Abstract
Following [1], we study quantum extremal surfaces in various families of cosmologies with Big-Crunch singularities, by extremizing the generalized entropy in 2-dimensional backgrounds which can be thought of as arising from dimensional reduction. Focussing first on the isotropic AdS Kasner case, introducing a spatial regulator enables relating the locations in time of the quantum extremal surface and the observer. This shows that the quantum extremal surface lags behind the observer location. A potential island-like region, upon analysing more closely near the island boundary, turns out to be inconsistent. Similar results arise for other holographic cosmologies. We then study certain families of null Kasner singularities where we find that the quantum extremal surface can reach the near singularity region although the on-shell generalized entropy is generically singular. We also study other cosmologies including de Sitter (Poincare slicing) and FRW cosmologies under certain conditions.
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References
A. Manu, K. Narayan and P. Paul, Cosmological singularities, entanglement and quantum extremal surfaces, JHEP 04 (2021) 200 [arXiv:2012.07351] [INSPIRE].
G. Penington, Entanglement Wedge Reconstruction and the Information Paradox, JHEP 09 (2020) 002 [arXiv:1905.08255] [INSPIRE].
A. Almheiri, N. Engelhardt, D. Marolf and H. Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole, JHEP 12 (2019) 063 [arXiv:1905.08762] [INSPIRE].
A. Almheiri, R. Mahajan, J. Maldacena and Y. Zhao, The Page curve of Hawking radiation from semiclassical geometry, JHEP 03 (2020) 149 [arXiv:1908.10996] [INSPIRE].
G. Penington, S.H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior, arXiv:1911.11977 [INSPIRE].
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, Replica Wormholes and the Entropy of Hawking Radiation, JHEP 05 (2020) 013 [arXiv:1911.12333] [INSPIRE].
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, The entropy of Hawking radiation, Rev. Mod. Phys. 93 (2021) 035002 [arXiv:2006.06872] [INSPIRE].
S. Raju, Lessons from the information paradox, Phys. Rept. 943 (2022) 2187 [arXiv:2012.05770] [INSPIRE].
B. Chen, B. Czech and Z.-z. Wang, Quantum information in holographic duality, Rept. Prog. Phys. 85 (2022) 046001 [arXiv:2108.09188] [INSPIRE].
T. Kibe, P. Mandayam and A. Mukhopadhyay, Holographic spacetime, black holes and quantum error correcting codes: A review, arXiv:2110.14669 [INSPIRE].
T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [INSPIRE].
N. Engelhardt and A.C. Wall, Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime, JHEP 01 (2015) 073 [arXiv:1408.3203] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
M. Rangamani and T. Takayanagi, Holographic Entanglement Entropy, Lect. Notes Phys. 931 (2017) 1 [arXiv:1609.01287] [INSPIRE].
Y. Chen, V. Gorbenko and J. Maldacena, Bra-ket wormholes in gravitationally prepared states, JHEP 02 (2021) 009 [arXiv:2007.16091] [INSPIRE].
T. Hartman, Y. Jiang and E. Shaghoulian, Islands in cosmology, JHEP 11 (2020) 111 [arXiv:2008.01022] [INSPIRE].
C. Krishnan, Critical Islands, JHEP 01 (2021) 179 [arXiv:2007.06551] [INSPIRE].
M. Van Raamsdonk, Comments on wormholes, ensembles, and cosmology, JHEP 12 (2021) 156 [arXiv:2008.02259] [INSPIRE].
V. Balasubramanian, A. Kar and T. Ugajin, Islands in de Sitter space, JHEP 02 (2021) 072 [arXiv:2008.05275] [INSPIRE].
W. Sybesma, Pure de Sitter space and the island moving back in time, Class. Quant. Grav. 38 (2021) 145012 [arXiv:2008.07994] [INSPIRE].
S. Choudhury et al., Circuit Complexity from Cosmological Islands, Symmetry 13 (2021) 1301 [arXiv:2012.10234] [INSPIRE].
R. Bousso and A. Shahbazi-Moghaddam, Island Finder and Entropy Bound, Phys. Rev. D 103 (2021) 106005 [arXiv:2101.11648] [INSPIRE].
