A Conformal Field Theory for Eternal Inflation

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.

30 pages, 8 figures

References in corpus (5)

• The Anthropic Landscape of String Theory
• A Holographic Framework for Eternal Inflation
• The cosmic microwave background temperature bispectrum from scalar perturbations induced by primordial magnetic fields
• Holographic Multiverse
• Eternal Inflation, Bubble Collisions, and the Disintegration of the Persistence of Memory

Cited by in corpus (21)

• Analytic Continuation of Liouville Theory
• Eternal Symmetree
• How to Run Through Walls: Dynamics of Bubble and Soliton Collisions
• Cosmic Bubble Collisions
• Eternal Inflation, Bubble Collisions, and the Disintegration of the Persistence of Memory
• Holographic multiverse and conformal invariance
• Conformal Correlation Functions in the Brownian Loop Soup
• On the Topological Phases of Eternal Inflation
• Cosmic curvature from de Sitter equilibrium cosmology
• Higher Spin de Sitter Hilbert Space
• de Sitter Harmonies: Cosmological Spacetimes as Resonances
• The Three Faces of a Fixed Point
• Tensor modes on the string theory landscape
• Is Eternal Inflation Past-Eternal? And What if It Is?
• Scalar Three-point Functions in a CDL Background
• Defect CFTs and holographic multiverse
• The grainy multiverse
• Exact Correlation Functions in the Brownian Loop Soup
• Scalar conformal primary fields in the Brownian loop soup
• New Recipes for Brownian Loop Soups
• Transition Amplitudes in de Sitter Space