Towards p-Adic Matter in the Universe

  • Branko Dragovich
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 36)


Starting from p-adic string theory with tachyons, we introduce a new kind of non-tachyonic matter which may play an important role in evolution of the Universe. This matter retains nonlocal and nonlinear p-adic string dynamics, but does not suffer of negative square mass. In space-time dimensions \(D = 2 + 4k\), what includes \(D = 6,\,10,\,\ldots\,,\,26, \) the kinetic energy term also maintains correct sign. In these spaces this p-adic matter provides negative cosmological constant and time-dependent scalar field solution with negative potential. Their possible cosmological role is discussed. We have also connected non-locality with string world-sheet in effective Lagrangian for p-adic string.


Dark Matter Dark Energy Scalar String Negative Cosmological Constant Tachyon Condensation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This investigation is supported by Ministry of Education and Science of the Republic of Serbia, grant No 174012. This article is based on the author talk presented at the IX International Workshop “Lie Theory and its Applications in Physics”, 20–26 June 2011, Varna, Bulgaria and the author thanks organizers for hospitality and creative scientific atmosphere. The author also thanks I.Ya. Aref’eva for useful discussions.


  1. 1.
    Li, M., Li, X.-D., Wang, S., Wang, Y.: Dark energy. Comm. Theor. Phys. 56, 525–604 (2011) [arXiv:1103.5870v6 [astro-ph.CO]]Google Scholar
  2. 2.
    Clifton, T., Ferreira, P.G., Padilla, A., Skordis, C.: Modified gravity and cosmology. Phys. Rep. 513(1), 1–189 (2012) [arXiv:1106.2476v2 [astro-ph.CO]]Google Scholar
  3. 3.
    Brekke, L., Freund, P.G.O.: p-Adic numbers in physics. Phys. Rep. JHEP. 12(1), 1–66 (2011)Google Scholar
  4. 4.
    Vladimirov, V.S., Volovich, I.V., Zelenov, E.I.: p-Adic Analysis and Mathematical Physics.World Scientific, Singapore. POS. (ICHP 2012)Google Scholar
  5. 5.
    Dimitrijevic, I., Dragovich, B., Grujic, J., Rakic, Z.: On modified gravity [arXiv:1202.2352v1 [hep-th]]Google Scholar
  6. 6.
    Aref’eva, I.Ya.: Nonlocal string tachyon as a model for cosmological dark energy. AIP Conf. Proc. 826, 301–311 (2006) [arXiv:astro-ph/0410443v2]Google Scholar
  7. 7.
    Koshelev, A.S., Vernov, S.Yu.: Analysis of scalar perturbations in cosmological models with a non-local scalar field. Class. Quant. Grav. 28, 085019 (2011) [arXiv:1009.0746v2 [hep-th]]Google Scholar
  8. 8.
    Volovich, I.V.: p-Adic string. Class. Quant. Grav. 4, L83–L87 (1987)Google Scholar
  9. 9.
    Freund, P.G.O., Olson, M.: Non-archimedean strings. Phys. Lett. B 199, 186–190 (1987)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Gelf’and, I.M., Graev, M.I., Pyatetskii-Shapiro, I.I.: Representation Theory and Automorphic Functions. Saunders, Philadelphia (1969)Google Scholar
  11. 11.
    Schikhof, W.: Ultrametric Calculus. Cambridge University Press, Cambridge (1984)MATHGoogle Scholar
  12. 12.
    Dragovich, B., Khrennikov, A.Yu., Kozyrev, S.V., Volovich, I.V.: On p-adic mathematical physics. p-Adic Numb. Ultr. Anal. Appl. 1(1), 1–17 (2009)Google Scholar
