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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)
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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 (217) ↓ Similar articles (16)

  1. Wolf W J, Thébault K P Y The British Journal For The Philosophy Of Science 77 (2) 441 (2026)
  2. Aman H, Rayimbaev Ja et al Indian J Phys 100 (2) 829 (2026)
  3. Vasquez I R, Oliveros A Eur. Phys. J. C 86 (2) (2026)
  4. Volkova V E, Mironov S A Teoreticheskaya Matematicheskaya Fizika 227 (3) 611 (2026)
  5. Mandal S, Shankaranarayanan S Encyclopedia of Astrophysics (2026) p. 73
  6. Yu D-H, Zhu M, Cai Y Phys. Rev. D 113 (6) (2026)
  7. Nashed G G L, Eid A Eur. Phys. J. C 86 (3) (2026)
  8. Caldwell R R, Linder E V J. Cosmol. Astropart. Phys. 2026 (05) 008 (2026)
  9. Figueruelo D, van der Westhuizen M et al Physics Of The Dark Universe 52 102238 (2026)
  10. Lehnert K Fortschritte Der Physik 74 (4) (2026)
  11. Chokyi Kh K, Chattopadhyay S Eur. Phys. J. C 86 (3) (2026)
  12. Gorji M A, Mukohyama Sh et al J. High Energ. Phys. 2026 (4) (2026)
  13. Kagirov R Eur. Phys. J. C 86 (4) (2026)
  14. de Souza R, Sousa-Neto A et al Phys. Rev. D 113 (10) (2026)
  15. Cheng H, Di Valentino E, Visinelli L Journal Of High Energy Astrophysics 53 100610 (2026)
  16. Dzhunushaliev V, Folomeev V et al Eur. Phys. J. C 85 (4) (2025)
  17. An O S, Kang J U et al J. High Energ. Phys. 2025 (5) (2025)
  18. Ye G, Cai Y Phys. Rev. D 112 (12) (2025)
  19. Eroshenko Yu N Uspekhi Fizicheskikh Nauk 195 (02) 221 (2025) [Eroshenko Yu N Phys. Usp. 68 (02) 208 (2025)]
  20. Mironov S, Sharov M Phys. Rev. D 111 (8) (2025)
  21. Green D, Meyers J Phys. Rev. D 111 (8) (2025)
  22. Fukuyama T Symmetry 17 (10) 1688 (2025)
  23. 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)]
  24. Ahmedov B, Caruana M et al Physics Of The Dark Universe 50 102100 (2025)
  25. Ignat’ev Yu G, Kokh I A Gravit. Cosmol. 31 (4) 476 (2025)
  26. Tessainer D, Maroto A L, Martín-Moruno P Physics Of The Dark Universe 47 101769 (2025)
  27. Choi H G, Petrov P, Yamaguchi M J. High Energ. Phys. 2025 (8) (2025)
  28. van der Westhuizen M, Abebe A, Di Valentino E Physics Of The Dark Universe 50 102119 (2025)
  29. Mironov S, Sharov M, Volkova V Eur. Phys. J. C 85 (1) (2025)
  30. Singh A, Shaily et al Annals Of Physics 483 170274 (2025)
  31. Panda A, Gangopadhyay D, Manna G Astroparticle Physics 165 103059 (2025)
  32. Moghtaderi E, Hull B R et al Phys. Rev. D 111 (12) (2025)
  33. Miranda M Gen Relativ Gravit 57 (1) (2025)
  34. Sharif M, Gul M Z, Fatima N Physics Of The Dark Universe 47 101760 (2025)
  35. Wolf W J, Ferreira P G, García-García C Phys. Rev. D 111 (4) (2025)
  36. Easson D A, Lesnefsky J E Phys. Rev. D 112 (6) (2025)
  37. R V I, Oliveros A Gen Relativ Gravit 57 (4) (2025)
  38. Alexandre Je, Backhouse D et al J. Phys. A: Math. Theor. 58 (47) 475402 (2025)
  39. Ageeva Y, Kotenko M, Petrov P Phys. Rev. D 112 (6) (2025)
  40. Mironov S, Volkova V Nuclear Physics B 1004 116550 (2024)
