Census Taking in the Hat: FRW/CFT Duality

TL;DR

<3-5 sentence high-level summary> The paper proposes a holographic FRW/CFT duality in which the interior of a CDL bubble ending in a hat is encoded by a 2D boundary CFT with Liouville gravity on $\Sigma$, and the Census Taker’s observations map to boundary correlators. Time emerges from the boundary theory via an RG flow along two lightlike directions $T^-$ and $T^+$, with RG-covariant and RG-invariant components corresponding to bulk holographic data. Scalar and metric correlators decompose into these components, providing a framework to study bubble collisions, memory effects, and symmetry breaking in eternal inflation. The central charge is tied to the ancestor horizon area, and Liouville dynamics implement the dynamical notion of time, enabling a boundary description of cosmological evolution and observational consequences for the CT sky.

Abstract

In this paper a holographic description of eternal inflation is developed. We focus on the description of an open FRW universe that results from a tunneling event in which a false vacuum with positive vacuum energy decays to a supersymmetric vacuum with vanishing cosmological constant. The observations of a "Census Taker" in the final vacuum can be organized into a holographic dual conformal field theory that lives on the asymptotic boundary of space. We refer to this bulk-boundary correspondence as FRW/CFT duality. The dual CFT is a Euclidean two-dimensional theory that includes a Liouville 2-D gravity sector describing geometric fluctuations of the boundary. The RG flow of the theory is richer than in the ADS/CFT correspondence, and generates two space-time dimensions--one space-like and one time-like. We discuss a number of phenomena such as bubble collisions, and the Garriga, Guth, Vilenkin "persistence of memory," from the dual viewpoint.

Figures (16)

• Figure 1: Conformal diagram for ordinary flat Minkowski space. The causal patch associated with the "Census Bureau" at $t=\infty$ is the entire space-time.
• Figure 2: Conformal diagrams for eternal de Sitter space. The causal past of the Census Bureau at $\bf{a}$ is shown in grey.
• Figure 3: A Conformal diagram for the FRW universe created by bubble nucleation from an "Ancestor" metastable vacuum. The Ancestor vacuum is shown in green. The red and blue curves are surfaces of constant $T$ and $R$. The two-sphere at spatial infinity is indicated by $\Sigma$.
• Figure 4: The Census Taker is indicated by the red dot. The thin black lines represent his past light-cone and the blue curve is a space-like surface of constant $T$.
• Figure 5: Escher's drawing of the Hyperbolic Plane, which represents Euclidean anti de Sitter space or a spatial slice of open FRW. The green circle shows the intersection of the Census Taker's past light-cone, which moves toward the boundary with Census-Taker-time.