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Computational complexity of the landscape. II: Cosmological considerations. (English) Zbl 1390.83337
Summary: We propose a new approach for multiverse analysis based on computational complexity, which leads to a new family of “computational” measure factors. By defining a cosmology as a space-time containing a vacuum with specified properties (for example small cosmological constant) together with rules for how time evolution will produce the vacuum, we can associate global time in a multiverse with clock time on a supercomputer which simulates it. We argue for a principle of “limited computational complexity” governing early universe dynamics as simulated by this supercomputer, which translates to a global measure for regulating the infinities of eternal inflation. The rules for time evolution can be thought of as a search algorithm, whose details should be constrained by a stronger principle of “minimal computational complexity”. Unlike previously studied global measures, ours avoids standard equilibrium considerations and the well-known problems of Boltzmann Brains and the youngness paradox. We also give various definitions of the computational complexity of a cosmology, and argue that there are only a few natural complexity classes.

MSC:
83E30 String and superstring theories in gravitational theory
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83F05 Cosmology
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[1] Denef, F.; Douglas, M. R., Ann. Physics, 322, 1096-1142, (2007), arXiv:hep-th/0602072 [hep-th]
[2] A. Vilenkin, Royal Astronomical Society National Astronomy Meeting (NAM 2011) Llandudno, North Wales, United Kingdom, April 17-21, 2011, 2011 arXiv:1108.4990 [hep-th].
[3] Garriga, J.; Schwartz-Perlov, D.; Vilenkin, A.; Winitzki, S., J. Cosmol. Astropart. Phys., 0601, 017, (2006), arXiv:hep-th/0509184 [hep-th]
[4] Brown, A. R.; Roberts, D. A.; Susskind, L.; Swingle, B.; Zhao, Y., Phys. Rev. Lett., 116, 19, 191301, (2016), arXiv:1509.07876 [hep-th]
[5] Garriga, J.; Vilenkin, A., J. Cosmol. Astropart. Phys., 1305, 037, (2013), arXiv:1210.7540 [hep-th]
[6] Guth, A. H., Phys. Rep., 333, 555-574, (2000), arXiv:astro-ph/0002156 [astro-ph]
[7] Guth, A. H., J. Phys. A, 40, 6811-6826, (2007), arXiv:hep-th/0702178 [hep-th]
[8] Freivogel, B., Classical Quantum Gravity, 28, 204007, (2011), arXiv:1105.0244 [hep-th]
[9] P.J. Steinhardt, Nuffield Workshop on the Very Early Universe Cambridge, England, June 21-July 9, 1982, 1982, pp. 251-266.
[10] A.D. Linde, Nonsingular Regenerating Inflationary Universe.
[11] A.D. Linde, Nuffield Workshop on the Very Early Universe Cambridge, England, June 21-July 9, 1982, 1982, pp. 205-249.
[12] Vilenkin, A., Phys. Rev. D, 27, 2848, (1983)
[13] Lindé, A. D., Modern Phys. Lett. A, 1, 81, (1986)
[14] Lindé, A. D.; Lindé, D. A.; Mezhlumian, A., Phys. Rev. D, 49, 1783-1826, (1994), arXiv:gr-qc/9306035 [gr-qc]
[15] Coleman, S. R.; Luccia, F. D., Phys. Rev. D, 21, 3305, (1980)
[16] Simone, A. D.; Guth, A. H.; Linde, A. D.; Noorbala, M.; Salem, M. P.; Vilenkin, A., Phys. Rev. D, 82, 063520, (2010), arXiv:0808.3778 [hep-th]
[17] Hartle, J. B.; Hawking, S. W., Phys. Rev. D, 28, 2960-2975, (1983)
[18] Schwartz-Perlov, D.; Vilenkin, A., J. Cosmol. Astropart. Phys., 0606, 010, (2006), arXiv:hep-th/0601162 [hep-th]
[19] M.R. Douglas, Strings, Gauge Fields, and the Geometry Behind: The legacy of Maximilian Kreuzer, in: A. Rebhan, L. Katzarkov, J. Knapp, R. Rashkov, and E. Scheidegger, (Eds.) 2012 pp. 261-288 arXiv:1204.6626 [hep-th].
[20] J.J. Halliwell, 7th Jerusalem Winter School for Theoretical Physics: Quantum Cosmology and Baby Universes Jerusalem, Israel, 27 December 1989 - 4 January 1990, pp. 159-243. 1990 arXiv:0909.2566 [gr-qc].
[21] T. Cubitt, A. Montanaro, S. Piddock, Universal Quantum Hamiltonians, arXiv:1701.05182 [quant-ph].
