Large Deviations in the Early Universe

TL;DR

This paper explores how large deviation principles can identify when cosmological fluctuations require a fundamental microphysical description, especially in rare events like primordial black hole formation and eternal inflation.

Contribution

It introduces the use of large deviation theory to analyze the validity of stochastic inflation models and highlights the role of instanton-like saddle points in rare fluctuation regimes.

Findings

Large deviations reveal when EFT descriptions break down due to microphysical effects.

The phase transition to eternal inflation is characterized by instanton saddle points.

Primordial black hole production involves tail behaviors governed by microscopic physics.

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.