H. Geng, Y. Nomura and H.-Y. Sun, Information paradox and its resolution in de Sitter holography, Phys. Rev. D 103 (2021) 126004 [arXiv:2103.07477] [INSPIRE].
S. Fallows and S.F. Ross, Islands and mixed states in closed universes, JHEP 07 (2021) 022 [arXiv:2103.14364] [INSPIRE].
D. Giataganas and N. Tetradis, Entanglement entropy in FRW backgrounds, Phys. Lett. B 820 (2021) 136493 [arXiv:2105.12614] [INSPIRE].
L. Aalsma, A. Cole, E. Morvan, J.P. van der Schaar and G. Shiu, Shocks and information exchange in de Sitter space, JHEP 10 (2021) 104 [arXiv:2105.12737] [INSPIRE].
K. Langhoff, C. Murdia and Y. Nomura, Multiverse in an inverted island, Phys. Rev. D 104 (2021) 086007 [arXiv:2106.05271] [INSPIRE].
S.E. Aguilar-Gutierrez, A. Chatwin-Davies, T. Hertog, N. Pinzani-Fokeeva and B. Robinson, Islands in multiverse models, JHEP 11 (2021) 212 [arXiv:2108.01278] [INSPIRE].
R. Bhattacharya, K. Narayan and P. Paul, Cosmological singularities and 2-dimensional dilaton gravity, JHEP 08 (2020) 062 [arXiv:2006.09470] [INSPIRE].
K. Narayan, Aspects of two-dimensional dilaton gravity, dimensional reduction, and holography, Phys. Rev. D 104 (2021) 026007 [arXiv:2010.12955] [INSPIRE].
D. Grumiller, R. Ruzziconi and C. Zwikel, Generalized dilaton gravity in 2d, SciPost Phys. 12 (2022) 032 [arXiv:2109.03266] [INSPIRE].
S.R. Das, J. Michelson, K. Narayan and S.P. Trivedi, Time dependent cosmologies and their duals, Phys. Rev. D 74 (2006) 026002 [hep-th/0602107] [INSPIRE].
S.R. Das, J. Michelson, K. Narayan and S.P. Trivedi, Cosmologies with Null Singularities and their Gauge Theory Duals, Phys. Rev. D 75 (2007) 026002 [hep-th/0610053] [INSPIRE].
A. Awad, S.R. Das, K. Narayan and S.P. Trivedi, Gauge theory duals of cosmological backgrounds and their energy momentum tensors, Phys. Rev. D 77 (2008) 046008 [arXiv:0711.2994] [INSPIRE].
A. Awad, S.R. Das, S. Nampuri, K. Narayan and S.P. Trivedi, Gauge Theories with Time Dependent Couplings and their Cosmological Duals, Phys. Rev. D 79 (2009) 046004 [arXiv:0807.1517] [INSPIRE].
K. Madhu and K. Narayan, String spectra near some null cosmological singularities, Phys. Rev. D 79 (2009) 126009 [arXiv:0904.4532] [INSPIRE].
N. Engelhardt, T. Hertog and G.T. Horowitz, Holographic Signatures of Cosmological Singularities, Phys. Rev. Lett. 113 (2014) 121602 [arXiv:1404.2309] [INSPIRE].
N. Engelhardt, T. Hertog and G.T. Horowitz, Further Holographic Investigations of Big Bang Singularities, JHEP 07 (2015) 044 [arXiv:1503.08838] [INSPIRE].
N. Engelhardt and G.T. Horowitz, Holographic Consequences of a No Transmission Principle, Phys. Rev. D 93 (2016) 026005 [arXiv:1509.07509] [INSPIRE].
N. Engelhardt and G.T. Horowitz, New Insights into Quantum Gravity from Gauge/gravity Duality, Int. J. Mod. Phys. D 25 (2016) 1643002 [arXiv:1605.04335] [INSPIRE].
B. Craps, Big Bang Models in String Theory, Class. Quant. Grav. 23 (2006) S849 [hep-th/0605199] [INSPIRE].
C.P. Burgess and L. McAllister, Challenges for String Cosmology, Class. Quant. Grav. 28 (2011) 204002 [arXiv:1108.2660] [INSPIRE].
N. Engelhardt and G.T. Horowitz, Entanglement Entropy Near Cosmological Singularities, JHEP 06 (2013) 041 [arXiv:1303.4442] [INSPIRE].