  13. 13.
    Brekke, L., Freund, P.G.O., Olson, M., Witten, E.: Nonarchimedean string dynamics. Nucl. Phys. B 302(3), 365–402 (1988)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Frampton, P.H., Okada, Y.: Effective scalar field theory of p-adic string. Phys. Rev. D 37, 3077–3084 (1988)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Ghoshal, D., Sen, A.: Tachyon condensation and brane descent relations in p-adic string theory. Nucl. Phys. B 584, 300–312 (2000) [arXiv:hep-th/0003278v1]MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Moeller, N., Zwiebach, B.: Dynamics with infinitely many time derivatives and rolling tachyons. JHEP 0210, 034 (2002) [arXiv:hep-th/0207107v2]MathSciNetCrossRefGoogle Scholar
  17. 17.
    Vladimirov, V.S.: On some exact solutions in p-adic open-closed string theory. p-Adic Numb. Ultr. Anal. Appl. 4(1), 57–63 (2012)Google Scholar
  18. 18.
    Weil, A.: Adeles and Algebraic Groups. Birkhauser, Basel (1982)MATHCrossRefGoogle Scholar
  19. 19.
    Dragovich, B.: Adeles in mathematical physics [arXiv:0707.3876v1 [math-ph]]Google Scholar
  20. 20.
    Freund, P.G.O., Witten, E.: Adelic string amplitudes. Phys. Lett. 199, 191–194 (1987)MathSciNetGoogle Scholar
  21. 21.
    Aref’eva, A.Ya., Dragovich, B., Frampton, P.H., Volovich, I.V.: The wave function of the Universe and p-adic gravity. Int. J. Mod. Phys. A 6, 4341–4358 (1991)MathSciNetMATHGoogle Scholar
  22. 22.
    Djordjevic, G., Dragovich, B., Nešić, Lj., Volovich, I.V.: p-Adic and adelic minisuperspace quantum cosmology. Int. J. Mod. Phys. A 17(10), 1413–1433 (2002) [arXiv:gr-qc/0105050v2]Google Scholar
  23. 23.
    Dragovich, B.: Adelic harmonic oscillator. Int. J. Mod. Phys. A 10, 2349–2365 (1995) [arXiv:hep-th/0404160v1]MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    Dragovich, B.: p-Adic and adelic cosmology: p-adic origin of dark energy and dark matter. p-Adic Mathematical Physics, AIP Conf. Proc. 826 (2006) 25–42 [arXiv:hep-th/0602044v1]Google Scholar
  25. 25.
    Barnaby, N., Biswas, T., Cline, J.M.: p-Adic inflation. JHEP 0704, 056 (2007) [arXiv:hep-th/0612230v1]Google Scholar
  26. 26.
    Aref’eva, I.Ya., Joukovskaya, L.V., Vernov, S.Yu.: Bouncing and accelerating solutions in nonlocal stringy models. JHEP 0707, 087 (2007) [arXiv:hep-th/0701184v4]Google Scholar
  27. 27.
    Aref’eva, I.Ya., Koshelev, A.S.: Cosmological signature of tachyon condensation. JHEP 0809, 068 (2008) [arXiv:0804.3570v2 [hep-th]]Google Scholar
  28. 28.
    Calcagni, G., Montobbio, M., Nardelli, G.: A route to nonlocal cosmology. Phys. Rev. D 76, 126001 (2007) [arXiv:0705.3043v3 [hep-th]]Google Scholar
  29. 29.
    Dragovich, B.: Nonlocal dynamics of p-adic strings. Theor. Math. Phys. 164(3), 1151–1155 (2010) [arXiv:1011.0912v1 [hep-th]]Google Scholar
  30. 30.
    Aref’eva, I.Ya., Joukovskaya, L.V.: Time lumps in nonlocal stringy models and cosmological applications. JHEP 0510, 087 (2005) [arXiv:hep-th/0504200v2]Google Scholar

Copyright information

© Springer Japan 2013

Authors and Affiliations

  1. 1.Institute of PhysicsUniversity of BelgradeZemun, BelgradeSerbia

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