Abstract
We study holographic volume complexity for various families of holographic cosmologies with Kasner-like singularities, in particular with AdS, hyperscaling violating and Lifshitz asymptotics. We find through extensive numerical studies that the complexity surface always bends in the direction away from the singularity and transitions from spacelike near the boundary to lightlike in the interior. As the boundary anchoring time slice approaches the singularity, the transition to lightlike is more rapid, with the spacelike part shrinking. The complexity functional has vanishing contributions from the lightlike region so in the vicinity of the singularity, complexity is vanishingly small, indicating a dual Kasner state of vanishingly low complexity, suggesting an extreme thinning of the effective degrees of freedom dual to the near singularity region. We also develop further previous studies on extremal surfaces for holographic entanglement entropy, and find that in the IR limit they reveal similar behaviour as complexity.
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Acknowledgments
We (especially KN) are particularly grateful to Sumit Das for very insightful early discusssions on low holographic complexity in the vicinity of cosmological singularities. We also thank Pawel Caputa, Abhijit Gadde, Alok Laddha, A. Manu and Rob Myers for useful discussions, and Sumit Das and Rob Myers for useful comments on a draft. GY would also like to thank Krishna Jalan, Pankaj Saini, Harsh Rana and Ashutosh Singh for helpful discussions about numerical calculations. GY would like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme “Bridges between holographic quantum information and quantum gravity” while this work was in progress. We thank the organizers of the Indian Strings Meeting 2023 (ISM2023), IIT Bombay, for hospitality while this work was in progress. This work is partially supported by a grant to CMI from the Infosys Foundation and by EPSRC Grant Number EP/R0146014/1.
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Narayan, K., Saini, H.K. & Yadav, G. Cosmological singularities, holographic complexity and entanglement. J. High Energ. Phys. 2024, 125 (2024). https://doi.org/10.1007/JHEP07(2024)125
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DOI: https://doi.org/10.1007/JHEP07(2024)125