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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.

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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 (214) ↓ Similar articles (16)

  1. Wolf W J, Thébault K P Y The British Journal For The Philosophy Of Science 000 (2026)
  2. Lehnert K Fortschritte Der Physik 74 (4) (2026)
  3. Mandal S, Shankaranarayanan S Encyclopedia of Astrophysics (2026) p. 73
  4. Nashed G G L, Eid A Eur. Phys. J. C 86 (3) (2026)
  5. Chokyi Kh K, Chattopadhyay S Eur. Phys. J. C 86 (3) (2026)
  6. Yu D-H, Zhu M, Cai Y Phys. Rev. D 113 (6) (2026)
  7. Figueruelo D, van der Westhuizen M et al Physics Of The Dark Universe 52 102238 (2026)
  8. Aman H, Rayimbaev Ja et al Indian J Phys 100 (2) 829 (2026)
  9. Kagirov R Eur. Phys. J. C 86 (4) (2026)
  10. Cheng H, Di Valentino E, Visinelli L Journal Of High Energy Astrophysics 53 100610 (2026)
  11. Gorji M A, Mukohyama Sh et al J. High Energ. Phys. 2026 (4) (2026)
  12. Vasquez I R, Oliveros A Eur. Phys. J. C 86 (2) (2026)
  13. 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)]
  14. Fukuyama T Symmetry 17 (10) 1688 (2025)
  15. Dzhunushaliev V, Folomeev V et al Eur. Phys. J. C 85 (4) (2025)
  16. Mironov S, Sharov M Phys. Rev. D 111 (8) (2025)
  17. An O S, Kang J U et al J. High Energ. Phys. 2025 (5) (2025)
  18. van der Westhuizen M, Abebe A, Di Valentino E Physics Of The Dark Universe 50 102119 (2025)
  19. Ignat’ev Yu G, Kokh I A Gravit. Cosmol. 31 (4) 476 (2025)
  20. Singh A, Shaily et al Annals Of Physics 483 170274 (2025)
  21. Mironov S, Sharov M, Volkova V Eur. Phys. J. C 85 (1) (2025)
  22. Ahmedov B, Caruana M et al Physics Of The Dark Universe 50 102100 (2025)
  23. Choi H G, Petrov P, Yamaguchi M J. High Energ. Phys. 2025 (8) (2025)
  24. Easson D A, Lesnefsky J E Phys. Rev. D 112 (6) (2025)
  25. Alexandre Je, Backhouse D et al J. Phys. A: Math. Theor. 58 (47) 475402 (2025)
  26. Ageeva Y, Kotenko M, Petrov P Phys. Rev. D 112 (6) (2025)
  27. Wolf W J, Ferreira P G, García-García C Phys. Rev. D 111 (4) (2025)
  28. Miranda M Gen Relativ Gravit 57 (1) (2025)
  29. Moghtaderi E, Hull B R et al Phys. Rev. D 111 (12) (2025)
  30. Eroshenko Yu N Uspekhi Fizicheskikh Nauk 195 (02) 221 (2025) [Eroshenko Yu N Phys. Usp. 68 (02) 208 (2025)]
  31. Tessainer D, Maroto A L, Martín-Moruno P Physics Of The Dark Universe 47 101769 (2025)
  32. Ye G, Cai Y Phys. Rev. D 112 (12) (2025)
  33. Green D, Meyers J Phys. Rev. D 111 (8) (2025)
  34. Sharif M, Gul M Z, Fatima N Physics Of The Dark Universe 47 101760 (2025)
  35. Panda A, Gangopadhyay D, Manna G Astroparticle Physics 165 103059 (2025)
  36. R V I, Oliveros A Gen Relativ Gravit 57 (4) (2025)
  37. de Cesare M, Gubitosi G J. Cosmol. Astropart. Phys. 2024 (01) 046 (2024)
  38. Dzhunushaliev V, Folomeev V et al Physics Letters B 855 138812 (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. Pan Sh, Cai Y, Piao Yu-S Eur. Phys. J. C 84 (9) (2024)
