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 (206) ↓ Similar articles (16)

  1. Mandal S, Shankaranarayanan S Encyclopedia of Astrophysics (2026) p. 73
  2. Vasquez I R, Oliveros A Eur. Phys. J. C 86 (2) (2026)
  3. Figueruelo D, van der Westhuizen M et al Physics Of The Dark Universe 52 102238 (2026)
  4. Ye G, Cai Y Phys. Rev. D 112 (12) (2025)
  5. Mironov S, Sharov M, Volkova V Eur. Phys. J. C 85 (1) (2025)
  6. van der Westhuizen M, Abebe A, Di Valentino E Physics Of The Dark Universe 50 102119 (2025)
  7. Ahmedov B, Caruana M et al Physics Of The Dark Universe 50 102100 (2025)
  8. Sharif M, Gul M Z, Fatima N Physics Of The Dark Universe 47 101760 (2025)
  9. Green D, Meyers J Phys. Rev. D 111 (8) (2025)
  10. Tessainer D, Maroto A L, Martín-Moruno P Physics Of The Dark Universe 47 101769 (2025)
  11. Choi H G, Petrov P, Yamaguchi M J. High Energ. Phys. 2025 (8) (2025)
  12. Easson D A, Lesnefsky J E Phys. Rev. D 112 (6) (2025)
  13. Ignat’ev Yu G, Kokh I A Gravit. Cosmol. 31 (4) 476 (2025)
  14. Volkova V E, Mironov S A Uspekhi Fizicheskikh Nauk 195 (02) 172 (2025) [Volkova V E, Mironov S A Phys. Usp. 68 (02) 163 (2025)]
  15. Fukuyama T Symmetry 17 (10) 1688 (2025)
  16. Dzhunushaliev V, Folomeev V et al Eur. Phys. J. C 85 (4) (2025)
  17. Mironov S, Sharov M Phys. Rev. D 111 (8) (2025)
  18. An O S, Kang J U et al J. High Energ. Phys. 2025 (5) (2025)
  19. Singh A, Shaily et al Annals Of Physics 483 170274 (2025)
  20. R V I, Oliveros A Gen Relativ Gravit 57 (4) (2025)
  21. Alexandre Je, Backhouse D et al J. Phys. A: Math. Theor. 58 (47) 475402 (2025)
  22. Aman H, Rayimbaev Ja et al Indian J Phys (2025)
  23. Wolf W J, Ferreira P G, García-García C Phys. Rev. D 111 (4) (2025)
  24. Eroshenko Yu N Uspekhi Fizicheskikh Nauk 195 (02) 221 (2025) [Eroshenko Yu N Phys. Usp. 68 (02) 208 (2025)]
  25. Panda A, Gangopadhyay D, Manna G Astroparticle Physics 165 103059 (2025)
  26. Miranda M Gen Relativ Gravit 57 (1) (2025)
  27. Moghtaderi E, Hull B R et al Phys. Rev. D 111 (12) (2025)
  28. Ageeva Y, Kotenko M, Petrov P Phys. Rev. D 112 (6) (2025)
  29. Kaur M, Nandi D et al Int. J. Mod. Phys. D 33 (02) (2024)
  30. Chen Z-Ch, Liu L J. Cosmol. Astropart. Phys. 2024 (06) 028 (2024)
  31. Battista E Phys. Rev. D 109 (2) (2024)
  32. Cai Y, Zhu M, Piao Yu-S Phys. Rev. Lett. 133 (2) (2024)
  33. Cesar e Silva Wagno, Shapiro I L Phys. Rev. D 110 (4) (2024)
  34. Wolf W J Studies In History And Philosophy Of Science 103 146 (2024)
  35. Mironov S, Volkova V Nuclear Physics B 1004 116550 (2024)
  36. Mehdizadeh M R, Ziaie A H Eur. Phys. J. Plus 139 (11) (2024)
  37. Borislavov V T, Bouhmadi-López M, Martín-Moruno P Physics Of The Dark Universe 46 101679 (2024)
  38. Chen Z-Ch, Liu L Eur. Phys. J. C 84 (11) (2024)
  39. Ai W-Yu, Alexandre Je et al J. High Energ. Phys. 2024 (5) (2024)
  40. Mironov S, Volkova V Int. J. Mod. Phys. A 39 (35) (2024)
