Holographic signatures of resolved cosmological singularities

  • N. BodendorferEmail author
  • A. Schäfer
  • J. Schliemann
Open Access
Regular Article - Theoretical Physics


The classical gravity approximation is often employed in AdS/CFT to study the dual field theory, as it allows for many computations. A drawback is however the generic presence of singularities in classical gravity, which limits the applicability of AdS/CFT to regimes where the singularities are avoided by bulk probes, or some other form of regularisation is applicable. At the same time, quantum gravity is expected to resolve those singularities and thus to extend the range of applicability of AdS/CFT also in classically singular regimes. This paper exemplifies such a computation. We use an effective quantum corrected Kasner-AdS metric inspired by results from non-perturbative canonical quantum gravity to compute the 2-point correlator in the geodesic approximation for a negative Kasner exponent. The correlator derived in the classical gravity approximation has previously been shown to contain a pole at finite distance as a signature of the singularity. Using the quantum corrected metric, we show explicitly how the pole is resolved and that a new subdominant long-distance contribution to the correlator emerges, caused by geodesics passing arbitrarily close to the resolved classical singularity. In order to compute analytically in this paper, two key simplifications in the quantum corrected metric are necessary. They are lifted in a companion paper using numerical techniques, leading to the same qualitative results.


Spacetime Singularities AdS-CFT Correspondence Gauge-gravity correspondence Models of Quantum Gravity 


