Journal of High Energy Physics

, 2010:17 | Cite as

Particle production near an AdS crunch

Open Access
Article

Abstract

We numerically study the dual field theory evolution of five-dimensional asymptotically anti-de Sitter solutions of supergravity that develop cosmological singularities. The dual theory is an unstable deformation of the \( \mathcal{N} = 4 \) gauge theory on \( \mathbb{R} \times {S^3} \), and the big crunch singularity in the bulk occurs when a boundary scalar field runs to infinity. Consistent quantum evolution requires one imposes boundary conditions at infinity. Modeling these by a steep regularization of the scalar potential, we find that when an initially nearly homogeneous wavepacket rolls down the potential, most of the potential energy of the initial configuration is converted into gradient energy during the first oscillation of the field. This indicates there is no transition from a big crunch to a big bang in the bulk for dual boundary conditions of this kind.

Keywords

AdS-CFT Correspondence Spacetime Singularities 

References

  1. [1]
    M. Gasperini and G. Veneziano, Pre-big bang in string cosmology, Astropart. Phys. 1 (1993) 317 [hep-th/9211021] [SPIRES].CrossRefADSGoogle Scholar
  2. [2]
    J. Khoury, B.A. Ovrut, N. Seiberg, P.J. Steinhardt and N. Turok, From big crunch to big bang, Phys. Rev. D 65 (2002) 086007 [hep-th/0108187] [SPIRES].ADSGoogle Scholar
  3. [3]
    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [SPIRES].MATHADSMathSciNetGoogle Scholar
  4. [4]
    T. Hertog and G.T. Horowitz, Towards a big crunch dual, JHEP 07 (2004) 073 [hep-th/0406134] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  5. [5]
    T. Hertog and G.T. Horowitz, Holographic description of AdS cosmologies, JHEP 04 (2005) 005 [hep-th/0503071] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  6. [6]
    B. Craps, T. Hertog and N. Turok, Quantum resolution of cosmological singularities using AdS/CFT, arXiv:0712.4180 [SPIRES].
  7. [7]
    S. Elitzur, A. Giveon, M. Porrati and E. Rabinovici, Multitrace deformations of vector and adjoint theories and their holographic duals, JHEP 02 (2006) 006 [hep-th/0511061] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  8. [8]
    J.L.F. Barbon and E. Rabinovici, Holography of AdS vacuum bubbles, JHEP 04 (2010) 123 [arXiv:1003.4966] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  9. [9]
    A. Bernamonti and B. Craps, D-brane potentials from multi-trace deformations in AdS/CFT, JHEP 08 (2009) 112 [arXiv:0907.0889] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  10. [10]
    V. Asnin, E. Rabinovici and M. Smolkin, On rolling, tunneling and decaying in some large-N vector models, JHEP 08 (2009) 001 [arXiv:0905.3526] [SPIRES].CrossRefADSGoogle Scholar
  11. [11]
    T. Hertog and G.T. Horowitz, Designer gravity and field theory effective potentials, Phys. Rev. Lett. 94 (2005) 221301 [hep-th/0412169] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  12. [12]
    T. Hertog and K. Maeda, Black holes with scalar hair and asymptotics in N = 8 supergravity, JHEP 07 (2004) 051 [hep-th/0404261] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  13. [13]
    M. Henneaux, C. Martinez, R. Troncoso and J. Zanelli, Asymptotically Anti-de Sitter spacetimes and scalar fields with a logarithmic branch, Phys. Rev. D 70 (2004) 044034 [hep-th/0404236] [SPIRES].ADSMathSciNetGoogle Scholar
  14. [14]
    E. Witten, Multi-trace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [SPIRES].
  15. [15]
    M. Berkooz, A. Sever and A. Shomer, Double-trace deformations, boundary conditions and spacetime singularities, JHEP 05 (2002) 034 [hep-th/0112264] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  16. [16]
    M. Reed and B. Simon, Methods of modern mathematical physics. 2. Fourier analysis, selfadjointness, Academic Press, New York U.S.A. (1975), pag. 361.Google Scholar
  17. [17]
    M. Carreau, E. Farhi, S. Gutmann and P.F. Mende, The functional integral for quantum systems with hamiltonians unbounded from below, Ann. Phys. 204 (1990) 186 [SPIRES].CrossRefMATHADSMathSciNetGoogle Scholar
  18. [18]
    L. Kofman, Tachyonic preheating, hep-ph/0107280 [SPIRES].
  19. [19]
    G.N. Felder, L. Kofman and A.D. Linde, Tachyonic instability and dynamics of spontaneous symmetry breaking, Phys. Rev. D 64 (2001) 123517 [hep-th/0106179] [SPIRES].ADSGoogle Scholar
  20. [20]
    M. Desroche, G.N. Felder, J.M. Kratochvil and A.D. Linde, Preheating in new inflation, Phys. Rev. D 71 (2005) 103516 [hep-th/0501080] [SPIRES].ADSGoogle Scholar
  21. [21]
    G.N. Felder and I. Tkachev, LATTICEEASY: a program for lattice simulations of scalar fields in an expanding universe, Comput. Phys. Commun. 178 (2008) [hep-ph/0011159] [SPIRES].
  22. [22]
    A.V. Frolov, DEFROST: a new code for simulating preheating after inflation, JCAP 11 (2008) 009 [arXiv:0809.4904] [SPIRES].ADSGoogle Scholar
  23. [23]
    N. Turok, Holographic singularity resolution, online at http://pirsa.org/10060026/.
  24. [24]
    B. Craps, T. Hertog and N. Turok, Self-adjoint extensions in field theory, unpublished manuscript.Google Scholar
  25. [25]
    B. Craps, T. Hertog and N. Turok, A multitrace deformation of ABJM theory, Phys. Rev. D 80 (2009) 086007 [arXiv:0905.0709] [SPIRES].ADSMathSciNetGoogle Scholar
  26. [26]
    L. Battarra and T. Hertog, Quasinormal modes of AdS hairy black holes and field theory condensates, in preparation.Google Scholar

Copyright information

© The Author(s) 2010

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  1. 1.APC, CNRS, Université Paris-DiderotParis Cedex 13France

Personalised recommendations