Issues

 / 

2015

 / 

September

  

Conferences and symposia. 100th anniversary of the birth of E.M. Lifshitz


Stochastic cosmology, perturbation theories and Lifshitz gravity

 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

This paper reviews E M Lifshitz's work on gravity and cosmology and discusses later work by others who drew on his ideas. The major topics covered include the stochastic cosmology of an anisotropic universe and of an isotropic scalar field universe; the quasi-isotropic (gradient) expansion in cosmology; and Horava—Lifshitz gravity and cosmology.

Fulltext is available at IOP
Keywords: gravitation, cosmology, chaos, perturbation theory
PACS: 04.20.−q, 04.60.−m, 98.80.−k (all)
DOI: 10.3367/UFNe.0185.201509f.0948
URL: https://ufn.ru/en/articles/2015/9/e/
Citation: Khalatnikov I M, Kamenshchik A Yu "Stochastic cosmology, perturbation theories and Lifshitz gravity" Phys. Usp. 58 878–891 (2015)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 30th, May 2015, 26th, March 2015

Оригинал: Халатников И М, Каменщик А Ю «Стохастическая космология, теории возмущений и гравитация Лифшица» УФН 185 948–963 (2015); DOI: 10.3367/UFNr.0185.201509f.0948

E.M. Lifshitz is author of Physics-Uspekhi

References (90) ↓ Cited by (2) Similar articles (20)

