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Cosmology at the end of the world

Nature Physics volume 16, pages 881–886 (2020)Cite this article

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Abstract

In the last two decades the anti-de Sitter/conformal field theory (AdS/CFT) correspondence has emerged as a focal point of many research interests. In particular, it functions as a stepping stone to a still-missing full quantum theory of gravity. In this context, a pivotal question is if and how cosmological physics can be studied using AdS/CFT. Motivated by string theory, braneworld cosmologies propose that our universe is a four-dimensional membrane embedded in a bulk five-dimensional AdS spacetime. We show how such a scenario can be microscopically realized in AdS/CFT using special field theory states dual to an ‘end-of-the-world brane’ moving in a charged black hole spacetime. Observers on the brane experience cosmological physics and approximately four-dimensional gravity, at least locally in spacetime. This result opens a path towards a description of quantum cosmology and the simulation of cosmology on quantum machines.

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Fig. 1: Brane trajectory.
Fig. 2: Euclidean brane trajectory.
Fig. 3: Euclidean-sensible solutions.
Fig. 4: Potential Vk[y(r*)]—large black hole.
Fig. 5: Quasibound mode.

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Code availability

The code used in this study is available from the corresponding author upon reasonable request.

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Acknowledgements

This work was supported in part by the US Department of Energy, Office of Science, Office of High Energy Physics QuantISED Award DE-SC0019380 and by the Simons Foundation via the It from Qubit collaboration. We thank M. Van Raamsdonk, C. Waddell, D. Wakeham, M. Rozali, S. Cooper, R. Sundrum, R. Bousso, S. Kumar, Y. Wang and J. Maldacena for discussions.

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Authors and Affiliations

  1. Maryland Center for Fundamental Physics and Department of Physics, University of Maryland, College Park, MD, USA

    Stefano Antonini & Brian Swingle

  2. Condensed Matter Theory Center and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, USA

    Brian Swingle

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  1. Stefano Antonini
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The authors contributed equally to this work.

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Correspondence to Stefano Antonini.

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Peer review information Nature Physics thanks Neven Bilic, Tadashi Takayanagi and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Action difference - Large black hole.

Results for four spatial dimensions (d = 4). We set the outer horizon radius to be r+ = 100, with the AdS length given by LAdS = 1. a, We chose r− = 50 for the inner horizon radius. When the tension T is not too close to its critical value Tcrit = 1/LAdS = 1, the preparation time τ0 is positive (i.e. the solution is Euclidean-sensible) and the action difference ΔI is negative, meaning that the non-extremal phase is always dominant in the path integral. b, For a near-critical brane (we chose a value T = 0.99999 ~ Tcrit for the brane tension), when the black hole is sufficiently close to extremality (i.e. r− → r+), the preparation time τ0 becomes positive, and therefore the Euclidean solution is sensible. The non-extremal phase is already dominant in the ensemble (i.e. the action difference ΔI is negative) well before it happens. The same properties hold also for the small black hole case.

Extended Data Fig. 2 Proper brane trajectory r(λ).

Results for four spatial dimensions (d = 4), where we chose the AdS length to be LAdS = 1. a, Brane radius r(λ) as a function of the brane proper time λ for a subcritical brane of tension T = 0.89. During its trajectory, the brane radius expands to a maximum value r0 larger than the black hole outer horizon r+ = 100, and shrinks to a minimum value \({r}_{0}^{-}\) smaller than the black hole inner horizon r− = 91. b, For larger values of the brane tension (T = 0.99999 ~ Tcrit = 1/LAdS = 1) and a near-extremal black hole (r+ = 100, r− = 99.9), the maximum radius of the brane r0 is larger, and the inversion at the minimum radius \({r}_{0}^{-}\) becomes sharper. In both cases the brane trajectory resembles the one qualitatively described in Fig. 1 of the main paper.

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Supplementary Information

Supplementary discussion, Figs. 1–13 and Table 1.

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Antonini, S., Swingle, B. Cosmology at the end of the world. Nat. Phys. 16, 881–886 (2020). https://doi.org/10.1038/s41567-020-0909-6

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