The Census Taker's Hat

TL;DR

The Census Taker framework proposes a holographic description of an open FRW cosmology (the hat) as a boundary 2D field theory on Σ, where time emerges from the RG flow of a Liouville sector that complements boundary matter. Boundary correlators include a leading dimension-2 TT term signaling a 2D CFT and a dimension-zero piece that motivates a Liouville description; the central charge connects to the Ancestor horizon entropy, while the c-theorem governs RG flow and entropy bounds. Bubble collisions and the Persistence of Memory provide a bridge between bulk eternal inflation phenomenology and boundary RG structure, suggesting a measure-like role for Census Taker data in exploring the Landscape. The program yields a coherent picture in which bulk cosmology maps to a boundary theory with proactive and reactive quantities, where time is an emergent, Liouville-driven and RG-controlled variable, with observable consequences in angular correlations and symmetry breaking. Practical implications include a potential boundary-based measure on the Landscape and a framework to interpret spatially anisotropic footprints as RG-flow–driven boundary phenomena, rather than fundamental bulk features.

Abstract

If the observable universe really is a hologram, then of what sort? Is it rich enough to keep track of an eternally inflating multiverse? What physical and mathematical principles underlie it? Is the hologram a lower dimensional quantum field theory, and if so, how many dimensions are explicit, and how many "emerge?" Does the Holographic description provide clues for defining a probability measure on the Landscape? The purpose of this lecture is first, to briefly review a proposal for a holographic cosmology by Freivogel, Sekino, Susskind, and Yeh (FSSY), and then to develop a physical interpretation in terms of a "Cosmic Census Taker:" an idea introduced in reference [1]. The mathematical structure--a hybrid of the Wheeler DeWitt formalism and holography--is a boundary "Liouville" field theory, whose UV/IR duality is closely related to the time evolution of the Census Taker's observations. That time evolution is represented by the renormalization-group flow of the Liouville theory. Although quite general, the Census Taker idea was originally introduced in \cite{shenker}, for the purpose of counting bubbles that collide with the Census Taker's bubble. The "Persistence of Memory" phenomenon discovered by Garriga, Guth, and Vilenkin, has a natural RG interpretation, as does slow roll inflation. The RG flow and the related C-theorem are closely connected with generalized entropy bounds.

Figures (15)

• Figure 1: Conformal diagram for ordinary flat Minkowski space. The causal patch associated with the "Census Bureau" is the entire space-time. A Census Taker and his past light-cone are also shown.
• Figure 2: Conformal diagrams for eternal and metastable de Sitter space. The grey areas are causal patches associated with the points $\bf{a}$. In the metastable case the causal patch is associated with the tip of a hat.
• 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 blue lines represent his past light-cone.
• 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.