AdS Crunches, CFT Falls And Cosmological Complementarity

TL;DR

This paper explores the holographic duality of crunching AdS cosmologies, showing they correspond to condensates in deformed de Sitter CFTs, and analyzes the implications for de Sitter space-time and black hole formation.

Contribution

It constructs a complementarity map revealing the crunch as a finite-time potential fall and links de Sitter invariance breaking to black hole formation and finite Hilbert space dimension.

Findings

Crunch corresponds to a finite potential energy fall in finite time.

De Sitter invariance breaking leads to black hole formation.

Finite Hilbert space dimension correlates with non-eternal de Sitter.

Abstract

We discuss aspects of the holographic description of crunching AdS cosmologies. We argue that crunching FRW models with hyperbolic spatial sections are dual to semiclassical condensates in deformed de Sitter CFTs. De Sitter-invariant condensates with a sharply defined energy scale are induced by effective negative-definite relevant or marginal operators, which may or may not destabilize the CFT. We find this result by explicitly constructing a `complementarity map' for this model, given by a conformal transformation of the de Sitter CFT into a static time-frame, which reveals the crunch as an infinite potential-energy fall in finite time. We show that, quite generically, the crunch is associated to a finite mass black hole if the de Sitter O(d,1)-invariance is an accidental IR symmetry, broken down to U(1)xO(d) in the UV. Any such regularization cuts off the eternity of de Sitter space-time. Equivalently, the dimension of the Hilbert space propagating into the crunch is finite only when de Sitter is not eternal.