Abstract
The de Sitter (dS) entropy bound gives the maximal number of e-folds that non-eternal inflation can last before violating the thermodynamical interpretation of dS space. This semiclassical argument is the analogue, for dS space, of the Black-Hole information paradox. We use techniques developed to address the latter, namely the island formula, to calculate semiclassically the fine-grained entropy as seen by a Minkowskian observer after inflation and find that this follows a Page-like curve, never exceeding the thermodynamic dS entropy. This calculation, performed for a CFT in 2D gravity, suggests that the semiclassical expectation should be modified in such a way that the entropy bound might actually not be present.
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References
N. Arkani-Hamed, S. Dubovsky, A. Nicolis, E. Trincherini and G. Villadoro, A Measure of de Sitter entropy and eternal inflation, JHEP 05 (2007) 055 [arXiv:0704.1814] [INSPIRE].
S.W. Hawking, Breakdown of Predictability in Gravitational Collapse, Phys. Rev. D 14 (1976) 2460 [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, JHEP 03 (2022) 205 [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. 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].
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].
D.N. Page, Information in black hole radiation, Phys. Rev. Lett. 71 (1993) 3743 [hep-th/9306083] [INSPIRE].
D.N. Page, Time Dependence of Hawking Radiation Entropy, JCAP 09 (2013) 028 [arXiv:1301.4995] [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].
L. Aalsma and W. Sybesma, The Price of Curiosity: Information Recovery in de Sitter Space, JHEP 05 (2021) 291 [arXiv:2104.00006] [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 [Addendum ibid. 05 (2022) 137] [arXiv:2108.01278] [INSPIRE].
J. Kames-King, E.M.H. Verheijden and E.P. Verlinde, No Page curves for the de Sitter horizon, JHEP 03 (2022) 040 [arXiv:2108.09318] [INSPIRE].
E. Shaghoulian, The central dogma and cosmological horizons, JHEP 01 (2022) 132 [arXiv:2110.13210] [INSPIRE].
R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].
A. Almheiri and J. Polchinski, Models of AdS2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
J. Maldacena, G.J. Turiaci and Z. Yang, Two dimensional Nearly de Sitter gravity, JHEP 01 (2021) 139 [arXiv:1904.01911] [INSPIRE].
J. Cotler, K. Jensen and A. Maloney, Low-dimensional de Sitter quantum gravity, JHEP 06 (2020) 048 [arXiv:1905.03780] [INSPIRE].
P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152] [INSPIRE].
H. Casini, C.D. Fosco and M. Huerta, Entanglement and alpha entropies for a massive Dirac field in two dimensions, J. Stat. Mech. 0507 (2005) P07007 [cond-mat/0505563] [INSPIRE].
R. Bousso, Z. Fisher, S. Leichenauer and A.C. Wall, Quantum focusing conjecture, Phys. Rev. D 93 (2016) 064044 [arXiv:1506.02669] [INSPIRE].
S. Dubovsky, L. Senatore and G. Villadoro, The Volume of the Universe after Inflation and de Sitter Entropy, JHEP 04 (2009) 118 [arXiv:0812.2246] [INSPIRE].
G. Dvali and C. Gomez, Quantum Exclusion of Positive Cosmological Constant?, Annalen Phys. 528 (2016) 68 [arXiv:1412.8077] [INSPIRE].
G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, de Sitter Space and the Swampland, arXiv:1806.08362 [INSPIRE].
S.K. Garg and C. Krishnan, Bounds on Slow Roll and the de Sitter Swampland, JHEP 11 (2019) 075 [arXiv:1807.05193] [INSPIRE].
G. Dvali, On S-Matrix Exclusion of de Sitter and Naturalness, arXiv:2105.08411 [INSPIRE].
H. Ooguri, E. Palti, G. Shiu and C. Vafa, Distance and de Sitter Conjectures on the Swampland, Phys. Lett. B 788 (2019) 180 [arXiv:1810.05506] [INSPIRE].
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Teresi, D. Islands and the de Sitter entropy bound. J. High Energ. Phys. 2022, 179 (2022). https://doi.org/10.1007/JHEP10(2022)179
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DOI: https://doi.org/10.1007/JHEP10(2022)179