  41. Sharif M, Gul M Z, Fatima N New Astronomy 109 102211 (2024)
  42. Chugreev Yu V Phys. Part. Nuclei Lett. 21 (5) 964 (2024)
  43. Chugreev Yu V Moscow Univ. Phys. 79 (4) 432 (2024)
  44. Chugreev Yu V VMU (№4_2024) 2440102–1 (2024)
  45. Giovannini M Eur. Phys. J. C 84 (1) (2024)
  46. Dzhunushaliev V, Folomeev V et al Physics Letters B 855 138812 (2024)
  47. Singh J K, Shaily et al Physics Of The Dark Universe 46 101658 (2024)
  48. de Cesare M, Gubitosi G J. Cosmol. Astropart. Phys. 2024 (01) 046 (2024)
  49. Pan Sh, Cai Y, Piao Yu-S Eur. Phys. J. C 84 (9) (2024)
  50. Matsui H, Sakamura Yu Progress of Theoretical and Experimental Physics 2024 (4) (2024)
  51. Alexandre Je, Backhouse D Phys. Rev. D 110 (12) (2024)
  52. Ye G, Zhu M, Cai Y J. High Energ. Phys. 2024 (2) (2024)
  53. Sharif M, Gul M Z, Fatima N Chinese Journal Of Physics 91 66 (2024)
  54. Maroto A L J. Cosmol. Astropart. Phys. 2024 (04) 037 (2024)
  55. Mironov S, Valencia-Villegas M J. Cosmol. Astropart. Phys. 2024 (07) 030 (2024)
  56. Garcia-Saenz S, Hua Ju, Zhao Yu Phys. Rev. D 110 (6) (2024)
  57. Maroto A L, Miravet A D Phys. Rev. D 109 (10) (2024)
  58. Yu Ya-H, Wang S Eur. Phys. J. C 84 (6) (2024)
  59. Ghaemi N, Kaviani K Int. J. Geom. Methods Mod. Phys. 20 (08) (2023)
  60. Mironov S, Volkova V Phys. Rev. D 107 (10) (2023)
  61. Alexandre Je, Clough K, Pla S Phys. Rev. D 108 (10) (2023)
  62. Cai Y Phys. Rev. D 107 (6) (2023)
  63. Alexandre Je, Backhouse D Phys. Rev. D 107 (8) (2023)
  64. Azhar F, Kaiser D I Phys. Rev. D 107 (4) (2023)
  65. Mironov S, Shtennikova A J. Cosmol. Astropart. Phys. 2023 (06) 037 (2023)
  66. Wolf W J, Thébault K P Y The British Journal For The Philosophy Of Science (2023)
  67. Hogg N B Monthly Notices of the Royal Astronomical Society: Letters 529 (1) L95 (2023)
  68. Tukhashvili G, Steinhardt P J Phys. Rev. Lett. 131 (9) (2023)
  69. Singh J K, Balhara H et al J. High Energ. Phys. 2023 (3) (2023)
  70. Mansoori S A H, Molaee Z J. Cosmol. Astropart. Phys. 2023 (01) 022 (2023)
  71. Mironov S, Valencia-Villegas M Phys. Rev. D 108 (2) (2023)
  72. Alexandre Je, Pla S J. High Energ. Phys. 2023 (5) (2023)
  73. Chokyi Kh K, Chattopadhyay S Astron Nachr 344 (7) (2023)
  74. Duerr P M, Wolf W J Studies In History And Philosophy Of Science 101 1 (2023)
  75. Capuano L, Santoni L, Barausse E Phys. Rev. D 108 (6) (2023)
  76. Ageeva Yu A, Petrov P K Uspekhi Fizicheskikh Nauk 193 (11) 1205 (2023)
  77. Ageeva Yu, Petrov P, Rubakov V J. High Energ. Phys. 2023 (1) (2023)
  78. Zhu M, Cai Y J. High Energ. Phys. 2023 (4) (2023)
  79. Khan A, Taylor A J. Cosmol. Astropart. Phys. 2022 (10) 075 (2022)
  80. Alexandre Je, Polonyi Ja Phys. Rev. D 106 (6) (2022)
  81. Yousaf Z Universe 8 (2) 131 (2022)
  82. Kadam S A, Mishra B, Tripathy S K Mod. Phys. Lett. A 37 (17) (2022)
  83. Gouttenoire Ya Beyond the Standard Model Cocktail Springer Theses Chapter 3 (2022) p. 73
