RSS feeds
РусскийEnglish
Issue 11, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2014

 / 

February

←  →

Physics of our days


The Null Energy Condition and its violation

 a, b
a Institute for Nuclear Research, Russian Academy of Sciences, prosp. 60-letiya Oktyabrya 7a, Moscow, 117312, Russian Federation
b Lomonosov Moscow State University, Faculty of Physics, Leninskie Gory 1 build. 2, Moscow, 119991, Russian Federation

A brief review is given of scalar field theories with second-derivative Lagrangians yielding second order field equations. Some of these theories admit solutions that violate the Null Energy Condition but which otherwise show no obvious inconsistencies. The use of these theories in constructing cosmological scenarios and in the context a laboratory-created universe is illustrated with examples.

Fulltext pdf (624 KB)
Fulltext is also available at DOI: 10.3367/UFNe.0184.201402b.0137
PACS: 04.20.Dw, 04.62.+v, 98.80.Bp (all)
DOI: 10.3367/UFNe.0184.201402b.0137
URL: https://ufn.ru/en/articles/2014/2/b/
000336162000002
2-s2.0-84900830538
2014PhyU...57..128R
Citation: Rubakov V A "The Null Energy Condition and its violation" Phys. Usp. 57 128–142 (2014)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 10th, January 2014, 10th, January 2014

Оригинал: Рубаков В А «Изотропное условие энергодоминантности и его нарушение» УФН 184 137–152 (2014); DOI: 10.3367/UFNr.0184.201402b.0137

References (124) ↓ Cited by (177) Similar articles (16)