  42. Sharif M, Gul M Z, Fatima N New Astronomy 109 102211 (2024)
  43. Chugreev Yu V Phys. Part. Nuclei Lett. 21 (5) 964 (2024)
  44. Matsui H, Sakamura Yu Progress of Theoretical and Experimental Physics 2024 (4) (2024)
  45. Chugreev Yu V Moscow Univ. Phys. 79 (4) 432 (2024)
  46. Mironov S, Volkova V Nuclear Physics B 1004 116550 (2024)
  47. Ye G, Zhu M, Cai Y J. High Energ. Phys. 2024 (2) (2024)
  48. Cesar e Silva Wagno, Shapiro I L Phys. Rev. D 110 (4) (2024)
  49. Borislavov V T, Bouhmadi-López M, Martín-Moruno P Physics Of The Dark Universe 46 101679 (2024)
  50. Singh J K, Shaily et al Physics Of The Dark Universe 46 101658 (2024)
  51. Wolf W J Studies In History And Philosophy Of Science 103 146 (2024)
  52. Cai Y, Zhu M, Piao Yu-S Phys. Rev. Lett. 133 (2) (2024)
  53. Maroto A L J. Cosmol. Astropart. Phys. 2024 (04) 037 (2024)
  54. Chen Z-Ch, Liu L J. Cosmol. Astropart. Phys. 2024 (06) 028 (2024)
  55. Kaur M, Nandi D et al Int. J. Mod. Phys. D 33 (02) (2024)
  56. Giovannini M Eur. Phys. J. C 84 (1) (2024)
  57. Chen Z-Ch, Liu L Eur. Phys. J. C 84 (11) (2024)
  58. Mehdizadeh M R, Ziaie A H Eur. Phys. J. Plus 139 (11) (2024)
  59. Maroto A L, Miravet A D Phys. Rev. D 109 (10) (2024)
  60. Sharif M, Gul M Z, Fatima N Chinese Journal Of Physics 91 66 (2024)
  61. Alexandre Je, Backhouse D Phys. Rev. D 110 (12) (2024)
  62. Battista E Phys. Rev. D 109 (2) (2024)
  63. Yu Ya-H, Wang S Eur. Phys. J. C 84 (6) (2024)
  64. Chugreev Yu V VMU (№4_2024) 2440102–1 (2024)
  65. Garcia-Saenz S, Hua Ju, Zhao Yu Phys. Rev. D 110 (6) (2024)
  66. Mironov S, Valencia-Villegas M J. Cosmol. Astropart. Phys. 2024 (07) 030 (2024)
  67. Cai Y Phys. Rev. D 107 (6) (2023)
  68. Zhu M, Cai Y J. High Energ. Phys. 2023 (4) (2023)
  69. Mansoori S A H, Molaee Z J. Cosmol. Astropart. Phys. 2023 (01) 022 (2023)
  70. Singh J K, Balhara H et al J. High Energ. Phys. 2023 (3) (2023)
  71. Ghaemi N, Kaviani K Int. J. Geom. Methods Mod. Phys. 20 (08) (2023)
  72. Ageeva Yu, Petrov P, Rubakov V J. High Energ. Phys. 2023 (1) (2023)
  73. Alexandre Je, Pla S J. High Energ. Phys. 2023 (5) (2023)
  74. Capuano L, Santoni L, Barausse E Phys. Rev. D 108 (6) (2023)
  75. Duerr P M, Wolf W J Studies In History And Philosophy Of Science 101 1 (2023)
  76. Ageeva Yu A, Petrov P K Uspekhi Fizicheskikh Nauk 193 (11) 1205 (2023)
  77. Mironov S, Valencia-Villegas M Phys. Rev. D 108 (2) (2023)
  78. Mironov S, Shtennikova A J. Cosmol. Astropart. Phys. 2023 (06) 037 (2023)
  79. Azhar F, Kaiser D I Phys. Rev. D 107 (4) (2023)
  80. Hogg N B Monthly Notices of the Royal Astronomical Society: Letters 529 (1) L95 (2023)
  81. Tukhashvili G, Steinhardt P J Phys. Rev. Lett. 131 (9) (2023)
  82. Alexandre Je, Clough K, Pla S Phys. Rev. D 108 (10) (2023)
  83. Mironov S, Volkova V Phys. Rev. D 107 (10) (2023)
  84. Chokyi Kh K, Chattopadhyay S Astron Nachr 344 (7) (2023)
  85. Alexandre Je, Backhouse D Phys. Rev. D 107 (8) (2023)