  41. Mehdizadeh M R, Ziaie A H Eur. Phys. J. Plus 139 (11) (2024)
  42. Wolf W J Studies In History And Philosophy Of Science 103 146 (2024)
  43. Battista E Phys. Rev. D 109 (2) (2024)
  44. Borislavov V T, Bouhmadi-López M, Martín-Moruno P Physics Of The Dark Universe 46 101679 (2024)
  45. Cai Y, Zhu M, Piao Yu-S Phys. Rev. Lett. 133 (2) (2024)
  46. Chugreev Yu V Phys. Part. Nuclei Lett. 21 (5) 964 (2024)
  47. Chen Z-Ch, Liu L Eur. Phys. J. C 84 (11) (2024)
  48. Chugreev Yu V Moscow Univ. Phys. 79 (4) 432 (2024)
  49. Sharif M, Gul M Z, Fatima N New Astronomy 109 102211 (2024)
  50. Ai W-Yu, Alexandre Je et al J. High Energ. Phys. 2024 (5) (2024)
  51. Chen Z-Ch, Liu L J. Cosmol. Astropart. Phys. 2024 (06) 028 (2024)
  52. Giovannini M Eur. Phys. J. C 84 (1) (2024)
  53. Mironov S, Volkova V Int. J. Mod. Phys. A 39 (35) (2024)
  54. Cesar e Silva Wagno, Shapiro I L Phys. Rev. D 110 (4) (2024)
  55. Chugreev Yu V VMU (№4_2024) 2440102–1 (2024)
  56. Garcia-Saenz S, Hua Ju, Zhao Yu Phys. Rev. D 110 (6) (2024)
  57. Maroto A L J. Cosmol. Astropart. Phys. 2024 (04) 037 (2024)
  58. Singh J K, Shaily et al Physics Of The Dark Universe 46 101658 (2024)
  59. Ye G, Zhu M, Cai Y J. High Energ. Phys. 2024 (2) (2024)
  60. Dzhunushaliev V, Folomeev V et al Physics Letters B 855 138812 (2024)
  61. Matsui H, Sakamura Yu Progress of Theoretical and Experimental Physics 2024 (4) (2024)
  62. Alexandre Je, Backhouse D Phys. Rev. D 110 (12) (2024)
  63. Sharif M, Gul M Z, Fatima N Chinese Journal Of Physics 91 66 (2024)
  64. Pan Sh, Cai Y, Piao Yu-S Eur. Phys. J. C 84 (9) (2024)
  65. de Cesare M, Gubitosi G J. Cosmol. Astropart. Phys. 2024 (01) 046 (2024)
  66. Mironov S, Valencia-Villegas M J. Cosmol. Astropart. Phys. 2024 (07) 030 (2024)
  67. Kaur M, Nandi D et al Int. J. Mod. Phys. D 33 (02) (2024)
  68. Yu Ya-H, Wang S Eur. Phys. J. C 84 (6) (2024)
  69. Maroto A L, Miravet A D Phys. Rev. D 109 (10) (2024)
  70. Chokyi Kh K, Chattopadhyay S Astron Nachr 344 (7) (2023)
  71. Ageeva Yu A, Petrov P K Uspekhi Fizicheskikh Nauk 193 (11) 1205 (2023)
  72. Alexandre Je, Pla S J. High Energ. Phys. 2023 (5) (2023)
  73. Duerr P M, Wolf W J Studies In History And Philosophy Of Science 101 1 (2023)
  74. Singh J K, Balhara H et al J. High Energ. Phys. 2023 (3) (2023)
  75. Azhar F, Kaiser D I Phys. Rev. D 107 (4) (2023)
  76. Mironov S, Shtennikova A J. Cosmol. Astropart. Phys. 2023 (06) 037 (2023)
  77. Alexandre Je, Clough K, Pla S Phys. Rev. D 108 (10) (2023)
  78. Ghaemi N, Kaviani K Int. J. Geom. Methods Mod. Phys. 20 (08) (2023)
  79. Mansoori S A H, Molaee Z J. Cosmol. Astropart. Phys. 2023 (01) 022 (2023)
  80. Zhu M, Cai Y J. High Energ. Phys. 2023 (4) (2023)
  81. Mironov S, Valencia-Villegas M Phys. Rev. D 108 (2) (2023)
  82. Ageeva Yu, Petrov P, Rubakov V J. High Energ. Phys. 2023 (1) (2023)
  83. Mironov S, Volkova V Phys. Rev. D 107 (10) (2023)
  84. Tukhashvili G, Steinhardt P J Phys. Rev. Lett. 131 (9) (2023)
  85. Hogg N B Monthly Notices of the Royal Astronomical Society: Letters 529 (1) L95 (2023)