  84. Korzyński M, Serbenta Ju Phys. Rev. D 105 (8) (2022)
  85. Alexandre Je, Backhouse D Phys. Rev. D 105 (10) (2022)
  86. Corman M, East W E, Ripley Ju L J. Cosmol. Astropart. Phys. 2022 (09) 063 (2022)
  87. Martens P, Mukohyama Sh, Namba R J. Cosmol. Astropart. Phys. 2022 (11) 047 (2022)
  88. Matsui H Gen Relativ Gravit 54 (10) (2022)
  89. Cai Y, Xu J et al J. High Energ. Phys. 2022 (10) (2022)
  90. Deffayet C, Mukohyama Sh, Vikman A Phys. Rev. Lett. 128 (4) (2022)
  91. Güngör Ö, Starkman G D J. Cosmol. Astropart. Phys. 2021 (04) 003 (2021)
  92. Bouhmadi-López M, Chen Ch-Yu et al Eur. Phys. J. C 81 (4) (2021)
  93. Bernardo H, Brahma S et al Phys. Rev. Lett. 127 (18) (2021)
  94. Gómez C, Jimenez R J. Cosmol. Astropart. Phys. 2021 (10) 052 (2021)
  95. Arora S, Santos J R L, Sahoo P K Physics Of The Dark Universe 31 100790 (2021)
  96. Kim J L, Geshnizjani G J. Cosmol. Astropart. Phys. 2021 (03) 104 (2021)
  97. Alexandre Je, Polonyi Ja Phys. Rev. D 103 (10) (2021)
  98. Colgáin E Ó, Sheikh-Jabbari M M Class. Quantum Grav. 38 (17) 177001 (2021)
  99. Cai Y, Piao Yu-S Phys. Rev. D 103 (8) (2021)
  100. Rincón Á, Contreras E et al Physics Of The Dark Universe 31 100783 (2021)
  101. Mandal S Mod. Phys. Lett. A 36 (25) 2150183 (2021)
  102. Hoyos C, Jokela N et al J. High Energ. Phys. 2021 (10) (2021)
  103. Ageeva Y, Petrov P, Rubakov V Phys. Rev. D 104 (6) (2021)
  104. Chakrabarti S Eur. Phys. J. C 81 (2) (2021)
  105. Sokolov V  A, Garmaev B  D, Rostovsky V  S Phys. Rev. D 101 (8) (2020)
  106. Ye G, Piao Yu-S Eur. Phys. J. C 80 (5) (2020)
  107. Easson D A, Manton T, Svesko A J. Cosmol. Astropart. Phys. 2020 (10) 026 (2020)
  108. Tretyakov N, Terletsky A Phys. Scr. 95 (7) 075301 (2020)
  109. Godani N, Samanta G C New Astronomy 80 101399 (2020)
  110. Ageeva Y, Evseev O et al Phys. Rev. D 102 (2) (2020)
  111. Lasukov V Symmetry 12 (3) 400 (2020)
  112. Giovannini M Progress In Particle And Nuclear Physics 112 103774 (2020)
  113. Kontou E-A, Sanders K Class. Quantum Grav. 37 (19) 193001 (2020)
  114. Godani N, Samanta G C Int. J. Mod. Phys. A 35 (08) 2050045 (2020)
  115. Papantonopoulos E, Vlachos Ch Phys. Rev. D 101 (6) (2020)
  116. Tahara Hiroaki W  H, Kobayashi T Phys. Rev. D 102 (12) (2020)
  117. Mironov S, Rubakov V, Volkova V J. Cosmol. Astropart. Phys. 2020 (05) 024 (2020)
  118. Artymowski M, Ben-Dayan I, Kumar U J. Cosmol. Astropart. Phys. 2020 (05) 015 (2020)
  119. Mironov S, Rubakov V, Volkova V Phys. Scr. 95 (8) 084002 (2020)
  120. Ripley Ju L, Pretorius F Phys. Rev. D 101 (4) (2020)
  121. Shankar K H Gen Relativ Gravit 52 (2) (2020)
  122. Gal’tsov D V Eur. Phys. J. C 80 (5) (2020)
  123. Eroshenko Yu N Phys.-Usp. 63 (1) 101 (2020)
  124. Petrov P K Mod. Phys. Lett. A 35 (37) 2050305 (2020)
  125. Petrov P  K Phys. Rev. D 100 (2) (2019)
  126. Volkova V E, Mironov S A, Rubakov V A J. Exp. Theor. Phys. 129 (4) 553 (2019)
