Lattice simulations directly calculate SIGW spectra with non-Gaussianity to all orders and show that modest non-Gaussianity alters ultraviolet spectral behavior.
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Logarithmic Duality of the Curvature Perturbation
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abstract
We study the comoving curvature perturbation $\mathcal{R}$ in the single-field inflation models whose potential can be approximated by a piecewise quadratic potential $V(\varphi)$ by using the $\delta N$ formalism. We find a general formula for $\mathcal{R}(\delta\varphi, \delta\pi)$, consisting of a sum of logarithmic functions of the field perturbation $\delta\varphi$ and the velocity perturbation $\delta\pi$ at the point of interest, as well as of $\delta\pi_*$ at the boundaries of each quadratic piece, which are functions of ($\delta\varphi, \delta\pi$) through the equation of motion. Each logarithmic expression has an equivalent dual expression, due to the second-order nature of the equation of motion for $\varphi$. We also clarify the condition under which $\mathcal{R}(\delta\varphi, \delta\pi)$ reduces to a single logarithm, which yields either the renowned ``exponential tail'' of the probability distribution function of $\mathcal{R}$ or a Gumbel-distribution-like tail.
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Shape dispersion around the average peak profile is a genuine statistical ingredient: rare deformed curvature profiles can dominate primordial black hole formation when the power spectrum is broad or non-Gaussianity is negative.
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.
Curvaton self-interactions in non-quadratic potentials produce a local non-Gaussian map that enables supermassive primordial black hole formation at peak amplitudes of order 10^{-5} while remaining consistent with μ-distortion bounds.
Analytical formulae for power spectrum peaks in constant-roll inflation enable parameter reconstruction from peak features and smoothed approximations for induced gravitational wave estimates.
Spectral solution of the Fokker-Planck operator for hilltop constant-roll inflation shows rare crossing trajectories dominate the mean, so the median yields a coarse-grained ΔN distribution whose exponential tail flattens into a peak near maximal value.
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.
For tachyonic models with ζ=A(φ²−σ²), the PBH abundance is exponentially set by the correlation ρ between field and radial gradient; narrow spectra drive ρ→−1 and suppress PBH formation without killing the induced GW signal.
Clustered primordial black holes may constitute all dark matter and produce a flat stochastic gravitational wave background detectable by the Einstein Telescope.
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.
Bulk viscosity raises the critical collapse threshold for primordial black holes by an amount comparable to the viscosity strength and increases the resulting black hole masses.
citing papers explorer
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Scalar-induced gravitational waves with non-Gaussianity up to all orders
Lattice simulations directly calculate SIGW spectra with non-Gaussianity to all orders and show that modest non-Gaussianity alters ultraviolet spectral behavior.
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The statistics of curvature-profile dispersion in primordial black hole formation
Shape dispersion around the average peak profile is a genuine statistical ingredient: rare deformed curvature profiles can dominate primordial black hole formation when the power spectrum is broad or non-Gaussianity is negative.
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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.
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Memoirs of the curvaton: non-perturbative non-Gaussianity and supermassive primordial black holes
Curvaton self-interactions in non-quadratic potentials produce a local non-Gaussian map that enables supermassive primordial black hole formation at peak amplitudes of order 10^{-5} while remaining consistent with μ-distortion bounds.
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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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Stochastic constant-roll inflation beyond the hilltop with the spectral method
Spectral solution of the Fokker-Planck operator for hilltop constant-roll inflation shows rare crossing trajectories dominate the mean, so the median yields a coarse-grained ΔN distribution whose exponential tail flattens into a peak near maximal value.
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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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Purely quadratic non-Gaussianity from tachyonic instability: Primordial black holes and scalar-induced gravitational waves
For tachyonic models with ζ=A(φ²−σ²), the PBH abundance is exponentially set by the correlation ρ between field and radial gradient; narrow spectra drive ρ→−1 and suppress PBH formation without killing the induced GW signal.
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Hunting Dark Matter with the Einstein Telescope
Clustered primordial black holes may constitute all dark matter and produce a flat stochastic gravitational wave background detectable by the Einstein Telescope.
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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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Primordial black hole formation in bulk-viscous cosmology
Bulk viscosity raises the critical collapse threshold for primordial black holes by an amount comparable to the viscosity strength and increases the resulting black hole masses.