T. Hartman and J. Maldacena, Time Evolution of Entanglement Entropy from Black Hole Interiors, JHEP 05 (2013) 014 [arXiv:1303.1080] [INSPIRE].
P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152] [INSPIRE].
P. Calabrese and J. Cardy, Entanglement entropy and conformal field theory, J. Phys. A 42 (2009) 504005 [arXiv:0905.4013] [INSPIRE].
R. Mahajan, A tutorial on entanglement island computations, in ICTS Bangalore String Seminars, August 26, 2020 [https://youtu.be/7wmpBWGAp44].
A. Almheiri, R. Mahajan and J. Maldacena, Islands outside the horizon, arXiv:1910.11077 [INSPIRE].
J.L.F. Barbón and E. Rabinovici, Holographic complexity and spacetime singularities, JHEP 01 (2016) 084 [arXiv:1509.09291] [INSPIRE].
P. Caputa, D. Das and S.R. Das, Path integral complexity and Kasner singularities, JHEP 01 (2022) 150 [arXiv:2111.04405] [INSPIRE].
G.T. Horowitz and A.R. Steif, Space-Time Singularities in String Theory, Phys. Rev. Lett. 64 (1990) 260 [INSPIRE].
B. Craps, S. Sethi and E.P. Verlinde, A Matrix big bang, JHEP 10 (2005) 005 [hep-th/0506180] [INSPIRE].
C.-S. Chu and P.-M. Ho, Time-dependent AdS/CFT duality and null singularity, JHEP 04 (2006) 013 [hep-th/0602054] [INSPIRE].
F.-L. Lin and W.-Y. Wen, Supersymmetric null-like holographic cosmologies, JHEP 05 (2006) 013 [hep-th/0602124] [INSPIRE].
B. Craps, F. De Roo and O. Evnin, Can free strings propagate across plane wave singularities?, JHEP 03 (2009) 105 [arXiv:0812.2900] [INSPIRE].
K. Narayan, Extremal surfaces in de Sitter spacetime, Phys. Rev. D 91 (2015) 126011 [arXiv:1501.03019] [INSPIRE].
Y. Sato, Comments on Entanglement Entropy in the dS/CFT Correspondence, Phys. Rev. D 91 (2015) 086009 [arXiv:1501.04903] [INSPIRE].
M. Miyaji and T. Takayanagi, Surface/State Correspondence as a Generalized Holography, PTEP 2015 (2015) 073B03 [arXiv:1503.03542] [INSPIRE].
K. Narayan, On extremal surfaces and de Sitter entropy, Phys. Lett. B 779 (2018) 214 [arXiv:1711.01107] [INSPIRE].
K. Narayan, de Sitter future-past extremal surfaces and the entanglement wedge, Phys. Rev. D 101 (2020) 086014 [arXiv:2002.11950] [INSPIRE].
A. Strominger, The dS/CFT correspondence, JHEP 10 (2001) 034 [hep-th/0106113] [INSPIRE].
E. Witten, Quantum gravity in de Sitter space, in Strings 2001: International Conference, (2001) [hep-th/0106109] [INSPIRE].
J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [INSPIRE].
E. Shaghoulian, The central dogma and cosmological horizons, JHEP 01 (2022) 132 [arXiv:2110.13210] [INSPIRE].
M. Trodden and S.M. Carroll, TASI lectures: Introduction to cosmology, in Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 2002): Particle Physics and Cosmology: The Quest for Physics Beyond the Standard Model(s), pp. 703–793 (2004) [astro-ph/0401547] [INSPIRE].
D. Baumann, Inflation, in Theoretical Advanced Study Institute in Elementary Particle Physics: Physics of the Large and the Small, pp. 523–686 (2011) [DOI] [arXiv:0907.5424] [INSPIRE].
H. Geng et al., Inconsistency of islands in theories with long-range gravity, JHEP 01 (2022) 182 [arXiv:2107.03390] [INSPIRE].
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Goswami, K., Narayan, K. & Saini, H.K. Cosmologies, singularities and quantum extremal surfaces. J. High Energ. Phys. 2022, 201 (2022). https://doi.org/10.1007/JHEP03(2022)201
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DOI: https://doi.org/10.1007/JHEP03(2022)201