  86. Alexandre Je, Backhouse D Phys. Rev. D 107 (8) (2023)
  87. Cai Y Phys. Rev. D 107 (6) (2023)
  88. Capuano L, Santoni L, Barausse E Phys. Rev. D 108 (6) (2023)
  89. Corman M, East W E, Ripley Ju L J. Cosmol. Astropart. Phys. 2022 (09) 063 (2022)
  90. Deffayet C, Mukohyama Sh, Vikman A Phys. Rev. Lett. 128 (4) (2022)
  91. Alexandre Je, Polonyi Ja Phys. Rev. D 106 (6) (2022)
  92. Cai Y, Xu J et al J. High Energ. Phys. 2022 (10) (2022)
  93. Matsui H Gen Relativ Gravit 54 (10) (2022)
  94. Khan A, Taylor A J. Cosmol. Astropart. Phys. 2022 (10) 075 (2022)
  95. Yousaf Z Universe 8 (2) 131 (2022)
  96. Gouttenoire Ya Beyond the Standard Model Cocktail Springer Theses Chapter 3 (2022) p. 73
  97. Korzyński M, Serbenta Ju Phys. Rev. D 105 (8) (2022)
  98. Kadam S A, Mishra B, Tripathy S K Mod. Phys. Lett. A 37 (17) (2022)
  99. Martens P, Mukohyama Sh, Namba R J. Cosmol. Astropart. Phys. 2022 (11) 047 (2022)
  100. Alexandre Je, Backhouse D Phys. Rev. D 105 (10) (2022)
  101. Colgáin E Ó, Sheikh-Jabbari M M Class. Quantum Grav. 38 (17) 177001 (2021)
  102. Gómez C, Jimenez R J. Cosmol. Astropart. Phys. 2021 (10) 052 (2021)
  103. Kim J L, Geshnizjani G J. Cosmol. Astropart. Phys. 2021 (03) 104 (2021)
  104. Alexandre Je, Polonyi Ja Phys. Rev. D 103 (10) (2021)
  105. Bernardo H, Brahma S et al Phys. Rev. Lett. 127 (18) (2021)
  106. Mandal S Mod. Phys. Lett. A 36 (25) 2150183 (2021)
  107. Chakrabarti S Eur. Phys. J. C 81 (2) (2021)
  108. Güngör Ö, Starkman G D J. Cosmol. Astropart. Phys. 2021 (04) 003 (2021)
  109. Ageeva Y, Petrov P, Rubakov V Phys. Rev. D 104 (6) (2021)
  110. Bouhmadi-López M, Chen Ch-Yu et al Eur. Phys. J. C 81 (4) (2021)
  111. Arora S, Santos J R L, Sahoo P K Physics Of The Dark Universe 31 100790 (2021)
  112. Hoyos C, Jokela N et al J. High Energ. Phys. 2021 (10) (2021)
  113. Rincón Á, Contreras E et al Physics Of The Dark Universe 31 100783 (2021)
  114. Cai Y, Piao Yu-S Phys. Rev. D 103 (8) (2021)
  115. Lasukov V Symmetry 12 (3) 400 (2020)
  116. Giovannini M Progress In Particle And Nuclear Physics 112 103774 (2020)
  117. Godani N, Samanta G C New Astronomy 80 101399 (2020)
  118. Sokolov V  A, Garmaev B  D, Rostovsky V  S Phys. Rev. D 101 (8) (2020)
  119. Kontou E-A, Sanders K Class. Quantum Grav. 37 (19) 193001 (2020)
  120. Papantonopoulos E, Vlachos Ch Phys. Rev. D 101 (6) (2020)
  121. Tretyakov N, Terletsky A Phys. Scr. 95 (7) 075301 (2020)
  122. Ageeva Y, Evseev O et al Phys. Rev. D 102 (2) (2020)
  123. Easson D A, Manton T, Svesko A J. Cosmol. Astropart. Phys. 2020 (10) 026 (2020)
  124. Godani N, Samanta G C Int. J. Mod. Phys. A 35 (08) 2050045 (2020)
  125. Tahara Hiroaki W  H, Kobayashi T Phys. Rev. D 102 (12) (2020)
  126. Ye G, Piao Yu-S Eur. Phys. J. C 80 (5) (2020)
  127. Mironov S, Rubakov V, Volkova V J. Cosmol. Astropart. Phys. 2020 (05) 024 (2020)
  128. Gal’tsov D V Eur. Phys. J. C 80 (5) (2020)
  129. Mironov S, Rubakov V, Volkova V Phys. Scr. 95 (8) 084002 (2020)
  130. Ripley Ju L, Pretorius F Phys. Rev. D 101 (4) (2020)