  127. de Cesare M Phys. Rev. D 99 (6) (2019)
  128. Azam M, Rahaman F et al Mod. Phys. Lett. A 34 (33) 1950268 (2019)
  129. Mironov S Universe 5 (2) 52 (2019)
  130. Ó C E, van Putten M H P M, Yavartanoo H Physics Letters B 793 126 (2019)
  131. Kobayashi T Rep. Prog. Phys. 82 (8) 086901 (2019)
  132. Mironov S, Rubakov V, Volkova V Phys. Rev. D 100 (8) (2019)
  133. Ye 叶 G 根, Piao 朴 Yu-S 云 Commun. Theor. Phys. 71 (4) 427 (2019)
  134. Vagenas E C, Ali A F, Alshal H Phys. Rev. D 99 (8) (2019)
  135. Graham P W, Kaplan D E, Rajendran S Phys. Rev. D 100 (1) (2019)
  136. Franciolini G, Hui L et al J. High Energ. Phys. 2019 (1) (2019)
  137. Bouhmadi-López M, Kiefer C, Martín-Moruno P Gen Relativ Gravit 51 (10) (2019)
  138. Mironov S, Rubakov V, Volkova V Class. Quantum Grav. 36 (13) 135008 (2019)
  139. Rincón Á, Contreras E et al Eur. Phys. J. C 78 (8) (2018)
  140. Chandrasekaran V, Remmen G N, Shahbazi-Moghaddam A J. High Energ. Phys. 2018 (11) (2018)
  141. Evseev O  A, Melichev O  I Phys. Rev. D 97 (12) (2018)
  142. Ijjas A Class. Quantum Grav. 35 (7) 075010 (2018)
  143. Graham P W, Kaplan D E, Rajendran S Phys. Rev. D 97 (4) (2018)
  144. Cunha P V P, Herdeiro C A R Gen Relativ Gravit 50 (4) (2018)
  145. Volkova V, Aharonov Y et al EPJ Web Conf. 182 02127 (2018)
  146. Bari P, Bhattacharya K, Chakraborty S Gen Relativ Gravit 50 (9) (2018)
  147. Dobre D A, Frolov A V et al J. Cosmol. Astropart. Phys. 2018 (03) 020 (2018)
  148. Addazi A, Alexander S et al Chinese Phys. C 42 (6) 065101 (2018)
  149. Ageeva Yu, Evseev O et al EPJ Web Conf. 191 07010 (2018)
  150. Contreras E, Rincón Á et al Eur. Phys. J. C 78 (3) (2018)
  151. Chowdhury T A, Rahman R, Sabuj Z A Nuclear Physics B 936 364 (2018)
  152. Abbassi M  H, Jozani A, Sepangi H  R Phys. Rev. D 97 (12) (2018)
  153. Boruah S S, Kim H J et al J. Cosmol. Astropart. Phys. 2018 (08) 031 (2018)
  154. Mironov S, Rubakov V, Volkova V J. Cosmol. Astropart. Phys. 2018 (10) 050 (2018)
  155. Mironov S, Rubakov V et al EPJ Web Conf. 191 07014 (2018)
  156. Nikiforova V, Damour T Phys. Rev. D 97 (12) (2018)
  157. Rincón Á, Koch B Eur. Phys. J. C 78 (12) (2018)
  158. Labraña P, del Campo S et al J. Phys.: Conf. Ser. 1043 012026 (2018)
  159. Kolevatov R, Mironov S et al Phys. Rev. D 96 (12) (2017)
  160. Evseev O  A, Melichev O  I Phys. Rev. D 96 (2) (2017)
  161. Addazi A, Ketov S V J. Cosmol. Astropart. Phys. 2017 (03) 061 (2017)
  162. Martín–Moruno Prado, Visser M Fundamental Theories Of Physics Vol. Wormholes, Warp Drives and Energy ConditionsClassical and Semi-classical Energy Conditions189 Chapter 9 (2017) p. 193
  163. Parikh M, Svesko A Phys. Rev. D 95 (10) (2017)
  164. Cai Y, Wan Y et al J. High Energ. Phys. 2017 (1) (2017)
  165. Sberna L, Pani P Phys. Rev. D 96 (12) (2017)
  166. Cai Y, Piao Yu-S Phys. Rev. D 96 (12) (2017)
  167. Di Grezia E, Battista E et al Eur. Phys. J. Plus 132 (12) (2017)