  1. Flanagan E E, Wald R M Phys. Rev. D 54 6233 (1996); Flanagan E E, Wald R M gr-qc/9602052
  2. Penrose R Phys. Rev. Lett. 14 57 (1965)
  3. Starobinskii A A Pis’ma Astron. Zhurn. 4 155 (1978); Starobinskii A A Sov. Astron. Lett. 4 82 (1978)
  4. Berezin V A, Kuzmin V A, Tkachev I I Quantum Gravity. Proc. Of The Third Seminar On Quantum Gravity, October 23 - 25, 1984, Moscow, USSR (Eds M A Markov, V A Berezin, V P Frolov) (Singapore: World Scientific, 1985) p. 605
  5. Berezin V A, Kuz’min V A, Tkachev I I Pis’ma ZhETF 41 446 (1985); Berezin V A, Kuz’min V A, Tkachev I I JETP Lett. 41 547 (1985)
  6. Farhi E, Guth A H Phys. Lett. B 183 149 (1987)
  7. Starobinskii A A Pis’ma ZhETF 30 719 (1979); Starobinskii A A JETP Lett. 30 682 (1979)
  8. Starobinsky A A Phys. Lett. B 91 99 (1980)
  9. Guth A H Phys. Rev. D 23 347 (1981)
  10. Linde A D Phys. Lett. B 108 389 (1982)
  11. Albrecht A, Steinhardt P J Phys. Rev. Lett. 48 1220 (1982)
  12. Linde A D Phys. Lett. B 129 177 (1983)
  13. Berezin V A, Kuz’min V A, Tkachev I I Zh. Eksp. Teor. Fiz. 93 1159 (1987); Berezin V A, Kuz’min V A, Tkachev I I Sov. Phys. JETP 66 654 (1987)
  14. Berezin V A, Kuzmin V A, Tkachev I I Phys. Lett. B 207 397 (1988)
  15. Farhi E, Guth A H, Guven J Nucl. Phys. B 339 417 (1990)
  16. Fischler W, Morgan D, Polchinski J Phys. Rev. D 41 2638 (1990); Fischler W, Morgan D, Polchinski J Phys. Rev. D 42 4042 (1990)
  17. Linde A Nucl. Phys. B 372 421 (1992); Linde A hep-th/9110037
  18. Garriga J, Vilenkin A Phys. Rev. D 57 2230 (1998); Garriga J, Vilenkin A astro-ph/9707292
  19. Garriga J et al. Int. J. Theor. Phys. 39 1887 (2000); Garriga J et al. astro-ph/9909143
  20. Dutta S, Vachaspati T Phys. Rev. D 71 083507 (2005); Dutta S, Vachaspati T astro-ph/0501396
  21. Aguirre A, Johnson M C Phys. Rev. D 73 123529 (2006); Aguirre A, Johnson M C gr-qc/0512034
  22. Lee W et al. Phys. Rev. D 74 123520 (2006); Lee W et al. hep-th/0604064
  23. Piao Y-S Nucl. Phys. B 803 194 (2008); Piao Y-S arXiv:0712.4184
  24. Frolov V P, Markov M A, Mukhanov V F Phys. Lett. B 216 272 (1989); Frolov V P, Markov M A, Mukhanov V F Phys. Rev. D 41 383 (1990)
  25. Guendelman E I Int. J. Mod. Phys. D 19 1357 (2010); Guendelman E I arXiv:1003.3975
  26. Lukash V N, Mikheeva E V, Strokov V N Usp. Fiz. Nauk 182 216 (2012); Lukash V N, Mikheeva E V, Strokov V N Phys. Usp. 55 204 (2012); Lukash V N, Mikheeva E V, Strokov V N arXiv:1110.6820
  27. Lukash V N, Strokov V N Int. J. Mod. Phys. A 28 1350007 (2013); Lukash V N, Strokov V N arXiv:1301.5544
  28. Mukhanov V, Brandenberger R Phys. Rev. Lett. 68 1969 (1992)
  29. Brandenberger R, Mukhanov V, Sornborger A Phys. Rev. D 48 1629 (1993); Brandenberger R, Mukhanov V, Sornborger A gr-qc/9303001
  30. Trodden M, Mukhanov V F, Brandenberger R H Phys. Lett. B 316 483 (1993); Trodden M, Mukhanov V F, Brandenberger R H hep-th/9305111
  31. Lee B-H et al. Phys. Rev. D 77 063502 (2008); Lee B-H et al. arXiv:0710.4599
  32. Guendelman E I, Sakai N Phys. Rev. D 77 125002 (2008); Guendelman E I, Sakai N Phys. Rev. D 80 049901(E) (2009), Erratum; Guendelman E I, Sakai N arXiv:0803.0268
