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We investigate the proposed connection between de Sitter spacetime and theMERA (Multiscale Entanglement Renormalization Ansatz) tensor network, and askwhat can be learned via such a construction. We show that the quantum stateobeys a cosmic no-hair theorem: the reduced density operator describing acausal patch of the MERA asymptotes to a fixed point of a quantum channel, justas spacetimes with a positive cosmological constant asymptote to de Sitter. TheMERA is potentially compatible with a weak form of complementarity (localphysics only describes single patches at a time, but the overall Hilbert spaceis infinite-dimensional) or, with certain specific modifications to the tensorstructure, a strong form (the entire theory describes only a single patch plusits horizon, in a finite-dimensional Hilbert space). We also suggest that deSitter evolution has an interpretation in terms of circuit complexity, as hasbeen conjectured for anti-de Sitter space.

De Sitter Space as a Tensor Network: Cosmic No-Hair, Complementarity, and Complexity