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arXiv · 1709.03513

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

Ning Bao·ChunJun Cao·Sean M. Carroll·Aidan Chatwin-Davies
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Abstract

We investigate the proposed connection between de Sitter spacetime and the MERA (Multiscale Entanglement Renormalization Ansatz) tensor network, and ask what can be learned via such a construction. We show that the quantum state obeys a cosmic no-hair theorem: the reduced density operator describing a causal patch of the MERA asymptotes to a fixed point of a quantum channel, just as spacetimes with a positive cosmological constant asymptote to de Sitter. The MERA is potentially compatible with a weak form of complementarity (local physics only describes single patches at a time, but the overall Hilbert space is infinite-dimensional) or, with certain specific modifications to the tensor structure, a strong form (the entire theory describes only a single patch plus its horizon, in a finite-dimensional Hilbert space). We also suggest that de Sitter evolution has an interpretation in terms of circuit complexity, as has been conjectured for anti-de Sitter space.

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Ning Bao, ChunJun Cao, Sean M. Carroll, Aidan Chatwin-Davies. 2017-09-11. De Sitter Space as a Tensor Network: Cosmic No-Hair, Complementarity, and Complexity. https://doi.org/10.1103/physrevd.96.123536

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