  33. Yeom D arXiv:0912.0068
  34. Hwang D, Yeom D Class. Quantum Grav. 28 155003 (2011); Hwang D, Yeom D arXiv:1010.3834
  35. Morris M S, Thorne K S Am. J. Phys. 56 395 (1988)
  36. Morris M S, Thorne K S, Yurtsever U Phys. Rev. Lett. 61 1446 (1988)
  37. Visser M Lorentzian Wormholes: From Einstein To Hawking (Woodbury, N.Y.: American Institute of Physics, 1995)
  38. Hochberg D, Visser M Phys. Rev. D 58 044021 (1998); Hochberg D, Visser M gr-qc/9802046
  39. Novikov I D, Kardashev N S, Shatskii A A Usp. Fiz. Nauk 177 1017 (2007); Novikov I D, Kardashev N S, Shatskii A A Phys. Usp. 50 965 (2007)
  40. Shatskii A A, Novikov I D, Kardashev N S Usp. Fiz. Nauk 178 481 (2008); Shatskii A A, Novikov I D, Kardashev N S Phys. Usp. 51 457 (2008)
  41. Rubakov V A Teor. Mat. Fiz. 149 409 (2006); Rubakov V A Theor. Math. Phys. 149 1651 (2006); Rubakov V A hep-th/0604153
  42. Libanov M et al. JCAP (08) 010 (2007); Libanov M et al. arXiv:0704.1848
  43. Horndeski G W Int. J. Theor. Phys. 10 363 (1974)
  44. Fairlie D B, Govaerts J, Morozov A Nucl. Phys. B 373 214 (1992); Fairlie D B, Govaerts J, Morozov A hep-th/9110022
  45. Fairlie D B, Govaerts J Phys. Lett. B 281 49 (1992); Fairlie D B, Govaerts J hep-th/9202056
  46. Fairlie D B, Govaerts J J. Math. Phys. 33 3543 (1992); Fairlie D B, Govaerts J hep-th/9204074
  47. Dvali G, Gabadadze G, Porrati M Phys. Lett. B 485 208 (2000); Dvali G, Gabadadze G, Porrati M hep-th/0005016
  48. Luty M A, Porrati M, Rattazzi R JHEP (09) 029 (2003); Luty M A, Porrati M, Rattazzi R hep-th/0303116
  49. Nicolis A, Rattazzi R JHEP (06) 059 (2004); Nicolis A, Rattazzi R hep-th/0404159
  50. Nicolis A, Rattazzi R, Trincherini E Phys. Rev. D 79 064036 (2009); Nicolis A, Rattazzi R, Trincherini E arXiv:0811.2197
  51. Deffayet C, Esposito-Farèse G, Vikman A Phys. Rev. D 79 084003 (2009); Deffayet C, Esposito-Farèse G, Vikman A arXiv:0901.1314
  52. de Rham C, Tolley A J JCAP (05) 015 (2010); de Rham C, Tolley A J arXiv:1003.5917
  53. Goon G L, Hinterbichler K, Trodden M Phys. Rev. Lett. 106 231102 (2011); Goon G L, Hinterbichler K, Trodden M arXiv:1103.6029
  54. Goon G, Hinterbichler K, Trodden M JCAP (07) 017 (2011); Goon G, Hinterbichler K, Trodden M arXiv:1103.5745
  55. Kamada K et al. Phys. Rev. D 83 083515 (2011); Kamada K et al. arXiv:1012.4238
  56. Kobayashi T, Yamaguchi M, Yokoyama J Prog. Theor. Phys. 126 511 (2011); Kobayashi T, Yamaguchi M, Yokoyama J arXiv:1105.5723
  57. Babichev E, Deffayet C, Ziour R Int. J. Mod. Phys. D 18 2147 (2009); Babichev E, Deffayet C, Ziour R arXiv:0905.2943
  58. Deffayet C et al. JCAP (10) 026 (2010); Deffayet C et al. arXiv:1008.0048
  59. Kobayashi T, Yamaguchi M, Yokoyama J Phys. Rev. Lett. 105 231302 (2010); Kobayashi T, Yamaguchi M, Yokoyama J arXiv:1008.0603
  60. Pujolàs O, Sawicki I, Vikman A JHEP (11) 156 (2011); Pujolàs O, Sawicki I, Vikman A arXiv:1103.5360
  61. Charmousis C et al. Phys. Rev. Lett. 108 051101 (2012); Charmousis C et al. arXiv:1106.2000
  62. Charmousis C et al. Phys. Rev. D 85 104040 (2012); Charmousis C et al. arXiv:1112.4866
  63. Deffayet C et al. Phys. Rev. D 84 064039 (2011); Deffayet C et al. arXiv:1103.3260
