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.

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

References in corpus (19)

• The large deviation approach to statistical mechanics
• The Effective Field Theory of Inflation
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Primordial Black Holes as Dark Matter: Recent Developments
• Starting the Universe: Stable Violation of the Null Energy Condition and Non-standard Cosmologies
• 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
• Non-Gaussian Spikes from Chaotic Billiards in Inflation Preheating
• Eternal Inflation: The Inside Story
• Separate Universes Do Not Constrain Primordial Black Hole Formation
• Simple Bounds from the Perturbative Regime of Inflation
• Highly non-Gaussian tails and primordial black holes from single-field inflation
• Stochastic Inflation at NNLO
• Feynman diagrams and the large charge expansion in $3-\epsilon$ dimensions
• Higher N-point function data analysis techniques for heavy particle production and WMAP results
• Probability distribution function of the aperture mass field with large deviation theory
• Large deviations theory approach to cosmic shear calculations: the one-point aperture mass

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• Quantum loop effects on the power spectrum and constraints on primordial black holes
• Galileon inflation evades the no-go for PBH formation in the single-field framework
• 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