  131. Petrov P K Mod. Phys. Lett. A 35 (37) 2050305 (2020)
  132. Shankar K H Gen Relativ Gravit 52 (2) (2020)
  133. Artymowski M, Ben-Dayan I, Kumar U J. Cosmol. Astropart. Phys. 2020 (05) 015 (2020)
  134. Eroshenko Yu N Phys.-Usp. 63 (1) 101 (2020)
  135. Kobayashi T Rep. Prog. Phys. 82 (8) 086901 (2019)
  136. Mironov S, Rubakov V, Volkova V Phys. Rev. D 100 (8) (2019)
  137. Volkova V E, Mironov S A, Rubakov V A J. Exp. Theor. Phys. 129 (4) 553 (2019)
  138. Graham P W, Kaplan D E, Rajendran S Phys. Rev. D 100 (1) (2019)
  139. Mironov S Universe 5 (2) 52 (2019)
  140. Vagenas E C, Ali A F, Alshal H Phys. Rev. D 99 (8) (2019)
  141. Mironov S, Rubakov V, Volkova V Class. Quantum Grav. 36 (13) 135008 (2019)
  142. Franciolini G, Hui L et al J. High Energ. Phys. 2019 (1) (2019)
  143. Ó C E, van Putten M H P M, Yavartanoo H Physics Letters B 793 126 (2019)
  144. Azam M, Rahaman F et al Mod. Phys. Lett. A 34 (33) 1950268 (2019)
  145. de Cesare M Phys. Rev. D 99 (6) (2019)
  146. Bouhmadi-López M, Kiefer C, Martín-Moruno P Gen Relativ Gravit 51 (10) (2019)
  147. Mandal S JHEPGC 05 (01) 82 (2019)
  148. Petrov P  K Phys. Rev. D 100 (2) (2019)
  149. Ye 叶 G 根, Piao 朴 Yu-S 云 Commun. Theor. Phys. 71 (4) 427 (2019)
  150. Addazi A, Alexander S et al Chinese Phys. C 42 (6) 065101 (2018)
  151. Dobre D A, Frolov A V et al J. Cosmol. Astropart. Phys. 2018 (03) 020 (2018)
  152. Evseev O  A, Melichev O  I Phys. Rev. D 97 (12) (2018)
  153. Rincón Á, Contreras E et al Eur. Phys. J. C 78 (8) (2018)
  154. Graham P W, Kaplan D E, Rajendran S Phys. Rev. D 97 (4) (2018)
  155. Boruah S S, Kim H J et al J. Cosmol. Astropart. Phys. 2018 (08) 031 (2018)
  156. Cunha P V P, Herdeiro C A R Gen Relativ Gravit 50 (4) (2018)
  157. Chandrasekaran V, Remmen G N, Shahbazi-Moghaddam A J. High Energ. Phys. 2018 (11) (2018)
  158. Abbassi M  H, Jozani A, Sepangi H  R Phys. Rev. D 97 (12) (2018)
  159. Volkova V, Aharonov Y et al EPJ Web Conf. 182 02127 (2018)
  160. Bari P, Bhattacharya K, Chakraborty S Gen Relativ Gravit 50 (9) (2018)
  161. Mironov S, Rubakov V, Volkova V J. Cosmol. Astropart. Phys. 2018 (10) 050 (2018)
  162. Chowdhury T A, Rahman R, Sabuj Z A Nuclear Physics B 936 364 (2018)
  163. Nikiforova V, Damour T Phys. Rev. D 97 (12) (2018)
  164. Contreras E, Rincón Á et al Eur. Phys. J. C 78 (3) (2018)
  165. Ijjas A Class. Quantum Grav. 35 (7) 075010 (2018)
  166. Mironov S, Rubakov V et al EPJ Web Conf. 191 07014 (2018)
  167. Ageeva Yu, Evseev O et al EPJ Web Conf. 191 07010 (2018)
  168. Labraña P, del Campo S et al J. Phys.: Conf. Ser. 1043 012026 (2018)
  169. Rincón Á, Koch B Eur. Phys. J. C 78 (12) (2018)
  170. Rincón Á, Koch B, Reyes I J. Phys.: Conf. Ser. 831 012007 (2017)
  171. Addazi A, Ketov S V J. Cosmol. Astropart. Phys. 2017 (03) 061 (2017)
  172. Evseev O  A, Melichev O  I Phys. Rev. D 96 (2) (2017)
  173. Giovannini M Phys. Rev. D 95 (8) (2017)
  174. Cai Y, Wan Y et al J. High Energ. Phys. 2017 (1) (2017)
  175. Parikh M, Svesko A Phys. Rev. D 95 (10) (2017)
