Towards a dS/MERA correspondence

TL;DR

This paper proposes a tensor network-based approach to model the emergence of de Sitter spacetime from boundary conformal theories, extending the MERA framework from AdS to de Sitter space and exploring cosmological implications.

Contribution

It introduces a novel dS/MERA correspondence, providing a discrete model of de Sitter spacetime and its horizons using tensor networks, which was not previously established.

Findings

Recovered a discrete de Sitter Penrose diagram using MERA.

Suggested entanglement across the cosmological horizon relates to horizon entropy.

Proposed emergent time as a consequence of the tensor network structure.

Abstract

Recent advances have suggested that spacetime itself emerges from the entanglement of the quantum degrees of freedom living on the boundary. In the case of the AdS spacetimes, a particular class of tensor networks has been shown to realize the same via Multi-Scale Entanglement Renormalization Ansatz (MERA). In this paper we suggest a prescription for the dS/MERA correspondence and recover a discrete version of de Sitter Penrose diagram by using the MERA on conformal theories identified with the future/past conformal boundaries of the de Sitter spacetime. As anticipated, time appears as the emergent direction. We comment on the possible interpretation that the de Sitter cosmological horizon entropy involves entanglement with degrees of freedom across the cosmological horizon as well as the implications of our construction for cosmology.