Open Access

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  1. [1]
    J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
  4. [4]
    M. Ammon and J. Erdmenger, Gauge/gravity duality: foundations and applications, Cambridge University Press, Cambridge, U.K. (2015) [INSPIRE].
  5. [5]
    N. Engelhardt, T. Hertog and G.T. Horowitz, Holographic signatures of cosmological singularities, Phys. Rev. Lett. 113 (2014) 121602 [arXiv:1404.2309] [INSPIRE].CrossRefGoogle Scholar
  6. [6]
    N. Engelhardt, T. Hertog and G.T. Horowitz, Further holographic investigations of big bang singularities, JHEP 07 (2015) 044 [arXiv:1503.08838] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    M. Ammon, M. Gutperle, P. Kraus and E. Perlmutter, Spacetime geometry in higher spin gravity, JHEP 10 (2011) 053 [arXiv:1106.4788] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    C. Krishnan and S. Roy, Desingularization of the Milne universe, Phys. Lett. B 734 (2014) 92 [arXiv:1311.7315] [INSPIRE].
  9. [9]
    B. Craps, C. Krishnan and A. Saurabh, Low tension strings on a cosmological singularity, JHEP 08 (2014) 065 [arXiv:1405.3935] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    K.S. Kiran, C. Krishnan, A. Saurabh and J. Simón, Strings vs. spins on the null orbifold, JHEP 12 (2014) 002 [arXiv:1408.3296] [INSPIRE].
  11. [11]
    M. Hanada, What lattice theorists can do for superstring/M-theory, Int. J. Mod. Phys. A 31 (2016) 1643006 [arXiv:1604.05421] [INSPIRE].
  12. [12]
    T. Hertog and G.T. Horowitz, Towards a big crunch dual, JHEP 07 (2004) 073 [hep-th/0406134] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  13. [13]
    T. Hertog and G.T. Horowitz, Holographic description of AdS cosmologies, JHEP 04 (2005) 005 [hep-th/0503071] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  14. [14]
    S.R. Das, J. Michelson, K. Narayan and S.P. Trivedi, Time dependent cosmologies and their duals, Phys. Rev. D 74 (2006) 026002 [hep-th/0602107] [INSPIRE].
  15. [15]
    N. Turok, B. Craps and T. Hertog, From big crunch to big bang with AdS/CFT, arXiv:0711.1824 [INSPIRE].
  16. [16]
    S.R. Das, J. Michelson, K. Narayan and S.P. Trivedi, Cosmologies with null singularities and their gauge theory duals, Phys. Rev. D 75 (2007) 026002 [hep-th/0610053] [INSPIRE].
  17. [17]
    B. Craps, T. Hertog and N. Turok, On the quantum resolution of cosmological singularities using AdS/CFT, Phys. Rev. D 86 (2012) 043513 [arXiv:0712.4180] [INSPIRE].
  18. [18]
    A. Awad, S.R. Das, K. Narayan and S.P. Trivedi, Gauge theory duals of cosmological backgrounds and their energy momentum tensors, Phys. Rev. D 77 (2008) 046008 [arXiv:0711.2994] [INSPIRE].
  19. [19]
    A. Awad, S.R. Das, S. Nampuri, K. Narayan and S.P. Trivedi, Gauge theories with time dependent couplings and their cosmological duals, Phys. Rev. D 79 (2009) 046004 [arXiv:0807.1517] [INSPIRE].
  20. [20]
    J.L.F. Barbón and E. Rabinovici, AdS crunches, CFT falls and cosmological complementarity, JHEP 04 (2011) 044 [arXiv:1102.3015] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    M. Smolkin and N. Turok, Dual description of a 4d cosmology, arXiv:1211.1322 [INSPIRE].
  22. [22]
    S. Chatterjee, S.P. Chowdhury, S. Mukherji and Y.K. Srivastava, Nonvacuum AdS cosmology and comments on gauge theory correlator, Phys. Rev. D 95 (2017) 046011 [arXiv:1608.08401] [INSPIRE].
  23. [23]
    V. Balasubramanian and S.F. Ross, Holographic particle detection, Phys. Rev. D 61 (2000) 044007 [hep-th/9906226] [INSPIRE].
  24. [24]
    A. Ashtekar and E. Wilson-Ewing, The covariant entropy bound and loop quantum cosmology, Phys. Rev. D 78 (2008) 064047 [arXiv:0805.3511] [INSPIRE].
  25. [25]
    R. Bousso, A covariant entropy conjecture, JHEP 07 (1999) 004 [hep-th/9905177] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    N. Bodendorfer, F.M. Mele and J. Münch, Holographic signatures of resolved cosmological singularities II: numerical investigations, arXiv:1804.01387 [INSPIRE].
  27. [27]
    A. Ashtekar, A. Corichi and P. Singh, Robustness of key features of loop quantum cosmology, Phys. Rev. D 77 (2008) 024046 [arXiv:0710.3565] [INSPIRE].
  28. [28]
    N. Bodendorfer, An elementary introduction to loop quantum gravity, arXiv:1607.05129 [INSPIRE].
  29. [29]
    N. Bodendorfer, State refinements and coarse graining in a full theory embedding of loop quantum cosmology, Class. Quant. Grav. 34 (2017) 135016 [arXiv:1607.06227] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    N. Bodendorfer, An embedding of loop quantum cosmology in (b, v) variables into a full theory context, Class. Quant. Grav. 33 (2016) 125014 [arXiv:1512.00713] [INSPIRE].
  31. [31]
    D. Oriti, L. Sindoni and E. Wilson-Ewing, Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates, Class. Quant. Grav. 33 (2016) 224001 [arXiv:1602.05881] [INSPIRE].
  32. [32]
    E. Alesci and F. Cianfrani, Improved regularization from quantum reduced loop gravity, arXiv:1604.02375 [INSPIRE].
  33. [33]
    A.H. Chamseddine and V. Mukhanov, Resolving cosmological singularities, JCAP 03 (2017) 009 [arXiv:1612.05860] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  34. [34]
    I. Agullo, A. Ashtekar and W. Nelson, A quantum gravity extension of the inflationary scenario, Phys. Rev. Lett. 109 (2012) 251301 [arXiv:1209.1609] [INSPIRE].CrossRefGoogle Scholar