  1. Lorenz E N J. Atmos. Sci. 20 130 (1963)
  2. Feigenbaum M J J. Stat. Phys. 19 25 (1978)
  3. Mandelbrot B The Fractal Geometry Of Nature (New York: W.H. Freeman, 1977)
  4. Gutzwiller M Chaos In Classical And Quantum Mechanics (Berlin: Springer-Verlag, 1990)
  5. Penrose R Structure Of Space-Time (New York: W.A. Benjamin, 1968); Penrouz R Struktura Prostranstva-vremeni (M.: Mir, 1972)
  6. Hawking S W, Ellis G F R The Large Scale Structure Of Space-Time (Cambridge: Univ. Press, 1973); Khoking S, Ellis Dzh Krupnomasshtabnaya Struktura Prostranstva-vremeni (M.: Mir, 1977)
  7. Hawking S W, Penrose R Proc. R. Soc. London A 314 529 (1970)
  8. Lifshits E M, Khalatnikov I M Usp. Fiz. Nauk 80 391 (1963); Lifshitz E M, Khalatnikov I M Sov. Phys. Usp. 6 495 (1964)
  9. Lifshitz E M, Khalatnikov I M Adv. Phys. 12 185 (1963)
  10. Khalatnikov I M, Lifshitz E M Phys. Rev. Lett. 24 76 (1970)
  11. Lifshits E M, Khalatnikov I M Pis’ma ZhETF 11 200 (1970); Lifshitz E M, Khalatnikov I M JETP Lett. 11 123 (1970)
  12. Belinskii V A, Khalatnikov I M Zh. Eksp. Teor. Fiz. 56 1701 (1969); Belinskii V A, Khalatnikov I M Sov. Phys. JETP 29 911 (1969)
  13. Belinskii V A, Lifshits E M, Khalatnikov I M Usp. Fiz. Nauk 102 463 (1970); Belinskii V A, Lifshitz E M, Khalatnikov I M Sov. Phys. Usp. 13 745 (1971)
  14. Belinskii V A, Khalatnikov I M, Lifshitz E M Adv. Phys. 31 639 (1982)
  15. Misner C W Phys. Rev. Lett. 22 1071 (1969)
  16. Lifshits E M, Lifshits I M, Khalatnikov I M Zh. Eksp. Teor. Fiz. 59 322 (1970); Lifshitz E M, Lifshitz I M, Khalatnikov I M Sov. Phys. JETP 32 173 (1971)
  17. Khalatnikov I M et al. J. Stat. Phys. 38 97 (1985)
  18. Demaret J, Henneaux M, Spindel P Phys. Lett. B 164 27 (1985)
  19. Demaret J et al. Phys. Lett. B 175 129 (1986)
  20. Demaret J, de Rop Y, Henneaux M Int. J. Theor. Phys. 28 1067 (1989)
  21. Kasner E Am. J. Math. 43 217 (1921)
  22. Damour T, Henneaux M Phys. Rev. Lett. 85 920 (2000)
  23. Damour T et al. Phys. Lett. B 509 323 (2001)
  24. Damour T, Henneaux M, Nicolai H Class. Quantum Grav. 20 R145 (2003)
  25. Kac V G Infinite Dimensional Lie Algebras (Cambridge: Cambridge Univ. Press, 1990)
  26. Starobinsky A A Phys. Lett. B 91 99 (1980)
  27. Guth A H Phys. Rev. D 23 347 (1981)
  28. Linde A D Phys. Lett. B 129 177 (1983)
  29. Gamow G Phys. Rev. 70 572 (1946)
  30. Belinskii V A, Grishchuk L P, Zel’dovich Ya B, Khalatnikov I M Zh. Eksp. Teor. Fiz. 89 346 (1985); Belinskii V A, Grishchuk L P, Zel’dovich Ya B, Khalatnikov I M Sov. Phys. JETP 62 195 (1985)
  31. Belinskii V A, Khalatnikov I M Zh. Eksp. Teor. Fiz. 93 784 (1987); Belinskii V A, Khalatnikov I M Sov. Phys. JETP 66 441 (1987)
  32. Page D N Class. Quantum Grav. 1 417 (1984)
  33. Kamenshchik A Yu, Khalatnikov I M, Toporensky A V Int. J. Mod. Phys. D 06 673 (1997)
  34. Kamenshchik A Yu, Khalatnikov I M, Toporensky A V Int. J. Mod. Phys. D 07 129 (1998)
  35. Cornish N J, Shellard E P S Phys. Rev. Lett. 81 3571 (1998)
  36. Cornish N J, Levin J J Phys. Rev. D 55 7489 (1997)
  37. Kamenshchik A Yu, Khalatnikov I M, Savchenko S V, Toporensky A V Phys. Rev. D 59 123516 (1999)
  38. Lifshits E M Zh. Eksp. Teor. Fiz. 16 587 (1946)
  39. Bardeen J M Phys. Rev. D 22 1882 (1980)
  40. Mukhanov V F Zh. Eksp. Teor. Fiz. 94 1 (1988); Mukhanov V F Sov. Phys. JETP 67 1297 (1988)
  41. Sasaki M Prog. Theor. Phys. 76 1036 (1986)
  42. Lifshits E M, Khalatnikov I M Zh. Eksp. Teor. Fiz. 39 149 (1960); Lifshitz E M, Khalatnikov I M Sov. Phys. JETP 12 108 (1961)
  43. Khalatnikov I M, Kamenshchik A Yu, Starobinsky A A Class. Quantum Grav. 19 3845 (2002)
