Crunches, Hats, and a Conjecture

TL;DR

The paper investigates when a quantum gravity dual can precisely describe a cosmology, arguing that dual accuracy cannot exceed the observational limits intrinsic to the spacetime. It analyzes Maldacena's crunch program via the CDL instanton construction, bound-state structure, and analytic continuation, and then surveys several limiting cases (Flat Ancestor, AdS/CFT, Flat Bubble) to connect to FRW/CFT and dS/CFT paradigms. A key result is that many ADS-crunch and dS cases exhibit intrinsic ambiguities set by finite entropy bounds, while hat geometries may admit UV-complete FRW/CFT descriptions; the authors propose a conjecture that the maximal Census Taker’s entropy bound governs dual precision. This framework offers a criterion to assess the UV completeness of cosmological holography and clarifies when FRW/CFT or dS/CFT constructions can be expected to be exact or only approximate.

Abstract

Our purpose in this paper is to discuss criteria for the existence of a precise dual description of a cosmology. A number of exact descriptions exist for flat and anti de Sitter backgrounds and possibly for open FRW universes that nucleate in an eternally inflating background. In addition duals have been proposed for de Sitter space, and for crunching FRW bubbles with negative cosmological constant. In the latter cases there is reason to think the dualities are at best approximate. One of our primary purposes is to analyze the quality of these descriptions, i.e., how exact they can be made. Maldacena's recent discussion of dualities involving crunching FRW cosmologies provides an opportunity for exploring some of these question.

Figures (6)

• Figure 1: The six steps in defining a dual to a crunch.
• Figure 2: Coleman DeLuccia instanton for a transition from de Sitter space to a vacuum with negative cosmological constant . The spherical region to the left is the de Sitter region. The region to the right is a piece of a hyperbolic space with negative curvature.
• Figure 3: The action of the O(3,1) group on the Coleman DeLuccia geometry.
• Figure 4: Buosso-Penrose diagram for the hat geometry.
• Figure 5: Penrose diagram of a UV-complete crunch. The "UV" CFT is shown in blue and the "IR" CFT in pink. The backward lightcone of an observer who hits the crunch is the blue line.