  176. 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
  177. Rincón Á, Contreras E et al Eur. Phys. J. C 77 (7) (2017)
  178. Di Grezia E, Battista E et al Eur. Phys. J. Plus 132 (12) (2017)
  179. Kolevatov R, Mironov S et al Phys. Rev. D 96 (12) (2017)
  180. Brandenberger R, Peter P Found Phys 47 (6) 797 (2017)
  181. Katanaev M O, Katanaev M O Teoreticheskaya Matematicheskaya Fizika 191 (2) 219 (2017) [Katanaev M O Theor Math Phys 191 (2) 661 (2017)]
  182. Wang Yu-T, Cai Y et al J. Cosmol. Astropart. Phys. 2017 (01) 010 (2017)
  183. Akama Sh, Kobayashi T Phys. Rev. D 95 (6) (2017)
  184. Addazi A Int. J. Mod. Phys. A 32 (28n29) 1750174 (2017)
  185. Cai Y, Piao Yu-S J. High Energ. Phys. 2017 (9) (2017)
  186. Kolevatov R, Mironov S et al J. Cosmol. Astropart. Phys. 2017 (08) 038 (2017)
  187. Sberna L, Pani P Phys. Rev. D 96 (12) (2017)
  188. Cai Y, Piao Yu-S Phys. Rev. D 96 (12) (2017)
  189. Giovannini M Phys. Rev. D 96 (10) (2017)
  190. Nishi S, Kobayashi T Phys. Rev. D 95 (6) (2017)
  191. Adshead P, Blas D et al J. Cosmol. Astropart. Phys. 2016 (11) 009 (2016)
  192. Ijjas A, Steinhardt P J Phys. Rev. Lett. 117 (12) (2016)
  193. Koch B, Reyes I A, Rincón Á Class. Quantum Grav. 33 (22) 225010 (2016)
  194. Pucheu M  L, Alves Junior F  A  P et al Phys. Rev. D 94 (6) (2016)
  195. Kobayashi T Phys. Rev. D 94 (4) (2016)
  196. Pozdeeva E O, Skugoreva M A et al J. Cosmol. Astropart. Phys. 2016 (12) 006 (2016)
  197. Parikh M, Svesko A Physics Letters B (2016)
  198. Libanov M, Mironov S, Rubakov V J. Cosmol. Astropart. Phys. 2016 (08) 037 (2016)
  199. Pozdeeva E, Vernov S et al EPJ Web Conf. 125 03008 (2016)
  200. Kolevatov R, Mironov S Phys. Rev. D 94 (12) (2016)
  201. Beltrán J J, Lazkoz R et al Eur. Phys. J. C 76 (11) (2016)
  202. Ijjas A, Steinhardt P J Class. Quantum Grav. 33 (4) 044001 (2016)
  203. Rubakov V A, Rubakov V A Teoreticheskaya Matematicheskaya Fizika 187 (2) 338 (2016) [Rubakov V A Theor Math Phys 187 (2) 743 (2016)]
  204. Campo Sergio del, Guendelman E I et al J. Cosmol. Astropart. Phys. 2016 (08) 049 (2016)
  205. Ijjas A, Ripley Ju, Steinhardt P J Physics Letters B 760 132 (2016)
  206. Arefeva I, Bagrov A et al Phys. Rev. D 94 (4) (2016)
  207. Kobayashi T, Yamaguchi M, Yokoyama Ju J. Cosmol. Astropart. Phys. 2015 (07) 017 (2015)
  208. Kirillov A A, Savelova E P Gen Relativ Gravit 47 (9) (2015)
  209. Parikh M, van der Schaar Ja P Phys. Rev. D 91 (8) (2015)
  210. Chatterjee S, Parikh M, van der Schaar Ja P Physics Letters B 744 34 (2015)
  211. Kolevatov R  S Phys. Rev. D 92 (12) (2015)
  212. Parikh M J. High Energ. Phys. 2015 (10) (2015)
  213. Nishi S, Kobayashi T J. Cosmol. Astropart. Phys. 2015 (03) 057 (2015)
  214. Bao N, Pollack Ja, Remmen G N Fortschritte Der Physik 63 (11-12) 705 (2015)
  215. Yang R, Chen B et al Astrophys Space Sci 356 (2) 399 (2015)
  216. Liu Zh-G, Li H, Piao Yu-S Phys. Rev. D 90 (8) (2014)
  217. Battarra L, Lavrelashvili G, Lehners Je-L Phys. Rev. D 90 (12) (2014)
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