  168. Kolevatov R, Mironov S et al J. Cosmol. Astropart. Phys. 2017 (08) 038 (2017)
  169. Katanaev M O, Katanaev M O Teoreticheskaya Matematicheskaya Fizika 191 (2) 219 (2017) [Katanaev M O Theor Math Phys 191 (2) 661 (2017)]
  170. Brandenberger R, Peter P Found Phys 47 (6) 797 (2017)
  171. Rincón Á, Contreras E et al Eur. Phys. J. C 77 (7) (2017)
  172. Giovannini M Phys. Rev. D 95 (8) (2017)
  173. Giovannini M Phys. Rev. D 96 (10) (2017)
  174. Cai Y, Piao Yu-S J. High Energ. Phys. 2017 (9) (2017)
  175. Addazi A Int. J. Mod. Phys. A 32 (28n29) 1750174 (2017)
  176. Wang Yu-T, Cai Y et al J. Cosmol. Astropart. Phys. 2017 (01) 010 (2017)
  177. Nishi S, Kobayashi T Phys. Rev. D 95 (6) (2017)
  178. Akama Sh, Kobayashi T Phys. Rev. D 95 (6) (2017)
  179. Rincón Á, Koch B, Reyes I J. Phys.: Conf. Ser. 831 012007 (2017)
  180. Parikh M, Svesko A Physics Letters B (2016)
  181. Rubakov V A, Rubakov V A Teoreticheskaya Matematicheskaya Fizika 187 (2) 338 (2016) [Rubakov V A Theor Math Phys 187 (2) 743 (2016)]
  182. Ijjas A, Steinhardt P J Phys. Rev. Lett. 117 (12) (2016)
  183. Campo Sergio del, Guendelman E I et al J. Cosmol. Astropart. Phys. 2016 (08) 049 (2016)
  184. Pucheu M  L, Alves Junior F  A  P et al Phys. Rev. D 94 (6) (2016)
  185. Ijjas A, Steinhardt P J Class. Quantum Grav. 33 (4) 044001 (2016)
  186. Adshead P, Blas D et al J. Cosmol. Astropart. Phys. 2016 (11) 009 (2016)
  187. Kobayashi T Phys. Rev. D 94 (4) (2016)
  188. Beltrán J J, Lazkoz R et al Eur. Phys. J. C 76 (11) (2016)
  189. Pozdeeva E, Vernov S et al EPJ Web Conf. 125 03008 (2016)
  190. Kolevatov R, Mironov S Phys. Rev. D 94 (12) (2016)
  191. Ijjas A, Ripley Ju, Steinhardt P J Physics Letters B 760 132 (2016)
  192. Arefeva I, Bagrov A et al Phys. Rev. D 94 (4) (2016)
  193. Koch B, Reyes I A, Rincón Á Class. Quantum Grav. 33 (22) 225010 (2016)
  194. Libanov M, Mironov S, Rubakov V J. Cosmol. Astropart. Phys. 2016 (08) 037 (2016)
  195. Pozdeeva E O, Skugoreva M A et al J. Cosmol. Astropart. Phys. 2016 (12) 006 (2016)
  196. Parikh M J. High Energ. Phys. 2015 (10) (2015)
  197. Parikh M, van der Schaar Ja P Phys. Rev. D 91 (8) (2015)
  198. Kolevatov R  S Phys. Rev. D 92 (12) (2015)
  199. Nishi S, Kobayashi T J. Cosmol. Astropart. Phys. 2015 (03) 057 (2015)
  200. Yang R, Chen B et al Astrophys Space Sci 356 (2) 399 (2015)
  201. Kirillov A A, Savelova E P Gen Relativ Gravit 47 (9) (2015)
  202. Chatterjee S, Parikh M, van der Schaar Ja P Physics Letters B 744 34 (2015)
  203. Bao N, Pollack Ja, Remmen G N Fortschritte Der Physik 63 (11-12) 705 (2015)
  204. Kobayashi T, Yamaguchi M, Yokoyama Ju J. Cosmol. Astropart. Phys. 2015 (07) 017 (2015)
  205. Battarra L, Lavrelashvili G, Lehners Je-L Phys. Rev. D 90 (12) (2014)
  206. Liu Zh-G, Li H, Piao Yu-S Phys. Rev. D 90 (8) (2014)

© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions