Large Deviations in the Early Universe

Abstract

Fluctuations play a critical role in cosmology. They are relevant across a range of phenomena from the dynamics of inflation to the formation of structure. In many cases, these fluctuations are coarse grained and follow a Gaussian distribution as a consequence of the Central Limit Theorem. Yet, some classes of observables are dominated by rare fluctuations and are sensitive to the details of the underlying microphysics. In this paper, we argue that the Large Deviation Principle can be used to diagnose when one must to appeal to the fundamental description. Concretely, we investigate the regime of validity for the Fokker-Planck equation that governs Stochastic Inflation. For typical fluctuations, this framework leads to the central limit-type behavior expected of a random walk. However, fluctuations in the regime of the Large Deviation Principle are determined by instanton-like saddle points accompanied by a new energy scale. When this energy scale is above the UV cutoff of the EFT, the tail is only calculable in the microscopic description. We explicitly demonstrate this phenomenon in the context of determining the phase transition to eternal inflation, the distribution of scalar field fluctuations in de Sitter, and the production of primordial black holes.

arXiv comment32 pages + references, 3 figures. v2: typos corrected, published version

References in corpus (76)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• The large deviation approach to statistical mechanics
• The Effective Field Theory of Inflation
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• A new approach to the evolution of cosmological perturbations on large scales
• Equilibrium State of a Massless Self-Interacting Scalar Field in the De Sitter Background
• Primordial Black Holes as Dark Matter: Recent Developments
• Single field consistency relation for the 3-point function
• Starting the Universe: Stable Violation of the Null Energy Condition and Non-standard Cosmologies
• Threshold of primordial black hole formation
• Primordial non-gaussianities from multiple-field inflation
• Non-Gaussianity in multi-field inflation
• Stochastic Quantum Gravitational Inflation
• Conformal consistency relations for single-field inflation
• Equilateral Non-Gaussianity and New Physics on the Horizon
• Super-Hubble de Sitter Fluctuations and the Dynamical RG
• Primordial Black Holes from Inflation and non-Gaussianity
• Seeding primordial black holes in multifield inflation
• Conformal Symmetries of Adiabatic Modes in Cosmology
• A Measure of de Sitter Entropy and Eternal Inflation
• Special invited paper. Large deviations
• Stochastic growth of quantum fluctuations during slow-roll inflation
• Open EFTs, IR Effects and Late-Time Resummations: Systematic Corrections in Stochastic Inflation
• Signs of Analyticity in Single-Field Inflation
• One-loop corrections to a scalar field during inflation
• Local non-Gaussianity from inflation
• Non-Gaussian Spikes from Chaotic Billiards in Inflation Preheating
• Productive Interactions: heavy particles and non-Gaussianity
• Eternal Inflation: The Inside Story
• Separate Universes Do Not Constrain Primordial Black Hole Formation
• The Epsilon Expansion Meets Semiclassics
• Summing tree graphs at threshold
• Eternal Inflation and the Refined Swampland Conjecture
• A Leading Logarithm Approximation for Inflationary Quantum Field Theory
• On Squeezed Limits in Single-Field Inflation - Part I
• Eternal Inflation and Swampland Conjectures
• On the CFT Operator Spectrum at Large Global Charge
• Highly non-Gaussian tails and primordial black holes from single-field inflation
• Simple Bounds from the Perturbative Regime of Inflation
• The Phase Transition to Eternal Inflation
• De Sitter Diagrammar and the Resummation of Time
• Semiclassical approach for multiparticle production in scalar theories
• Soft de Sitter Effective Theory
• Exponentiation of Multiparticle Amplitudes in Scalar Theories
• A parton picture of de Sitter space during slow-roll inflation
• Selected Topics in the Large Quantum Number Expansion
• Back in the saddle: Large-deviation statistics of the cosmic log-density field
• A Field Range Bound for General Single-Field Inflation
• Stochastic Inflation at NNLO
• B-modes and the Nature of Inflation
• Cumulative effects in inflation with ultra-light entropy modes
• A manifestly covariant theory of multifield stochastic inflation in phase space: solving the discretisation ambiguity in stochastic inflation
• Feynman diagrams and the large charge expansion in $3-\epsilon$ dimensions
• Scalar correlation functions in de Sitter space from the stochastic spectral expansion
• Extremal Correlators and Random Matrix Theory
• Landscape tomography through primordial non-Gaussianity
• Non-Perturbative Production of Multi-Boson States and Quantum Bubbles
• Game of cones: A nulling strategy for modelling lensing convergence in cones with large deviation theory
• Infrared dynamics of a light scalar field in de Sitter
• Inflation in Motion: Unitarity Constraints in Effective Field Theories with Broken Lorentz Symmetry
• Beyond Perturbation Theory in Inflation
• Markovian Dynamics in de Sitter
• Stochastic eternal inflation is in the swampland
• Squeezed Bispectrum in the $\delta N$ Formalism: Local Observer Effect in Field Space
• A Large Deviation Principle at play in Large-Scale Structure cosmology
• Rare Events Are Nonperturbative: Primordial Black Holes From Heavy-Tailed Distributions
• Non-perturbative probability distribution function for cosmological counts in cells
• Higher N-point function data analysis techniques for heavy particle production and WMAP results
• The structure of correlation functions in single field inflation
• Probability distribution function of the aperture mass field with large deviation theory
• Power-counting during single-field slow-roll inflation
• The matter density PDF for modified gravity and dark energy with Large Deviations Theory
• Large deviations theory approach to cosmic shear calculations: the one-point aperture mass
• Post-Born corrections to the one-point statistics of (CMB) lensing convergence obtained via large deviation theory
• Non-Gaussian CMB and LSS statistics beyond polyspectra
• Keeping an Eye on DBI: Power-counting for small-$c_s$ Cosmology

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• Bootstrapping Multi-Field Inflation: non-Gaussianities from light scalars revisited
• The Open Effective Field Theory of Inflation
• Realisation of the ultra-slow roll phase in Galileon inflation and PBH overproduction
• Large fluctuations and Primordial Black Holes
• Uphill inflation
• Obviating PBH overproduction for SIGWs generated by Pulsar Timing Arrays in loop corrected EFT of bounce
• Regularized-Renormalized-Resummed loop corrected power spectrum of non-singular bounce with Primordial Black Hole formation
• Untangling PBH overproduction in $w$-SIGWs generated by Pulsar Timing Arrays for MST-EFT of single field inflation
• Primordial Black Holes from Effective Field Theory of Stochastic Single Field Inflation at NNNLO
• Negative non-Gaussianity as a salvager for PBHs with PTAs in bounce
• Itô, Stratonovich, and zoom-in schemes in stochastic inflation
• Stochastic origin of primordial fluctuations in the Sky