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Singularity, initial conditions and quantum tunneling in modern cosmology

 a,  a, b
a Landau Institute for Theoretical Physics, Russian Academy of Sciences, ul. Kosygina 2, Moscow, 119334, Russian Federation
b Dipartimento di Fizica e Astronomia and Istituto Nazionale di Fizica Nucleare, via Irnerio 46, Bologna, 40126, Italy

The key problems of modern cosmology, such as the cosmological singularity, initial conditions, and the quantum tunneling hypothesis, are discussed. The relationship between the latest cosmological trends and L D Landau’s old ideas is analyzed. Particular attention is given to the oscillatory approach to singularity; quantum tunneling processes determining wave function of the Universe in the presence of a compex scalar field; and the role of quantum corrections in these processes. The classical dynamics of closed models with a real scalar field is investigated from the standpoint of chaotic, fractal, and singularity-avoiding properties.

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Fulltext is also available at DOI: 10.1070/PU1998v041n06ABEH000401
PACS: 98.80.Hw, 98.80.Bp, 04.60.Ds (all)
DOI: 10.1070/PU1998v041n06ABEH000401
URL: https://ufn.ru/en/articles/1998/6/a/
000075347000001
Citation: Khalatnikov I M, Kamenshchik A Yu "Singularity, initial conditions and quantum tunneling in modern cosmology" Phys. Usp. 41 525–542 (1998)
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Оригинал: Халатников И М, Каменщик А Ю «Сингулярность, начальные условия и квантовое туннелирование в современной космологии» УФН 168 593–611 (1998); DOI: 10.3367/UFNr.0168.199806a.0593

References (94) ↓ Cited by (6) Similar articles (4)

  1. Landau L D, Private communication
  2. Bardeen J, Cooper L N, Schrieffer J R Phys. Rev. 108 1175 (1957)
  3. Wilson K G, Kogut J "The renormalization group and the $epsilon$-expansion" Phys. Rep. 12 75 (1974) [Translated into Russian (Moscow: Mir, 1975)]
  4. Penrose R Structure of Space-Time (New York, Amsterdam: W.A. Benjamin, 1968) [Translated into Russian (Moscow: Mir, 1972)]; Hawking S W, Ellis G F R The Large Scale Structure of Space-Time (Cambridge, New York: Cambridge Univ. Press, 1973) [Translated into Russian (Moscow: Mir, 1977)]; Hawking S W, Penrose R Proc. R. Soc. London Ser. A 314 529 (1970)
  5. Khalatnikov I M, Lifshitz E M Phys. Rev. Lett. 24 76 (1970)
  6. Lifshitz E M, Khalatnikov I M Pis’ma Zh. Eksp. Teor. Fiz. 11 200 (1970) [JETP Lett. 11 123 (1970)]
  7. Belinskii V A, Lifshitz E M, Khalatnikov I M Usp. Fiz. Nauk 102 463 (1970) [Sov. Phys. Usp. 13 745 (1971)]
  8. Belinsky V A, Khalatnikov I M Zh. Eksp. Teor. Fiz. 56 1700 (1969) [Sov. Phys. JETP 29 911 (1969)]
  9. Landau L D, Lifshitz E M Teoriya Polya (The Classical Theory of Fields, Moscow: Nauka, 1988) [Translated into English (Oxford: Pergamon Press, 1975)]
  10. Lifshitz E M, Khalatnikov I M Usp. Fiz. Nauk 80 391 (1963) [Sov. Phys. Usp. 6 495 (1964)]
  11. Lifshitz E M, Lifshitz I M, Khalatnikov I M Zh. Eksp. Teor. Fiz. 59 322 (1970) [Sov. Phys. JETP 32 173 (1971)]
  12. Belinskii V A, Khalatnikov I M, Lifshitz E M Adv. Phys. 31 639 (1982)
