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大尺度有效引力的E(2)规范理论模型

魏文叶 申佳音 吴奕暐 杨礼想 薛迅 阮自强

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大尺度有效引力的E(2)规范理论模型

魏文叶, 申佳音, 吴奕暐, 杨礼想, 薛迅, 阮自强

E(2) gauge theory model of effective gravitational theory at large scale

Wei Wen-Ye, Shen Jia-Yin, Wu Yi-Wei, Yang Li-Xiang, Xue Xun, Yuan Tzu-Chiang
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  • 微波背景辐射的低l极矩的各向异性可能不能用微波背景辐射静止系boost到本动参考系来解释,我们推断boost对称性在宇宙学尺度上缺失,又由于单纯结合广义相对论和物质结构的标准模型不能解释星系以上尺度的引力现象,需要引入暗物质和暗能量.而迄今为止所有寻找暗物质粒子的实验给出的都是否定结果,暗能量的本质更是一个谜.因此,我们假设洛伦兹对称性是从星系以上尺度开始部分破缺,以非常狭义相对论对称群E(2)为例,用E(2)规范理论来构造大尺度有效引力理论,并分析了此规范理论的自洽性.从这些讨论中发现,当物质源即使为普通标量物质时,contortion也一般非零,非零contortion的存在会贡献一个等效能量动量张量的分布,它可能对暗物质效应给出至少部分的贡献.我们从对称性出发修改引力,有别于其他的修改引力理论.
    At the cosmological scale, there exist many anisotropic anomalies in the low-l multipoles of the CMB angular power spectrum. Especially, the normals to the octopole and quadrupole planes are aligned with the direction of the cosmological dipole at a level inconsistent with Gaussian random. The inconsistency indicates that the anomalies may not be boost effect from the CMB rest frame to the peculiar frame. It hints us that the boost invariance might be violated on a cosmological scale. There are some discrepancies between the astronomical and cosmological observations, and the predictions are solely based on general relativity and the standard model for elementary particle physics. The solutions are the introduction of dark matter and dark energy. However, all the experiments aiming at finding dark matter particles give negative result and it is still a mystery:what the dark energy is comprised of. We suppose that the Lorentz symmetry begins to be violated partly from the scale of galaxy and utilize the very special relativity symmetry group E(2) as an example to illustrate the Lorentz violation effect on the large-scale effective gravity. A local E(2) but Lorentz invariant gauge theory can be constructed based on the equivalence principle and the gauge principle. To realize the E(2) symmetry, the closure requirement of Maurer-Cartan eqnarray on E(2) algebra needs to be satisfied by postulating constraint conditions among the components of the Lorentz connection. The local Lorentz invariant gauge theory with a Hilbert-Einstein action is a theory with torsion in general case. However in the case of scalar matter source, the theory is exactly the theory of general relativity with Levi-Civita connection and zero torsion. In the E(2) gauge theory case, the closure requirement of Maurer-Cartan eqnarray for E(2) algebra postulates 12 constraint eqnarrays among the components of the Lorentz connection and the eqnarrays of motion for connection reduce the number of independent components of connection to 12. The eqnarrays of motion for the tetrad field do not contain only the involved tetrad field components nor these relevant independent components. So the whole number of variables needed to be solved is 12 more than that in general relativity while there are 12 more eqnarrays in the meantime. The torsion or the contortion field of the E(2) gauge theory is non-trivial even in the case of scalar matter source distribution. Decompose the connection into Levi-Civita one and the contortion part and rewrite the eqnarrays for tetrad field in the formalism of general relativity, then there will appear an effective energy-momentum tensor contributed by the contortion distribution, in addition to the ordinary matter source distribution even for the case of scalar matter source. We expect it to contribute at least part of the dark matter effect. We also examine the holding of the first and second Bianchi identities induced by Jacobi identity of the E(2) gauge theory. The approach of our modified gravity is different from other approach of modified gravity in the sense that we construct the modified gravity by modifying the spacetime symmetry on a large scale and the emergence of effective energy-momentum tensor caused by Lorentz violation effect is due to a purely large scale effect.
      通信作者: 薛迅, xxue@phy.ecnu.edu.cn
    • 基金项目: 国家自然科学基金(批准号:11435005)资助的课题.
      Corresponding author: Xue Xun, xxue@phy.ecnu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos.11435005).
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    Colladay D, Kostelecky V A 1998 Phys. Rev. D 58 116002

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    Li X, Chang Z 2013 Chin. Phys. C 37 123103

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    Wu Y W, Xue X, Yang L X, Yuan T 2016 Chin. Sci. Bull. 10 1360

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    Wu Y W, Xue X, Yang L X, Yuan T 2015 arXiv: 151000814v3

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    Wu Y W, Xue X 2016 J. East China Normal Univ. 10 3969

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    Cohen A G, Glashow S L 2006 Phys. Rev. Lett. 97 021601

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    Micheletti S, Abdalla E, Wang B 2009 Phys. Rev. D 79 123506

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    He J H, Wang B 2011 Phys. Rev. D 83 063515

  • [1]

    Zwicky F 1937 Astrophys. J. 86 217

    [2]

    Rubin V C, Ford Jr W K, Thonnard N 1980 Astrophys. J. 238 471

    [3]

    Shojai F, Shojai A 2014 General Relat. Gravit. 46 1704

    [4]

    Moffat J W 2006 J. Cosmol. Astropart. Phys. 03 004

    [5]

    Bekenstein J D 2004 Phys. Rev. D 70 083509

    [6]

    Agnese R, Anderson A J, Asai M, et al. 2014 Phys. Rev. Lett. 112 241302

    [7]

    Kim S C, Bhang H, Choi J H, et al. 2012 Phys. Rev. Lett. 108 181301

    [8]

    Geringer-Sameth A, Koushiappas S M 2011 Phys. Rev. Lett. 107 241303

    [9]

    Ji X D 2017 Nature 542 172

    [10]

    Akerib D S, Akerlof C W, Akimov D Y, et al. 2017 Phys. Rev. Lett. 118 021303

    [11]

    Weinberg S 2008 Cosmology (New York:Oxford University Press) pp1-6

    [12]

    Aghanim N, Armitage-Caplan C, Arnaud M, et al. 2014 Astron. Astrophys. 571 A27

    [13]

    Ade P A R, Aghanim N, Armitage-Caplan C, et al. 2014 Astron. Astrophys. 571 A20

    [14]

    Ade P A R, Aghanim N, Akrami Y, et al. 2016 Astron. Astrophys. 594 A16

    [15]

    Coleman S R, Glashow S L 1999 Phys. Rev. D 59 116008

    [16]

    Colladay D, Kostelecky V A 1998 Phys. Rev. D 58 116002

    [17]

    Li X, Chang Z 2013 Chin. Phys. C 37 123103

    [18]

    Wu Y W, Xue X, Yang L X, Yuan T 2016 Chin. Sci. Bull. 10 1360

    [19]

    Wu Y W, Xue X, Yang L X, Yuan T 2015 arXiv: 151000814v3

    [20]

    Wu Y W, Xue X 2016 J. East China Normal Univ. 10 3969

    [21]

    Cohen A G, Glashow S L 2006 Phys. Rev. Lett. 97 021601

    [22]

    Micheletti S, Abdalla E, Wang B 2009 Phys. Rev. D 79 123506

    [23]

    He J H, Wang B 2011 Phys. Rev. D 83 063515

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出版历程
  • 收稿日期:  2017-02-04
  • 修回日期:  2017-04-06
  • 刊出日期:  2017-07-05

大尺度有效引力的E(2)规范理论模型

  • 1. 华东师范大学物理系, 上海 200241;
  • 2. 中央研究院物理研究所, 台北 11529
  • 通信作者: 薛迅, xxue@phy.ecnu.edu.cn
    基金项目: 国家自然科学基金(批准号:11435005)资助的课题.

摘要: 微波背景辐射的低l极矩的各向异性可能不能用微波背景辐射静止系boost到本动参考系来解释,我们推断boost对称性在宇宙学尺度上缺失,又由于单纯结合广义相对论和物质结构的标准模型不能解释星系以上尺度的引力现象,需要引入暗物质和暗能量.而迄今为止所有寻找暗物质粒子的实验给出的都是否定结果,暗能量的本质更是一个谜.因此,我们假设洛伦兹对称性是从星系以上尺度开始部分破缺,以非常狭义相对论对称群E(2)为例,用E(2)规范理论来构造大尺度有效引力理论,并分析了此规范理论的自洽性.从这些讨论中发现,当物质源即使为普通标量物质时,contortion也一般非零,非零contortion的存在会贡献一个等效能量动量张量的分布,它可能对暗物质效应给出至少部分的贡献.我们从对称性出发修改引力,有别于其他的修改引力理论.

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