  86. Martens P, Mukohyama Sh, Namba R J. Cosmol. Astropart. Phys. 2022 (11) 047 (2022)
  87. Alexandre Je, Polonyi Ja Phys. Rev. D 106 (6) (2022)
  88. Yousaf Z Universe 8 (2) 131 (2022)
  89. Deffayet C, Mukohyama Sh, Vikman A Phys. Rev. Lett. 128 (4) (2022)
  90. Cai Y, Xu J et al J. High Energ. Phys. 2022 (10) (2022)
  91. Kadam S A, Mishra B, Tripathy S K Mod. Phys. Lett. A 37 (17) (2022)
  92. Gouttenoire Ya Beyond the Standard Model Cocktail Springer Theses Chapter 3 (2022) p. 73
  93. Khan A, Taylor A J. Cosmol. Astropart. Phys. 2022 (10) 075 (2022)
  94. Corman M, East W E, Ripley Ju L J. Cosmol. Astropart. Phys. 2022 (09) 063 (2022)
  95. Korzyński M, Serbenta Ju Phys. Rev. D 105 (8) (2022)
  96. Matsui H Gen Relativ Gravit 54 (10) (2022)
  97. Alexandre Je, Backhouse D Phys. Rev. D 105 (10) (2022)
  98. Güngör Ö, Starkman G D J. Cosmol. Astropart. Phys. 2021 (04) 003 (2021)
  99. Gómez C, Jimenez R J. Cosmol. Astropart. Phys. 2021 (10) 052 (2021)
  100. Kim J L, Geshnizjani G J. Cosmol. Astropart. Phys. 2021 (03) 104 (2021)
  101. Bernardo H, Brahma S et al Phys. Rev. Lett. 127 (18) (2021)
  102. Arora S, Santos J R L, Sahoo P K Physics Of The Dark Universe 31 100790 (2021)
  103. Alexandre Je, Polonyi Ja Phys. Rev. D 103 (10) (2021)
  104. Ageeva Y, Petrov P, Rubakov V Phys. Rev. D 104 (6) (2021)
  105. Hoyos C, Jokela N et al J. High Energ. Phys. 2021 (10) (2021)
  106. Mandal S Mod. Phys. Lett. A 36 (25) 2150183 (2021)
  107. Colgáin E Ó, Sheikh-Jabbari M M Class. Quantum Grav. 38 (17) 177001 (2021)
  108. Cai Y, Piao Yu-S Phys. Rev. D 103 (8) (2021)
  109. Chakrabarti S Eur. Phys. J. C 81 (2) (2021)
  110. Rincón Á, Contreras E et al Physics Of The Dark Universe 31 100783 (2021)
  111. Bouhmadi-López M, Chen Ch-Yu et al Eur. Phys. J. C 81 (4) (2021)
  112. Tretyakov N, Terletsky A Phys. Scr. 95 (7) 075301 (2020)
  113. Easson D A, Manton T, Svesko A J. Cosmol. Astropart. Phys. 2020 (10) 026 (2020)
  114. Papantonopoulos E, Vlachos Ch Phys. Rev. D 101 (6) (2020)
  115. Giovannini M Progress In Particle And Nuclear Physics 112 103774 (2020)
  116. Kontou E-A, Sanders K Class. Quantum Grav. 37 (19) 193001 (2020)
  117. Sokolov V  A, Garmaev B  D, Rostovsky V  S Phys. Rev. D 101 (8) (2020)
  118. Godani N, Samanta G C Int. J. Mod. Phys. A 35 (08) 2050045 (2020)
  119. Ageeva Y, Evseev O et al Phys. Rev. D 102 (2) (2020)
  120. Lasukov V Symmetry 12 (3) 400 (2020)
  121. Godani N, Samanta G C New Astronomy 80 101399 (2020)
  122. Tahara Hiroaki W  H, Kobayashi T Phys. Rev. D 102 (12) (2020)
  123. Ye G, Piao Yu-S Eur. Phys. J. C 80 (5) (2020)
  124. Artymowski M, Ben-Dayan I, Kumar U J. Cosmol. Astropart. Phys. 2020 (05) 015 (2020)
  125. Mironov S, Rubakov V, Volkova V J. Cosmol. Astropart. Phys. 2020 (05) 024 (2020)
  126. Gal’tsov D V Eur. Phys. J. C 80 (5) (2020)
  127. Mironov S, Rubakov V, Volkova V Phys. Scr. 95 (8) 084002 (2020)
  128. Ripley Ju L, Pretorius F Phys. Rev. D 101 (4) (2020)
  129. Eroshenko Yu N Phys.-Usp. 63 (1) 101 (2020)
  130. Shankar K H Gen Relativ Gravit 52 (2) (2020)
  131. Petrov P K Mod. Phys. Lett. A 35 (37) 2050305 (2020)
  132. Franciolini G, Hui L et al J. High Energ. Phys. 2019 (1) (2019)
  133. Vagenas E C, Ali A F, Alshal H Phys. Rev. D 99 (8) (2019)
  134. Mironov S, Rubakov V, Volkova V Phys. Rev. D 100 (8) (2019)
  135. Bouhmadi-López M, Kiefer C, Martín-Moruno P Gen Relativ Gravit 51 (10) (2019)
  136. Volkova V E, Mironov S A, Rubakov V A J. Exp. Theor. Phys. 129 (4) 553 (2019)
  137. Mandal S JHEPGC 05 (01) 82 (2019)
  138. Mironov S Universe 5 (2) 52 (2019)
  139. de Cesare M Phys. Rev. D 99 (6) (2019)
  140. Mironov S, Rubakov V, Volkova V Class. Quantum Grav. 36 (13) 135008 (2019)
  141. Graham P W, Kaplan D E, Rajendran S Phys. Rev. D 100 (1) (2019)
  142. Kobayashi T Rep. Prog. Phys. 82 (8) 086901 (2019)
  143. Petrov P  K Phys. Rev. D 100 (2) (2019)
  144. Azam M, Rahaman F et al Mod. Phys. Lett. A 34 (33) 1950268 (2019)
  145. Ye 叶 G 根, Piao 朴 Yu-S 云 Commun. Theor. Phys. 71 (4) 427 (2019)
  146. Ó C E, van Putten M H P M, Yavartanoo H Physics Letters B 793 126 (2019)
  147. Addazi A, Alexander S et al Chinese Phys. C 42 (6) 065101 (2018)
  148. Volkova V, Aharonov Y et al EPJ Web Conf. 182 02127 (2018)
  149. Evseev O  A, Melichev O  I Phys. Rev. D 97 (12) (2018)
  150. Graham P W, Kaplan D E, Rajendran S Phys. Rev. D 97 (4) (2018)
  151. Boruah S S, Kim H J et al J. Cosmol. Astropart. Phys. 2018 (08) 031 (2018)
  152. Cunha P V P, Herdeiro C A R Gen Relativ Gravit 50 (4) (2018)
  153. Chandrasekaran V, Remmen G N, Shahbazi-Moghaddam A J. High Energ. Phys. 2018 (11) (2018)
  154. Abbassi M  H, Jozani A, Sepangi H  R Phys. Rev. D 97 (12) (2018)
  155. Bari P, Bhattacharya K, Chakraborty S Gen Relativ Gravit 50 (9) (2018)
  156. Dobre D A, Frolov A V et al J. Cosmol. Astropart. Phys. 2018 (03) 020 (2018)
  157. Contreras E, Rincón Á et al Eur. Phys. J. C 78 (3) (2018)
  158. Rincón Á, Contreras E et al Eur. Phys. J. C 78 (8) (2018)
  159. Ijjas A Class. Quantum Grav. 35 (7) 075010 (2018)
  160. Rincón Á, Koch B Eur. Phys. J. C 78 (12) (2018)
  161. Mironov S, Rubakov V, Volkova V J. Cosmol. Astropart. Phys. 2018 (10) 050 (2018)
  162. Labraña P, del Campo S et al J. Phys.: Conf. Ser. 1043 012026 (2018)
  163. Ageeva Yu, Evseev O et al EPJ Web Conf. 191 07010 (2018)
  164. Mironov S, Rubakov V et al EPJ Web Conf. 191 07014 (2018)
  165. Nikiforova V, Damour T Phys. Rev. D 97 (12) (2018)
  166. Chowdhury T A, Rahman R, Sabuj Z A Nuclear Physics B 936 364 (2018)
  167. Kolevatov R, Mironov S et al Phys. Rev. D 96 (12) (2017)
  168. Di Grezia E, Battista E et al Eur. Phys. J. Plus 132 (12) (2017)
  169. 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
  170. Parikh M, Svesko A Phys. Rev. D 95 (10) (2017)
  171. Katanaev M O, Katanaev M O Teoreticheskaya Matematicheskaya Fizika 191 (2) 219 (2017) [Katanaev M O Theor Math Phys 191 (2) 661 (2017)]
  172. Cai Y, Wan Y et al J. High Energ. Phys. 2017 (1) (2017)
  173. Giovannini M Phys. Rev. D 95 (8) (2017)
  174. Addazi A, Ketov S V J. Cosmol. Astropart. Phys. 2017 (03) 061 (2017)
  175. Evseev O  A, Melichev O  I Phys. Rev. D 96 (2) (2017)
  176. Rincón Á, Koch B, Reyes I J. Phys.: Conf. Ser. 831 012007 (2017)
  177. Rincón Á, Contreras E et al Eur. Phys. J. C 77 (7) (2017)
  178. Brandenberger R, Peter P Found Phys 47 (6) 797 (2017)
  179. Cai Y, Piao Yu-S Phys. Rev. D 96 (12) (2017)
  180. Sberna L, Pani P Phys. Rev. D 96 (12) (2017)
  181. Cai Y, Piao Yu-S J. High Energ. Phys. 2017 (9) (2017)
  182. Giovannini M Phys. Rev. D 96 (10) (2017)
  183. Nishi S, Kobayashi T Phys. Rev. D 95 (6) (2017)
  184. Wang Yu-T, Cai Y et al J. Cosmol. Astropart. Phys. 2017 (01) 010 (2017)
  185. Addazi A Int. J. Mod. Phys. A 32 (28n29) 1750174 (2017)
  186. Akama Sh, Kobayashi T Phys. Rev. D 95 (6) (2017)
  187. Kolevatov R, Mironov S et al J. Cosmol. Astropart. Phys. 2017 (08) 038 (2017)
  188. Arefeva I, Bagrov A et al Phys. Rev. D 94 (4) (2016)
  189. Ijjas A, Ripley Ju, Steinhardt P J Physics Letters B 760 132 (2016)
  190. Koch B, Reyes I A, Rincón Á Class. Quantum Grav. 33 (22) 225010 (2016)
  191. Parikh M, Svesko A Physics Letters B (2016)
  192. Adshead P, Blas D et al J. Cosmol. Astropart. Phys. 2016 (11) 009 (2016)
  193. Pozdeeva E O, Skugoreva M A et al J. Cosmol. Astropart. Phys. 2016 (12) 006 (2016)
  194. Ijjas A, Steinhardt P J Phys. Rev. Lett. 117 (12) (2016)
  195. Libanov M, Mironov S, Rubakov V J. Cosmol. Astropart. Phys. 2016 (08) 037 (2016)
  196. Rubakov V A, Rubakov V A Teoreticheskaya Matematicheskaya Fizika 187 (2) 338 (2016) [Rubakov V A Theor Math Phys 187 (2) 743 (2016)]
  197. Campo Sergio del, Guendelman E I et al J. Cosmol. Astropart. Phys. 2016 (08) 049 (2016)
  198. Pucheu M  L, Alves Junior F  A  P et al Phys. Rev. D 94 (6) (2016)
  199. Kolevatov R, Mironov S Phys. Rev. D 94 (12) (2016)
  200. Ijjas A, Steinhardt P J Class. Quantum Grav. 33 (4) 044001 (2016)
  201. Pozdeeva E, Vernov S et al EPJ Web Conf. 125 03008 (2016)
  202. Kobayashi T Phys. Rev. D 94 (4) (2016)
  203. Beltrán J J, Lazkoz R et al Eur. Phys. J. C 76 (11) (2016)
  204. Parikh M J. High Energ. Phys. 2015 (10) (2015)
  205. Parikh M, van der Schaar Ja P Phys. Rev. D 91 (8) (2015)
  206. Chatterjee S, Parikh M, van der Schaar Ja P Physics Letters B 744 34 (2015)
  207. Kobayashi T, Yamaguchi M, Yokoyama Ju J. Cosmol. Astropart. Phys. 2015 (07) 017 (2015)
  208. Bao N, Pollack Ja, Remmen G N Fortschritte Der Physik 63 (11-12) 705 (2015)
  209. Nishi S, Kobayashi T J. Cosmol. Astropart. Phys. 2015 (03) 057 (2015)
  210. Kirillov A A, Savelova E P Gen Relativ Gravit 47 (9) (2015)
  211. Kolevatov R  S Phys. Rev. D 92 (12) (2015)
  212. Yang R, Chen B et al Astrophys Space Sci 356 (2) 399 (2015)
  213. Liu Zh-G, Li H, Piao Yu-S Phys. Rev. D 90 (8) (2014)
  214. Battarra L, Lavrelashvili G, Lehners Je-L Phys. Rev. D 90 (12) (2014)
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