  13. Khalatnikov I M, Lifshitz E M, Khanin K M, Shchur L N, Sinai Ya G J. Stat. Phys. 38 97 (1985)
  14. Misner C W Phys. Rev. Lett. 22 1071 (1969)
  15. Cornish N J, Levin J J Phys. Rev. D 55 7489 (1997)
  16. Cotsakis S, Lemmer R L, Leach P G L "Adiabatic invariants and Mixmaster catastrophes" Phys. Rev. D 57 4691 (1998); gr-qc/9712027
  17. Hartle J B, Hawking S W Phys. Rev. D 28 2960 (1983); Hawking S W Nucl. Phys. B 239 257 (1984)
  18. Vilenkin A Phys. Lett. B 117 25 (1982); Phys. Rev. D 27 2848 (1983); 30 509 (1984); 37 888 (1988); Linde A D Zh. Eksp. Teor. Fiz. 87 369 (1984) [Sov. Phys. JETP 60 211 (1984)]; Zel’dovich Ya B, Starobinskii A A Pis’ma Astron. Zh. 10 323 (1984) [Sov. Astron. Lett. 10 135 (1984)]; Rubakov V A Phys. Lett. B 148 280 (1984)
  19. Landau L D, Private communication
  20. Al’tshuler B L, Barvinsky A O Usp. Fiz. Nauk 166 459 (1996) [Phys. Usp. 39 429 (1996)]
  21. Halliwell J J, Hartle J B Phys. Rev. D 41 1815 (1990)
  22. Barvinsky A O, Kamenshchik A Yu Phys. Rev. D 50 5093 (1994)
  23. Barvinsky A O, Kamenshchik A Yu, Mishakov I V Nucl. Phys. B 491 387 (1997)
  24. Landau L D, Lifshitz E M Kvantovaya Mekhanika (Quantum Mechanics, Moscow: Nauka, 1974) [Translated into English (Oxford: Pergamon Press, 1977)]
  25. Parker L, Fulling S A Phys. Rev. D 7 2357 (1973)
  26. Starobinskii A A Pis’ma Astron. Zh. 4 155 (1978) [Sov. Astron. Lett. 4 82 (1978)]
  27. Barrow J D, Matzner R A Phys. Rev. D 21 336 (1980)
  28. Hawking S W, in Relativity, Groups and Topology II (Amsterdam: North-Holland Physics Publ., 1984)
  29. Page D N Class. Quantum Grav. 1 417 (1984)
  30. Kamenshchik A Yu, Khalatnikov I M, Toporensky A V Int. J. Mod. Phys. D 6 673 (1997); gr-qc/9801064
  31. Kamenshchik A Yu, Khalatnikov I M, Toporensky A V Int. J. Mod. Phys. D 7 129 (1998)
  32. Khalatnikov I M, Kamenshchik A Yu, Toporensky A V, in Proc. of 5th Course on Current Topics in Astrofundamental Physics, Erice, Italy, September 7-15, 1996 (Eds N Sanchez, A Zichichi, Singapore: World Scientific, 1997) p. 271
  33. Khalatnikov I M, Kamenshchik A Yu Phys. Rep. 288 513 (1997)
  34. Glashow S L, Iliopoulos J, Maiani L Phys. Rev. D 2 1285 (1970)
  35. Green M B, Schwarz J H, Witten E Superstring Theory Vols 1, 2 (Cambridge, New York: Cambridge Univ. Press, 1987) [Translated into Russian (Moscow: Mir, 1990)]; Brink L, Henneaux M Principles of String Theory (New York: Plenum Press, 1988) [Translated into Russian (Moscow: Mir, 1991)]; Polyakov A M Gauge Fields and Strings (New York: Harwood Academic Publ., 1987) [Translated into Russian (Moscow: Landau Institute of Theoretical Physics, 1995)]
  36. Polyakov A M Phys. Lett. B 103 211 (1981)
  37. Linde A D Fizika Elementarnykh Chastits i Inflyatsionnaya Kosmologiya (Particle Physics and Inflationary Cosmology, Moscow: Nauka, 1990) [Translated into English (Chur, Switzerland, New York: Harwood Academic Publ., 1990)]
  38. Barvinsky A O, Kamenshchik A Yu Class. Quantum Grav. 7 L181 (1990)
  39. Barvinsky A O Phys. Rep. 230 237 (1993);
  40. Kamenshchik A Yu Phys. Lett. B 316 45 (1993)
  41. Barvinsky A O, Kamenshchik A Yu Phys. Lett. B 332 270 (1994)
  42. Barvinsky A O, Kamenshchik A Yu Int. J. Mod. Phys. D 5 825 (1996)
  43. Esposito G, Kamenshchik A Yu, Miele G Phys. Rev. D 56 1328 (1997)
