Stochastic binary tree method computes compaction function in inflation to distinguish type I/II PBH fluctuations, finding broader mass distributions and type-II dominance in quantum regimes of a toy model.
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Correlation Functions in Stochastic Inflation
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abstract
Combining the stochastic and $\delta N$ formalisms, we derive non perturbative analytical expressions for all correlation functions of scalar perturbations in single-field, slow-roll inflation. The standard, classical formulas are recovered as saddle-point limits of the full results. This yields a classicality criterion that shows that stochastic effects are small only if the potential is sub-Planckian and not too flat. The saddle-point approximation also provides an expansion scheme for calculating stochastic corrections to observable quantities perturbatively in this regime. In the opposite regime, we show that a strong suppression in the power spectrum is generically obtained, and comment on the physical implications of this effect.
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representative citing papers
Exact solution of time-reversed stochastic inflation in the quantum well yields curvature perturbation distributions with faster-decaying exponential tails than forward stochastic inflation.
Constructs open EFT for stochastic inflation with stochastic RG channel, nonlocal Wilson kernels, and derived master equations matched to full theory via method-of-regions.
The conventional truncation in stochastic inflation is inconsistent because quadratic-noise contributions are the same perturbative order as the deterministic non-Markovian corrections.
Stochastic inflationary fluctuations cannot supply the large dark-Higgs displacement required for broad parametric resonance production of vector dark matter, but a classically sourced Hubble-induced minimum can, with distinct relic scaling and consistency conditions.
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.
A new eigenvalue method is introduced to compute the PDF of stochastic e-folds in inflation, recovering a known flat-potential result and analyzing constant-drift cases in narrow and broad well limits.
Stochastic effects in multifield inflation make the number of fields relevant for e-fold statistics and power spectrum, with a general formula for higher moments and an upper bound on fields for successful inflation.
Derives stochastic equations from Schwinger-Keldysh formalism that include quantum diffusion and classical metric perturbations for non-perturbative ultra-slow-roll inflation, validated on Starobinsky and critical Higgs models.
A light axion spectator induces post-inflation tachyonic phases that produce a nearly scale-invariant boost to the curvature power spectrum and alter key inflationary observables in a largely potential-independent manner.
Compares two methods to resolve disagreements and prove positivity of anomalous dimensions for principal series fields coupled to compact scalar operators in de Sitter space.
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.
Stochastic inflation with Gauss-Bonnet coupling to the inflaton yields first-passage-time estimates of the scalar power spectrum and PBH mass fraction in slow-roll and ultra-slow-roll limits.
Surviving inflationary histories develop a universal inward drift near any hard swampland boundary — two times the diffusion over the distance to the edge — regardless of the cutoff's microscopic origin.
citing papers explorer
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Compaction function in stochastic inflation: a \texttt{FOREST} of type I and II primordial black holes
Stochastic binary tree method computes compaction function in inflation to distinguish type I/II PBH fluctuations, finding broader mass distributions and type-II dominance in quantum regimes of a toy model.
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Time-reversed stochastic inflation in the quantum well
Exact solution of time-reversed stochastic inflation in the quantum well yields curvature perturbation distributions with faster-decaying exponential tails than forward stochastic inflation.
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Stochastic inflation as an open quantum system II: open effective field theory and stochastic matching
Constructs open EFT for stochastic inflation with stochastic RG channel, nonlocal Wilson kernels, and derived master equations matched to full theory via method-of-regions.
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A consistent formulation of stochastic inflation I: Non-Markovian effects and issues beyond linear perturbations
The conventional truncation in stochastic inflation is inconsistent because quadratic-noise contributions are the same perturbative order as the deterministic non-Markovian corrections.
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Parametric Resonance of Higgsed Vector Dark Matter: Inflationary Initial Conditions and Sourced Displacements
Stochastic inflationary fluctuations cannot supply the large dark-Higgs displacement required for broad parametric resonance production of vector dark matter, but a classically sourced Hubble-induced minimum can, with distinct relic scaling and consistency conditions.
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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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Eigenvalue formulation of Stochastic Inflation and application to large perturbation generating inflationary features
A new eigenvalue method is introduced to compute the PDF of stochastic e-folds in inflation, recovering a known flat-potential result and analyzing constant-drift cases in narrow and broad well limits.
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Multifield stochastic inflation: Relevance of number of fields in statistical moments
Stochastic effects in multifield inflation make the number of fields relevant for e-fold statistics and power spectrum, with a general formula for higher moments and an upper bound on fields for successful inflation.
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Nonperturbative stochastic inflation in perturbative dynamical background
Derives stochastic equations from Schwinger-Keldysh formalism that include quantum diffusion and classical metric perturbations for non-perturbative ultra-slow-roll inflation, validated on Starobinsky and critical Higgs models.
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Tachyonic Encore: A universal shift of inflationary observables
A light axion spectator induces post-inflation tachyonic phases that produce a nearly scale-invariant boost to the curvature power spectrum and alter key inflationary observables in a largely potential-independent manner.
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A Compact Story of Positivity in de Sitter
Compares two methods to resolve disagreements and prove positivity of anomalous dimensions for principal series fields coupled to compact scalar operators in de Sitter space.
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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.
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Towards Stochastic Inflation in Higher-Curvature Gravity
Stochastic inflation with Gauss-Bonnet coupling to the inflaton yields first-passage-time estimates of the scalar power spectrum and PBH mass fraction in slow-roll and ultra-slow-roll limits.
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Stochastic Survival near Swampland Boundaries
Surviving inflationary histories develop a universal inward drift near any hard swampland boundary — two times the diffusion over the distance to the edge — regardless of the cutoff's microscopic origin.
- Bouncing cosmologies from Born-Infeld-type gravity