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Published December 15, 2017 | Published + Submitted
Journal Article Open

de Sitter space as a tensor network: Cosmic no-hair, complementarity, and complexity


We investigate the proposed connection between de Sitter spacetime and the multiscale entanglement renormalization ansatz (MERA) 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 space. 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.

Additional Information

© 2017 American Physical Society. Received 6 October 2017; published 29 December 2017. We thank Aleksander Kubica, Yasunori Nomura, Jason Pollack, and Grant Remmen for helpful discussions. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, as well as by the Walter Burke Institute for Theoretical Physics at Caltech and the Foundational Questions Institute.

Attached Files

Published - PhysRevD.96.123536.pdf

Submitted - 1709.03513.pdf


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