  44. Kamenshchik A Yu, Lyakhovich S L Nucl. Phys. B 495 309 (1997)
  45. Khalatnikov I M, Mezhlumian A Phys. Lett. A 169 308 (1992)
  46. Khalatnikov I M, Schiller P Phys. Lett. B 302 176 (1993)
  47. Amendola L, Khalatnikov I M, Litterio M, Occhionero F Phys. Rev. D 49 1881 (1994)
  48. Kamenshchik A Yu, Khalatnikov I M, Toporensky A V Phys. Lett. B 357 36 (1995)
  49. Kamenshchik A Yu, Khalatnikov I M, Toporensky A V Int. J. Mod. Phys. D 6 649 (1997); gr-qc/9801064
  50. Kasner E M Am. J. Math. 43 217 (1921)
  51. Gross D J, Wilczek F Phys. Rev. Lett. 30 1343 (1973); Politzer D H Phys. Rev. Lett. 30 1346 (1973)
  52. Burd A, Buric N, Ellis G F R Gen. Rel. Grav. 22 349 (1990); Hobill D, Bernstein D, Welge M, Simkins D Class. Quantum Grav. 8 1155 (1991)
  53. Ramani A, Grammaticos B, Bountis T Phys. Rep. 180 159 (1989)
  54. Contopoulos G, Grammaticos B, Ramani A J. Phys. A 27 5357 (1994); Demare J, Scheen C J. Phys. A 29 59 (1996); Phys. Lett. B 399 207 (1997)
  55. Belinskii V A, Khalatnikov I M Zh. Eksp. Teor. Fiz. 63 1121 (1972) [Sov. Phys. JETP 36 591 (1973)]
  56. Barrow J D, Dabrowski M P "Is there chaos in low-energy string cosmology?" hep-th/9711049
  57. Gasperini M, Veneziano G Astron. Phys. 1 317 (1993)
  58. Calzetta E, Thibeault M "Perturbative analysis of Bianchi IX using Ashtekar formalism" gr-qc/9710128
  59. Ashtekar A Lectures on Non-Perturbative Quantum Gravity (Singapore: World Scientific, 1991)
  60. Gilmore R Catastrophe Theory for Scientists and Engineers (New York: Wiley, 1981)
  61. Starobinsky A A "Current trends in field theory, quantum gravity and strings" Lect. Notes Phys. 246 (Heidelberg: Springer-Verlag, 1986) p. 107; Kolb E W, Turner M The Early Universe (Frontiers in Physics, Vol. 69, Reading, Mass.: Addison-Wesley, 1990)
  62. Smoot J Aph. J. 396 L1 (1992); Strukov I A et al. Pis’ma Astron. Zh. 18 387 (1992) [Sov. Astron. Lett. 18 153 (1992)]
  63. Starobinskii A A Pis’ma Astron. Zh. 9 579 (1983) [Sov. Astron. Lett. 9 302 (1983)]
  64. Dirac P A M Proc. R. Soc. London Ser. A 246 333 (1958); Lectures on Quantum Mechanics (New York: Belfer Graduate School of Science, Yeshiva University, 1964); DeWitt B S Phys. Rev. 160 1113 (1967); Wheeler J A, in Batelles Rencontres (New York: Benjamin, 1968)
  65. Coleman S Phys. Rev. D 15 2929 (1977); Callan C G, Coleman S Phys. Rev. D 16 1762 (1977)
  66. Hawking S W, Page D N Nucl. Phys. B 264 185 (1986)
  67. Grishchuk L P, Rozhansky L V Phys. Lett. B 208 369 (1988); 234 9 (1990)
  68. Lavrelashvili G V, Rubakov V A, Serebryakov M S, Tinyakov P G Nucl. Phys. B 329 98 (1990); Rubakov V A, Tinyakov P G Nucl. Phys. B 342 430 (1990)
  69. Salopek D S, Bond J R, Bardeen J M Phys. Rev. D 40 1753 (1989); Fakir R, Unruh W G Phys. Rev. D 41 1783 (1990); Fakir R, Habib S, Unruh W G Aph. J. 394 396 (1992); Fakir R, Habib S Mod. Phys. Lett. A 8 2827 (1993)
  70. Barvinsky A O, Kamenshchik A Yu, Karmazin I P Phys. Rev. D 48 3677 (1993)
  71. Belinskii V A, Grishchuk L P, Zel’dovich Ya B, Khalatnikov I M Zh. Eksp. Teor. Fiz. 89 346 (1985) [Sov. Phys. JETP 62 195 (1985)]; Belinskii V A, Khalatnikov I M Zh. Eksp. Teor. Fiz. 93 784 (1987) [Sov. Phys. JETP 66 441 (1987)]
