A new observable for holographic cosmology

TL;DR

This paper introduces a generalized double-cone geometry incorporating Lorentzian cosmology, providing a new observable in holographic cosmology and connecting bulk geometries with boundary CFT correlations.

Contribution

It extends the double-cone geometry to include cosmological solutions with big bang/crunch singularities, satisfying stability criteria and offering a novel boundary CFT interpretation.

Findings

Regulated cosmological geometries satisfy the Kontsevich-Segal criterion.

New contributions to boundary CFT two-point functions involving different black hole microstates.

Describes correlations between heavy states and near-BTZ threshold states.

Abstract

The double-cone geometry is a saddle of the gravitational path integral, which explains the chaotic statistics of the spectrum of black hole microstates. This geometry is the usual AdS-Schwarzschild black hole, but with a periodic identification of the time coordinate; the resulting singularity at the black hole horizon is regulated by making the geometry slightly complex. Here, we consider generalizations of the double-cone geometry which include the Lorentzian cosmology that sits between the event horizon and the black hole singularity. We analyze this in two and three dimensions, where the cosmology has compact spatial sections and big bang/crunch singularities. These singularities are regulated in the same way by slightly complexifying the metric. We show that this is possible while satisfying the Kontsevich-Segal criterion, implying that these geometries can be interpreted as perturbatively stable saddle points in general relativity. This procedure leads to a novel description of the cosmology in terms of standard observables in the dual boundary CFT. In three dimensions, the cosmological solution gives a new contribution to the two-point function of the density of states in the boundary CFT. Unlike the usual double cone, it describes correlations between black hole microstates with different masses, and in a limit describes correlations between the statistics of heavy states and states near the BTZ threshold.