  64. Padilla A, Sivanesan V JHEP (04) 032 (2013); Padilla A, Sivanesan V arXiv:1210.4026
  65. Sivanesan V arXiv:1307.8081
  66. Creminelli P, Nicolis A, Trincherini E JCAP (11) 021 (2010); Creminelli P, Nicolis A, Trincherini E arXiv:1007.0027
  67. Creminelli P et al. JHEP (02) 006 (2013); Creminelli P et al. arXiv:1209.3768
  68. Hinterbichler K et al. JCAP (12) 030 (2012); Hinterbichler K et al. arXiv:1209.5742
  69. Hinterbichler K et al. Phys. Rev. Lett. 110 241303 (2013); Hinterbichler K et al. arXiv:1212.3607
  70. Rubakov V A Phys. Rev. D 88 044015 (2013); Rubakov V A arXiv:1305.2614
  71. Elder B, Joyce A, Khoury J Phys. Rev. D 89 044027 (2014); Elder B, Joyce A, Khoury J arXiv:1311.5889
  72. Adams A et al. JHEP (10) 014 (2006); Adams A et al. hep-th/0602178
  73. de Rham C, Fasiello M, Tolley A J arXiv:1308.2702
  74. Arkani-Hamed N et al. JHEP (05) 074 (2004); Arkani-Hamed N et al. hep-th/0312099
  75. Sergienko A V, Rubakov V A Teor. Mat. Fiz. 173 441 (2012); Sergienko A V, Rubakov V A Theor. Math. Phys. 173 1709 (2012); Sergienko A V, Rubakov V A arXiv:0803.3163
  76. Libanov M V, Rubakov V A, Sazhina O S, Sazhin M V Zh. Eksp. Teor. Fiz. 135 253 (2009); Libanov M V, Rubakov V A, Sazhina O S, Sazhin M V J. Exp. Theor. Phys. 108 226 (2009); Libanov M V, Rubakov V A, Sazhina O S, Sazhin M V Phys. Rev. D 79 083521 (2009); Libanov M V, Rubakov V A, Sazhina O S, Sazhin M V arXiv:0812.1459
  77. Cline J M, Jeon S, Moore G D Phys. Rev. D 70 043543 (2004); Cline J M, Jeon S, Moore G D hep-ph/0311312
  78. Buniy R V, Hsu S D H, Murray B M Phys. Rev. D 74 063518 (2006); Buniy R V, Hsu S D H, Murray B M hep-th/0606091
  79. Senatore L Phys. Rev. D 71 043512 (2005); Senatore L astro-ph/0406187
  80. Creminelli P et al. JHEP (12) 080 (2006); Creminelli P et al. hep-th/0606090
  81. Buchbinder E I, Khoury J, Ovrut B A Phys. Rev. D 76 123503 (2007); Buchbinder E I, Khoury J, Ovrut B A hep-th/0702154
  82. Creminelli P, Senatore L JCAP (11) 010 (2007); Creminelli P, Senatore L hep-th/0702165
  83. Khoury J et al. Phys. Rev. D 64 123522 (2001); Khoury J et al. hep-th/0103239
  84. Khoury J et al. Phys. Rev. D 65 086007 (2002); Khoury J et al. hep-th/0108187
  85. Padilla A, SaffP M, Zhou S-Y JHEP (12) 031 (2010); Padilla A, SaffP M, Zhou S-Y arXiv:1007.5424
  86. Padilla A, SaffP M, Zhou S-Y JHEP (01) 099 (2011); Padilla A, SaffP M, Zhou S-Y arXiv:1008.3312
  87. Padilla A, SaffP M, Zhou S-Y Phys. Rev. D 83 045009 (2011); Padilla A, SaffP M, Zhou S-Y arXiv:1008.0745
  88. Hinterbichler K, Trodden M, Wesley D Phys. Rev. D 82 124018 (2010); Hinterbichler K, Trodden M, Wesley D arXiv:1008.1305
  89. Nishi S et al. arXiv:1401.1045
  90. Levasseur L P, Brandenberger R, Davis A-C Phys. Rev. D 84 103512 (2011); Levasseur L P, Brandenberger R, Davis A-C arXiv:1105.5649
  91. Linde A, Mukhanov V Phys. Rev. D 56 R535 (1997); Linde A, Mukhanov V astro-ph/9610219
  92. Enqvist K, Sloth M S Nucl. Phys. B 626 395 (2002); Enqvist K, Sloth M S hep-ph/0109214
  93. Lyth D H, Wands D Phys. Lett. B 524 5 (2002); Lyth D H, Wands D hep-ph/0110002