  72. Bousso R, Hawking S W Phys. Rev. D 52 5659 (1995); 54 6312 (1996)
  73. Carriga J, Vilenkin A Phys. Rev. D 56 2464 (1997)
  74. Halliwell J J, Hawking S W Phys. Rev. D 31 1777 (1985); Laflamme R Phys. Lett. B 198 156 (1987)
  75. Hawking S W Commun. Math. Phys. 55 133 (1977); Dowker J S, Critchley R Phys. Rev. D 16 3390 (1977)
  76. DeWitt B S Dynamical Theory of Groups and Fields (New York: Gordon and Breach, 1965); Barvinsky A O, Vilkovisky G A Phys. Rep. 119 1 (1985)
  77. Fradkin E S, Vilkovisky G A Phys. Lett. B 55 224 (1975); Batalin I A, Vilkovisky G A Phys. Lett. B 69 309 (1977); Batalin I A, Fradkin E S Phys. Lett. B 128 303 (1983); J. Math. Phys. 25 2426 (1984); Riv. Nuovo Cimento 9 Ser. 3 (10) 1 (1986); Ann. Inst. Henri Poincare 49 145 (1988)
  78. Hwang S Phys. Rev. D 28 2614 (1983); Ohta N Phys. Rev. D 33 1681 (1986)
  79. Dirac P A M Lectures on Quantum Mechanics (New York: Belfer Graduate School of Science Yeshiva University, 1964) [Translated into Russian (Moscow: Mir, 1968)]
  80. Hanson A, Regge T, Teitelboim C Constrained Hamiltonian Systems (Roma: Accademia Nazionale dei Lincei, 1976); Sundermeyer K "Constrained dynamics: with applications to Yang-Mills theory, general relativity, classical spin, dual string model" Lect. Notes Phys. 169 (Berlin, New York: Springer-Verlag, 1982); Henneaux M, Teitelboim C Quantization of Gauge Systems (Princeton, N.J.: Princeton University, 1992)
  81. Lifshitz E M Zh. Eksp. Teor. Fiz. 16 587 (1946)
  82. Arnold V Ann. Inst. Fourier XVI 319 (1966)
  83. Floratos E G, Iliopoulos J Phys. Lett. B 201 237 (1988); Arakelyan T A, Savvidy G K Phys. Lett. B 214 350 (1988); 223 41 (1989); Bars I, Pope C N, Sezgin E Phys. Lett. B 210 85 (1988); DeWitt B, Marquard U, Nicolai H Commun. Math. Phys. 128 39 (1990)
  84. Wigner E P Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra (Pure and Applied Physics, Vol. 5, New York: Academic Press, 1959)
  85. Starobinsky A A Pis’ma Zh. Eksp. Teor. Fiz. 57 606 (1993) [JETP Lett. 55 489 (1993)]; Sokolov I Yu Pis’ma Zh. Eksp. Teor. Fiz. 57 601 (1993) [JETP Lett. 57 617 (1993)]; Stevens D, Scott D, Silk J Phys. Rev. Lett. 71 20 (1993); Lachieze-Rey M, Luminet J-P Phys. Rep. 254 135 (1995)
  86. Buchbinder I L, Fradkin E S, Lyakhovich S L, Pershin V D Int. J. Mod. Phys. A 6 1211 (1991)
  87. Burnett G A Phys. Rev. D 51 1621 (1995)
  88. Mandelbrot B B The Fractal Geometry of Nature (San Francisco: W.H. Freeman, 1982); Zel’dovich Ya B, Sokolov D D Usp. Fiz. Nauk 146 493 (1985) [Sov. Phys. Usp. 28 608 (1985)]
  89. Starobinsky A A, in Proc. of 15th Int. Conf. on General Relativity and Gravitation, Pune, India, 1997 (to be published)
  90. Nikomarov E S, Khalatnikov I M Zh. Eksp. Teor. Fiz. 75 1176 (1978) [Sov. Phys. JETP 48 592 (1978)]
  91. Giddings S B, Strominger A Nucl. Phys. B 306 890 (1988)
  92. Abramowitz M, Stegun I A (Eds) Handbook of Mathematical Functions (New York: Dover Publ., 1965) [Translated into Russian (Moscow: Nauka, 1979)]
  93. Landau L D, Abrikosov A A, Khalatnikov I M Dokl. Akad. Nauk SSSR 95 497, 773, 1177 (1954); 96 261 (1954)
  94. Landau L D Dokl. Akad. Nauk SSSR 44 339 (1944); Landau L D, Lifshitz E M Gidrodinamika
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