A Conformal Field Theory for Eternal Inflation

TL;DR

This paper introduces a conformally invariant statistical model inspired by cosmic bubble distributions in de Sitter space, providing analytical correlation functions and insights into its conformal properties across dimensions.

Contribution

The authors develop a conformal field theory-like model for cosmic bubble distributions, calculating key correlation functions and exploring its conformal invariance and relation to percolation models.

Findings

Correlation functions are free of infrared divergences.

The model exhibits conformal invariance and charge conservation.

An approximate central charge can be computed in 2D.

Abstract

We study a statistical model defined by a conformally invariant distribution of overlapping spheres in arbitrary dimension d. The model arises as the asymptotic distribution of cosmic bubbles in d+1 dimensional de Sitter space, and also as the asymptotic distribution of bubble collisions with the domain wall of a fiducial "observation bubble" in d+2 dimensional de Sitter space. In this note we calculate the 2-,3-, and 4-point correlation functions of exponentials of the "bubble number operator" analytically in d=2. We find that these correlators, when carefully defined, are free of infrared divergences, covariant under the global conformal group, charge conserving, and transform with positive conformal dimensions that are related in a novel way to the charge. Although by themselves these operators probably do not define a full-fledged conformal field theory, one can use the partition function on a sphere to compute an approximate central charge in the 2D case. The theory in any dimension has a noninteracting limit when the nucleation rate of the bubbles in the bulk is very large. The theory in two dimensions is related to some models of continuum percolation, but it is conformal for all values of the tunneling rate.