Holographic black hole cosmologies

Abstract

We describe and study a holographic construction of big-bang / big-crunch cosmological spacetimes where the matter consists of a lattice of black holes. The cosmological spacetime is dual to an entangled state of a collection of holographic CFTs associated with the second asymptotic regions of the black holes. For a cosmology with spatial slice geometry $Σ$, this state is constructed via a Euclidean path integral for the CFT on a geometry obtained by connecting two copies of $Σ$ by a lattice of tubes. In three-dimensional gravity, we describe the cosmological solutions and the associated Euclidean saddles explicitly. For the case of (globally) flat cosmology, we determine when the Euclidean solution associated with the cosmology provides the dominant saddle compared to other natural candidates that preserve the symmetries of the boundary space. We find that the cosmological saddle dominates when the black holes are sufficiently large and close together. Our cosmology has a mixed state version where the physics behind the black hole horizons is unspecified and the Euclidean construction involves a pair of CFTs with an ensemble of operator insertions correlated between the two CFTs. Various purifications (adding second asymptotic regions for the black holes) correspond to various ways to promote this ensemble to an interaction by adding auxiliary degrees of freedom that couple the two CFTs in the Euclidean picture. These auxiliary degrees of freedom provide a Hilbert space for the cosmology in the Lorentzian picture.