[22] Garriga, J.; Vilenkin, A., Phys. Rev. D, 57, 2230-2244, (1998), arXiv:astro-ph/9707292 [astro-ph]
[23] Weinberg, S., Phys. Rev. Lett., 59, 2607, (1987)
[24] Bousso, R.; Freivogel, B.; Yang, I.-S., Phys. Rev. D, 77, 103514, (2008), arXiv:0712.3324 [hep-th]
[25] Lindé, A. D., J. Cosmol. Astropart. Phys., 0706, 017, (2007), arXiv:0705.1160 [hep-th]
[26] Lindé, A. D.; Vanchurin, V.; Winitzki, S., J. Cosmol. Astropart. Phys., 0901, 031, (2009), arXiv:0812.0005 [hep-th]
[27] Lindé, A. D.; Mezhlumian, A., Phys. Lett. B, 307, 25-33, (1993), arXiv:gr-qc/9304015 [gr-qc]
[28] Bousso, R.; Zukowski, C., Phys. Rev. D, 87, 10, 103504, (2013), arXiv:1211.7021 [hep-th]
[29] Ashok, S.; Douglas, M. R., J. High Energy Phys., 01, 060, (2004), arXiv:hep-th/0307049 [hep-th]
[30] Denef, F.; Douglas, M. R., J. High Energy Phys., 05, 072, (2004), arXiv:hep-th/0404116 [hep-th]
[31] Taylor, W.; Wang, Y.-N., J. High Energy Phys., 12, 164, (2015), arXiv:1511.03209 [hep-th]
[32] Bousso, R.; Polchinski, J., J. High Energy Phys., 06, 006, (2000), arXiv:hep-th/0004134 [hep-th]
[33] Greene, B.; Kagan, D.; Masoumi, A.; Mehta, D.; Weinberg, E. J.; Xiao, X., Phys. Rev. D, 88, 2, 026005, (2013), arXiv:1303.4428 [hep-th]
[34] Susskind, L., Fortschr. Phys., 64, 24-43, (2016), arXiv:1403.5695 [hep-th]
[35] Brown, A. R.; Roberts, D. A.; Susskind, L.; Swingle, B.; Zhao, Y., Phys. Rev. D, 93, 8, 086006, (2016), arXiv:1512.04993 [hep-th]
[36] Gibbons, G. W.; Hawking, S. W., Phys. Rev. D, 15, 2752-2756, (1977)
[37] Hayward, G., Phys. Rev. D, 47, 3275-3280, (1993)
[38] Brill, D.; Hayward, G., Phys. Rev. D, 50, 4914-4919, (1994), arXiv:gr-qc/9403018 [gr-qc]
[39] Lehner, L.; Myers, R. C.; Poisson, E.; Sorkin, R. D., Phys. Rev. D, 94, 8, 084046, (2016), arXiv:1609.00207 [hep-th]
[40] Chapman, S.; Marrochio, H.; Myers, R. C., J. High Energy Phys., 01, 062, (2017), arXiv:1610.08063 [hep-th]
[41] Carmi, D.; Myers, R. C.; Rath, P., J. High Energy Phys., 03, 118, (2017), arXiv:1612.00433 [hep-th]
[42] Maltz, J., Phys. Rev. D, 95, 6, 066006, (2017), arXiv:1611.03491 [hep-th]
[43] Maltz, J.; Susskind, L., Phys. Rev. Lett., 118, 10, 101602, (2017), arXiv:1611.00360 [hep-th]
[44] Papadimitriou, C. H., Computational Complexity, (1994), Addison-Wesley · Zbl 0833.68049
[45] Arora, S.; Barak, B., Computational Complexity - A Modern Approach, (2009), Cambridge University Press, http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521424264 · Zbl 1193.68112
[46] Aaronson, S., Quantum Computing since Democritus, (2013), Cambridge University Press, http://www.cambridge.org/de/academic/subjects/physics/quantum-physics-quantum-information-and-quantum-computation/quantum-computing-democritus?format=PB
[47] Aaronson, S., Electron. Colloq. Comput. Complexity (ECCC), 24, 4, (2017), https://eccc.weizmann.ac.il/report/2017/004
[48] B.S. Acharya, M.R. Douglas, A finite landscape? arXiv:hep-th/0606212 [hep-th].
[49] Arvanitaki, A.; Dimopoulos, S.; Dubovsky, S.; Kaloper, N.; March-Russell, J., Phys. Rev. D, 81, 123530, (2010), arXiv:0905.4720 [hep-th]
[50] M.R. Douglas, Computational Complexity of Cosmology in String Theory, JHS 75, Caltech. Invited Talk, November 2016. Slides and video available at https://burkeinstitute.caltech.edu/workshops/JHS75.
[51] M.R. Douglas, Computational Complexity of Cosmology in String Theory, New Horizons in Inflationary Cosmology, Stanford ITP. Invited Talk, March 2017. Slides and video available at https://sitp.stanford.edu/conferences/new-horizons-inflationary-cosmology.
[52] M.R. Douglas, Computational Complexity of Cosmology in String Theory, Chris Hull Fest, Imperial College. Invited Talk, April 2017.
[53] N. Bao, R. Bousso, S. Jordan, B. Lackey, Fast optimization algorithms and the cosmological constant, arXiv:1706.08503 [hep-th].
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