  94. Moroi T, Takahashi T Phys. Lett. B 522 215 (2001); Moroi T, Takahashi T Phys. Lett. B 539 303 (2002), Erratum; Moroi T, Takahashi T hep-ph/0110096
  95. Dimopoulos K et al. JHEP (07) 053 (2003); Dimopoulos K et al. hep-ph/0304050
  96. Dvali G, Gruzinov A, Zaldarriaga M Phys. Rev. D 69 023505 (2004); Dvali G, Gruzinov A, Zaldarriaga M astro-ph/0303591
  97. Kofman L astro-ph/0303614
  98. Dvali G, Gruzinov A, Zaldarriaga M Phys. Rev. D 69 083505 (2004); Dvali G, Gruzinov A, Zaldarriaga M astro-ph/0305548
  99. Hinshaw G et al. (WMAP Collab.) Astrophys. J. Suppl. 208 19 (2013); Hinshaw G et al. (WMAP Collab.) arXiv:1212.5226
  100. Ade P A R et al. (Planck Collab.) arXiv:1303.5076
  101. Rubakov V A, Osipov M A Pis’ma ZhETF 93 56 (2011); Rubakov V A, Osipov M A JETP Lett. 93 52 (2011); Osipov M A, Rubakov V A arXiv:1007.3417
  102. Rubakov V A JCAP (09) 030 (2009); Rubakov V A arXiv:0906.3693
  103. Hinterbichler K, Khoury J JCAP (04) 023 (2012); Hinterbichler K, Khoury J arXiv:1106.1428
  104. Hinterbichler K, Joyce A, Khoury J JCAP (06) 043 (2012); Hinterbichler K, Joyce A, Khoury J arXiv:1202.6056
  105. Libanov M, Rubakov V JCAP (11) 045 (2010); Libanov M, Rubakov V arXiv:1007.4949
  106. Libanov M, Mironov S, Rubakov V Prog. Theor. Phys. Suppl. 190 120 (2011); Libanov M, Mironov S, Rubakov V arXiv:1012.5737
  107. Libanov M, Mironov S, Rubakov V Phys. Rev. D 84 083502 (2011); Libanov M, Mironov S, Rubakov V arXiv:1105.6230
  108. Libanov M, Ramazanov S, Rubakov V JCAP (06) 010 (2011); Libanov M, Ramazanov S, Rubakov V arXiv:1102.1390
  109. Mironov S A, Ramazanov S R, Rubakov V A arXiv:1312.7808
  110. Qiu T et al. JCAP (10) 036 (2011); Qiu T et al. arXiv:1108.0593
  111. Easson D A, Sawicki I, Vikman A JCAP (11) 021 (2011); Easson D A, Sawicki I, Vikman A arXiv:1109.1047
  112. Cai Y-F, Easson D A, Brandenberger R JCAP (08) 020 (2012); Cai Y-F, Easson D A, Brandenberger R arXiv:1206.2382
  113. Osipov M, Rubakov V JCAP (11) 031 (2013); Osipov M, Rubakov V arXiv:1303.1221
  114. Koehn M, Lehners J-L, Ovrut B A arXiv:1310.7577
  115. Lifshits E M, Khalatnikov I M Usp. Fiz. Nauk 80 391 (1963); Lifshitz E M, Khalatnikov I M Sov. Phys. Usp. 6 495 (1964)
  116. Lifshitz E M, Khalatnikov I M Adv. Phys. 12 185 (1963)
  117. 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)
  118. Belinskii V A, Khalatnikov I M, Lifshitz E M Adv. Phys. 19 525 (1970)
  119. Belinskii V A, Lifshits E M, Khalatnikov I M Zh. Eksp. Teor. Fiz. 62 1606 (1972); Belinskii V A, Lifshitz E M, Khalatnikov I M Sov. Phys. JETP 35 838 (1972)
  120. Erickson J K et al. Phys. Rev. D 69 063514 (2004); Erickson J K et al. hep-th/0312009
  121. Easson D A, Sawicki I, Vikman A JCAP (07) 014 (2013); Easson D A, Sawicki I, Vikman A arXiv:1304.3903
  122. Dubovsky S L, Sibiryakov S M Phys. Lett. B 638 509 (2006); Dubovsky S L, Sibiryakov S M hep-th/0603158
  123. Hawking S W Phys. Rev. D 46 603 (1992)
  124. Landau L D, Lifshits E M Teoriya Polya (M.: Nauka, 1988); Landau L D, Lifshitz E M The Classical Theory Of Fields (Oxford: Pergamon Press, 1975)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions