.
The authors define a locality condition for hard-mode states during inflation that unifies local effective dynamics for soft modes, suppression of loop corrections, generalized soft theorems, and absence of infrared divergences in observable correlators.
The stochastic noise amplitude is modified to (H/2π) * sqrt(1 + ΔP_R / P0_R) to account for one-loop corrections in interacting theories, demonstrated in a three-phase SR-USR-SR setup for PBH 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.
Tree-level multi-soft theorems for scalar and graviton correlation functions are derived at leading soft order via background-wave coordinate rescaling, including tensor exchanges in scalars and scalar exchanges in tensors.
One-loop time dependence in superhorizon curvature perturbations cancels when all-scale contributions and boundary terms are included consistently via the δN formalism.
Requiring decohered cosmological perturbations to admit a classical P-function forces their momentum variance above the vacuum value, and demanding a linear gravitational potential at reheating bounds that variance by ~10^14, excluding thermal decoherence states and restricting amplitude-basis model
Regular primordial black holes can evaporate completely like singular ones and yield the observed dark matter density under modified cosmological constraints.
Numerical solutions of the Mukhanov-Sasaki equation for inflaton perturbations across a slow-roll to ultra-slow-roll transition are well described by Hamilton-Jacobi theory when appropriate solution branches and a parameter shift are used for modes exiting in each phase.
Updated compilation shows PBHs are tightly constrained across 55 orders of magnitude in mass, ruling out dominant dark matter contributions except in narrow windows, with many limits carrying observational uncertainties.
Non-standard reheating imprints detectable features on SIGW spectra via non-Gaussianity, with dynamics that can suppress or boost the signal amplitude for LISA.
A tutorial deriving cosmological perturbation equations from inflation through reheating, with explicit gauge-invariant computations and Python scripts.
citing papers explorer
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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.
-
Primordial Black Holes from Vector-Induced Curvature Perturbations Sourced by Primordial Magnetic Fields
Vector modes from primordial magnetic fields remain constant in a kination epoch and source second-order curvature perturbations scaling as P_R(k) ∝ k^{-5}, sufficient for PBH dark matter abundance in a Ratra-type magnetogenesis model.
-
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 renormalized expressions.
-
Superhorizon curvature perturbations in hybrid inflation revisited
Hybrid inflation's waterfall tachyonic instability grows isocurvature modes that convert to curvature perturbations at the field-space turn, yielding a k^{3}-peaked spectrum with always-positive f_NL that enhances PBH formation.
-
Locality in effective field theory for inflationary soft modes
The authors define a locality condition for hard-mode states during inflation that unifies local effective dynamics for soft modes, suppression of loop corrections, generalized soft theorems, and absence of infrared divergences in observable correlators.
-
Stochastic Inflation with Interacting Noises
The stochastic noise amplitude is modified to (H/2π) * sqrt(1 + ΔP_R / P0_R) to account for one-loop corrections in interacting theories, demonstrated in a three-phase SR-USR-SR setup for PBH formation.
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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.
-
Multi-soft theorems for cosmological correlators: Background wave method for scalars & gravitons
Tree-level multi-soft theorems for scalar and graviton correlation functions are derived at leading soft order via background-wave coordinate rescaling, including tensor exchanges in scalars and scalar exchanges in tensors.
-
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.
-
A Landscape of Cosmological Decoherence
Requiring decohered cosmological perturbations to admit a classical P-function forces their momentum variance above the vacuum value, and demanding a linear gravitational potential at reheating bounds that variance by ~10^14, excluding thermal decoherence states and restricting amplitude-basis model
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Dark matter production from evaporation of regular primordial black holes
Regular primordial black holes can evaporate completely like singular ones and yield the observed dark matter density under modified cosmological constraints.
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Inflaton perturbations through an Ultra-Slow Roll transition and Hamilton-Jacobi attractors
Numerical solutions of the Mukhanov-Sasaki equation for inflaton perturbations across a slow-roll to ultra-slow-roll transition are well described by Hamilton-Jacobi theory when appropriate solution branches and a parameter shift are used for modes exiting in each phase.
-
Constraints on Primordial Black Holes
Updated compilation shows PBHs are tightly constrained across 55 orders of magnitude in mass, ruling out dominant dark matter contributions except in narrow windows, with many limits carrying observational uncertainties.
-
Probing non-Gaussianity during reheating with SIGW in the LISA band
Non-standard reheating imprints detectable features on SIGW spectra via non-Gaussianity, with dynamics that can suppress or boost the signal amplitude for LISA.
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From inflation to hot big bang -- a tutorial on cosmological perturbations
A tutorial deriving cosmological perturbation equations from inflation through reheating, with explicit gauge-invariant computations and Python scripts.