  44. Khalatnikov I M, Kamenshchik A Yu, Martellini M, Starobinsky A A JCAP (03) 001 (2003)
  45. Khalatnikov I M, Kamenshchik A Yu, Starobinsky A A arXiv:1312.0237
  46. Riess A G et al. Astron. J. 116 1009 (1998)
  47. Perlmutter S et al. Astrophys. J. 517 565 (1999)
  48. Sahni V, Starobinsky A Int. J. Mod. Phys. D 9 373 (2000)
  49. Sahni V, Starobinsky A Int. J. Mod. Phys. D 15 2105 (2006)
  50. Hořava P Phys. Rev. D 79 084008 (2009)
  51. Lifshits E M Zh. Eksp. Teor. Fiz. 11 255 (1941)
  52. Lifshits E M Zh. Eksp. Teor. Fiz. 11 269 (1941)
  53. Bini D, Cherubini C, Jantzen R T Class. Quantum Grav. 24 5627 (2007)
  54. Petrov A Z Prostranstva Einshteina (M.: Fizmatgiz, 1961); Petrov A Z Einstein Spaces (Oxford: Pergamon Press, 1969)
  55. Parker L, Fulling S A Phys. Rev. D 7 2357 (1973)
  56. Starobinskii A A Pis’ma Astron. Zhurn. 4 155 (1978); Starobinskii A A Sov. Astron. Lett. 4 82 (1978)
  57. Hawking S W Relativity, Groups And Topology II. Proc. Les Houches 1983, Session XL (Eds B S De Witt, R Stora) (Amsterdam: North-Holland, 1984) p. 333-379
  58. Khalatnikov I M, Kamenshchik A Yu Phys. Rep. 288 513 (1997)
  59. Khalatnikov I M, Kamenshchik A Yu Usp. Fiz. Nauk 168 593 (1998); Khalatnikov I M, Kamenshchik A Yu Phys. Usp. 41 525 (1998)
  60. Khalatnikov I M, Mezhlumian A Phys. Lett. A 169 308 (1992)
  61. Khalatnikov I M, Schiller P Phys. Lett. B 302 176 (1993)
  62. Amendola L, Khalatnikov I M, Litterio M, Occhionero F Phys. Rev. D 49 1881 (1994)
  63. Kamenshchik A Yu, Khalatnikov I M, Toporensky A V Phys. Lett. B 357 36 (1995)
  64. Kamenshchik A Yu, Khalatnikov I M, Toporensky A V Int. J. Mod. Phys. D 6 649 (1997)
  65. Comer G L et al. Phys. Rev. D 49 2759 (1994)
  66. Deruelle N, Langlois D Phys. Rev. D 52 2007 (1995)
  67. Starobinsky A A Phys. Lett. B 117 175 (1982)
  68. Starobinskii A A Pis’ma ZhETF 37 55 (1983); Starobinskii A A JETP Lett. 37 66 (1983)
  69. Salopek D S, Bond J R Phys. Rev. D 42 3936 (1990)
  70. Salopek D S Phys. Rev. D 43 3214 (1991)
  71. Salopek D S, Stewart J M Class. Quantum Grav. 9 1943 (1992)
  72. Wands D et al. Phys. Rev. D 62 043527 (2000)
  73. Nambu Y, Taruya A Class. Quantum Grav. 13 705 (1996)
  74. Tanaka Y, Sasaki M Prog. Theor. Phys. 117 633 (2007)
  75. Weinberg S General Relativity. An Einstein Centenary Survey (Eds S W Hawking, W Israel) (Cambridge: Cambridge Univ. Press, 1979) p. 790
  76. Arnowitt R, Deser S, Misner C W Gravitation: An Introduction To Current Research (Ed. L Witten) (New York: Wiley, 1962) p. 227-265, Ch. 7; republished in, Arnowitt R, Deser S, Misner C W Gen. Relat. Grav. 40 1997 (2008)
  77. Chen B, Huang Q-G Phys. Lett. B 683 108 (2010)
  78. Mukohyama Sh Class. Quantum Grav. 27 223101 (2010)
  79. Gao X et al. Phys. Rev. D 81 083508 (2010)
  80. Gümrükçüoglu A E, Mukohyama S, Wang A Phys. Rev. D 85 064042 (2012)
  81. Bakas I, Bourliot F, Lüst D, Petropoulos M Class. Quantum Grav. 27 045013 (2010)
  82. Myung Y S et al. JHEP (03) 085 (2010)
  83. Maeda K, Misonoh Y, Kobayashi T Phys. Rev. D 82 064024 (2010)
  84. Lifshits E M Zh. Eksp. Teor. Fiz. 29 94 (1955); Lifshitz E M Sov. Phys. JETP 2 73 (1956)
  85. Casimir H B G Proc. K. Ned. Akad. Wet. 51 793 (1948)
  86. Ford L H Phys. Rev. D 11 3370 (1975)
  87. Dzyaloshinskii I E, Lifshits E M, Pitaevskii L P Usp. Fiz. Nauk 73 381 (1961); Dzyaloshinskii I E, Lifshitz E M, Pitaevskii L P Sov. Phys. Usp. 4 153 (1961)
  88. Bordag M et al. Phys. Rev. B 74 205431 (2006)
  89. Antezza M et al. Phys. Rev. A 77 022901 (2008)
  90. Rosa F S S, Dalvit D A R, Milonni P W Phys. Rev. Lett. 100 183602 (2008)

© 1918–2021 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions