Geometric sigma model of the Universe

  • The purpose of this work is to demonstrate how an arbitrarily chosen background of the Universe can be made a solution of a simple geometric sigma model. Geometric sigma models are purely geometric theories in which spacetime coordinates are seen as scalar fields coupled to gravity. Although they look like ordinary sigma models, they have the peculiarity that their complete matter content can be gauged away. The remaining geometric theory possesses a background solution that is predefined in the process of constructing the theory. The fact that background configuration is specified in advance is another peculiarity of geometric sigma models. In this paper, I construct geometric sigma models based on different background geometries of the Universe. Whatever background geometry is chosen, the dynamics of its small perturbations is shown to have a generic classical stability. This way, any freely chosen background metric is made a stable solution of a simple model. Three particular models of the Universe are considered as examples of how this is done in practice.
      PCAS:
  • 加载中
  • [1] S. Perlmutter et al (SNCP Collaboration), Astrophys. J, 517: 565 (1999)
    [2] A. G. Riess et al (Supernova Search Team Collaboration), Astron. J, 116: 1009 (1998)
    [3] D. N. Spergel et al (WMAP Collaboration), Astrophys. J. Suppl., 148: 175 (2003); 170: 377 (2007)
    [4] E. Komatsu et al (WMAP Collaboration), Astrophys. J. Suppl., 180: 330 (2009); 192: 18 (2011)
    [5] M. Tegmark et al (SDSS Collaboration), Phys. Rev. D, 69: 103501 (2004)
    [6] U. Seljak et al (SDSS Collaboration), Phys. Rev. D, 71: 103515 (2005)
    [7] D. J. Eisenstein et al (SDSS Collaboration), Astrophys. J, 633: 560 (2005)
    [8] B. Jain and A. Taylor, Phys. Rev. Lett., 91: 141302 (2003)
    [9] P. Ade et al (Planck Collaboration), Astron. Astrophys., 571: A16 (2014); 571: A22 (2014)
    [10] P. Ade et al (BICEP2 Collaboration), Phys. Rev. Lett., 112: 241101 (2014)
    [11] R. R. Caldwell and M. Kamionkowski, Ann. Rev. Nucl. Part. Sci., 59: 397 (2009)
    [12] L. Amendola and S. Tsujikawa, Dark Energy (Cambridge University press, 2010)
    [13] M. Li, X. D. Li, S. Wang, and Y. Wang, Commun. Theor. Phys., 56: 525 (2011)
    [14] M. Kunz, Comptes Rendus Physique, 13: 539 (2012)
    [15] T. Chiba, N. Sugiyama, and T. Nakamura, Mon. Not. Roy. Astron. Soc., 289: L5 (1997)
    [16] R. R. Caldwell, R. Dave, and P. J. Steinhardt, Phys. Rev. Lett., 80: 1582 (1998)
    [17] Y. Fujii, Phys. Rev. D, 26: 2580 (1982)
    [18] R. R. Caldwell, Phys. Lett. B, 545: 23 (2002)
    [19] T. Padmanabhan, Phys. Rev. D, 66: 021301 (2002)
    [20] A. Y. Kamenshchik, U. Moschella, and V. Pasquier, Phys. Lett. B, 511: 265 (2001)
    [21] M. C. Bento, O. Bertolami, and A. A. Sen, Phys. Rev. D, 66: 043507 (2002)
    [22] N. Bilic, G. B. Tupper, and R. D. Viollier, Phys. Lett. B, 535: 17 (2002); Phys. Rev. D, 80: 023515 (2009)
    [23] M. Li, Phys. Lett. B, 603: 1 (2004)
    [24] E. Elizalde, S. Nojiri, S. D. Odintsov, and P. Wang, Phys. Rev. D, 71: 103504 (2005)
    [25] S. Nojiri and S. D. Odintsov, Gen. Rel. Grav., 38: 1285 (2006)
    [26] M. Vasilic, Class. Quant. Grav., 15: 29 (1998)
    [27] B. Guberina, R. Horvat and H. Stefancic, JCAP, 05: 001 (2005)
    [28] H. Kim, H. W. Lee and Y. S. Myung, Phys. Lett. B, 628: 11 (2005)
    [29] X. Zhang, Phys. Rev. D, 74: 103505 (2006); Phys. Lett. B, 648: 1 (2007)
    [30] M. R. Setare, Phys. Lett. B, 648: 329 (2007); 653: 116 (2007); Eur. Phys. J. C, 50: 991 (2007)
    [31] J. Zhang, X. Zhang and H. Liu, Phys. Lett. B, 651: 84 (2007)
    [32] W. Zhao, Phys. Lett. B, 655: 97 (2007)
    [33] M. R. Setare and E. N. Saridakis, Phys. Lett. B, 671: 331 (2009)
    [34] N. Cruz, P. F. Gonzalez-Diaz, A. Rozas-Fernandez and G. Sanchez, Phys. Lett. B, 679: 293 (2009)
    [35] K. Karami and J. Fehri, Phys. Lett. B, 684: 61 (2010)
    [36] A. Rozas-Fernandez, Eur. Phys. J. C, 71: 1536 (2011)
    [37] M. Blagojevic, Gravitation and Gauge Symmetries (Institute of Physics Publishing, Bristol, 2002)
    [38] L. F. Abbott and S. Deser, Nucl. Phys. B, 195: 76 (1982)
  • 加载中

Get Citation
null. Geometric sigma model of the Universe[J]. Chinese Physics C, 2017, 41(5): 055102. doi: 10.1088/1674-1137/41/5/055102
null. Geometric sigma model of the Universe[J]. Chinese Physics C, 2017, 41(5): 055102.  doi: 10.1088/1674-1137/41/5/055102 shu
Milestone
Received: 2016-12-08
Revised: 2017-01-15
Fund

    Supported by Serbian Ministry of Education, Science and Technological Development (171031)

Article Metric

Article Views(1228)
PDF Downloads(30)
Cited by(0)
Policy on re-use
To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Email This Article

Title:
Email:

Geometric sigma model of the Universe

Fund Project:  Supported by Serbian Ministry of Education, Science and Technological Development (171031)

Abstract: The purpose of this work is to demonstrate how an arbitrarily chosen background of the Universe can be made a solution of a simple geometric sigma model. Geometric sigma models are purely geometric theories in which spacetime coordinates are seen as scalar fields coupled to gravity. Although they look like ordinary sigma models, they have the peculiarity that their complete matter content can be gauged away. The remaining geometric theory possesses a background solution that is predefined in the process of constructing the theory. The fact that background configuration is specified in advance is another peculiarity of geometric sigma models. In this paper, I construct geometric sigma models based on different background geometries of the Universe. Whatever background geometry is chosen, the dynamics of its small perturbations is shown to have a generic classical stability. This way, any freely chosen background metric is made a stable solution of a simple model. Three particular models of the Universe are considered as examples of how this is done in practice.

    HTML

Reference (38)

目录

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return