  35. [35]
    A. Ashtekar and A. Barrau, Loop quantum cosmology: from pre-inflationary dynamics to observations, Class. Quant. Grav. 32 (2015) 234001 [arXiv:1504.07559] [INSPIRE].CrossRefzbMATHGoogle Scholar
  36. [36]
    B. Bolliet, A. Barrau, J. Grain and S. Schander, Observational exclusion of a consistent loop quantum cosmology scenario, Phys. Rev. D 93 (2016) 124011 [arXiv:1510.08766] [INSPIRE].
  37. [37]
    A. Ashtekar, T. Pawlowski and P. Singh, Quantum nature of the big bang: improved dynamics, Phys. Rev. D 74 (2006) 084003 [gr-qc/0607039] [INSPIRE].
  38. [38]
    B. Gupt and P. Singh, Quantum gravitational Kasner transitions in Bianchi-I spacetime, Phys. Rev. D 86 (2012) 024034 [arXiv:1205.6763] [INSPIRE].
  39. [39]
    N. Bodendorfer, Quantum reduction to Bianchi I models in loop quantum gravity, Phys. Rev. D 91 (2015) 081502 [arXiv:1410.5608] [INSPIRE].
  40. [40]
    T. Cailleteau, J. Mielczarek, A. Barrau and J. Grain, Anomaly-free scalar perturbations with holonomy corrections in loop quantum cosmology, Class. Quant. Grav. 29 (2012) 095010 [arXiv:1111.3535] [INSPIRE].
  41. [41]
    M. Bojowald and J. Mielczarek, Some implications of signature-change in cosmological models of loop quantum gravity, JCAP 08 (2015) 052 [arXiv:1503.09154] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  42. [42]
    J. Ben Achour, S. Brahma, J. Grain and A. Marciano, A new look at scalar perturbations in loop quantum cosmology: (un)deformed algebra approach using self dual variables, arXiv:1610.07467 [INSPIRE].
  43. [43]
    A. Ashtekar, W. Kaminski and J. Lewandowski, Quantum field theory on a cosmological, quantum space-time, Phys. Rev. D 79 (2009) 064030 [arXiv:0901.0933] [INSPIRE].
  44. [44]
    S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  45. [45]
    V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  46. [46]
    T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [INSPIRE].CrossRefzbMATHGoogle Scholar
  47. [47]
    N. Engelhardt and A.C. Wall, Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime, JHEP 01 (2015) 073 [arXiv:1408.3203] [INSPIRE].CrossRefGoogle Scholar
  48. [48]
    N. Bodendorfer, A note on quantum supergravity and AdS/CFT, arXiv:1509.02036 [INSPIRE].
  49. [49]
    P. Singh, Is classical flat Kasner spacetime flat in quantum gravity?, Int. J. Mod. Phys. D 25 (2016) 1642001 [arXiv:1604.03828] [INSPIRE].
  50. [50]
    S.G. Naculich, H.J. Schnitzer and N. Wyllard, 1/N corrections to anomalies and the AdS/CFT correspondence for orientifolded N = 2 orbifold and N = 1 conifold models, Int. J. Mod. Phys. A 17 (2002) 2567 [hep-th/0106020] [INSPIRE].
  51. [51]
    S.S. Gubser and I. Mitra, Double trace operators and one loop vacuum energy in AdS/CFT, Phys. Rev. D 67 (2003) 064018 [hep-th/0210093] [INSPIRE].
  52. [52]
    F. Denef, S.A. Hartnoll and S. Sachdev, Black hole determinants and quasinormal modes, Class. Quant. Grav. 27 (2010) 125001 [arXiv:0908.2657] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  53. [53]
    S. Caron-Huot and O. Saremi, Hydrodynamic long-time tails from anti de Sitter space, JHEP 11 (2010) 013 [arXiv:0909.4525] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  54. [54]
    D. Jorrin, N. Kovensky and M. Schvellinger, Towards 1/N corrections to deep inelastic scattering from the gauge/gravity duality, JHEP 04 (2016) 113 [arXiv:1601.01627] [INSPIRE].
  55. [55]
    D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Correlation functions in the CFT d /AdS d+1 correspondence, Nucl. Phys. B 546 (1999) 96 [hep-th/9804058] [INSPIRE].
  56. [56]
    D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  57. [57]
    L. Freidel, Reconstructing AdS/CFT, arXiv:0804.0632 [INSPIRE].
  58. [58]
    N. Bodendorfer, T. Thiemann and A. Thurn, Towards loop quantum supergravity (LQSG), Phys. Lett. B 711 (2012) 205 [arXiv:1106.1103] [INSPIRE].
  59. [59]
    B. Dittrich and J. Hnybida, Ising model from intertwiners, arXiv:1312.5646 [INSPIRE].
  60. [60]
    V. Bonzom, F. Costantino and E.R. Livine, Duality between spin networks and the 2D Ising model, Commun. Math. Phys. 344 (2016) 531 [arXiv:1504.02822] [INSPIRE].
  61. [61]
    V. Bonzom and B. Dittrich, 3D holography: from discretum to continuum, JHEP 03 (2016) 208 [arXiv:1511.05441] [INSPIRE].
  62. [62]
    L. Smolin, Holographic relations in loop quantum gravity, arXiv:1608.02932 [INSPIRE].
  63. [63]
    M. Han and L.-Y. Hung, Loop quantum gravity, exact holographic mapping and holographic entanglement entropy, Phys. Rev. D 95 (2017) 024011 [arXiv:1610.02134] [INSPIRE].
  64. [64]
    B. Dittrich, C. Goeller, E. Livine and A. Riello, Quasi-local holographic dualities in non-perturbative 3d quantum gravity Iconvergence of multiple approaches and examples of Ponzano-Regge statistical duals, Nucl. Phys. B 938 (2019) 807 [arXiv:1710.04202] [INSPIRE].
  65. [65]
    B. Dittrich, C. Goeller, E.R. Livine and A. Riello, Quasi-local holographic dualities in non-perturbative 3d quantum gravity IIfrom coherent quantum boundaries to BMS 3 characters, Nucl. Phys. B 938 (2019) 878 [arXiv:1710.04237] [INSPIRE].
  66. [66]
    A. Ashtekar and M. Bojowald, Black hole evaporation: a paradigm, Class. Quant. Grav. 22 (2005) 3349 [gr-qc/0504029] [INSPIRE].
  67. [67]
    A.H. Chamseddine and V. Mukhanov, Nonsingular black hole, Eur. Phys. J. C 77 (2017) 183 [arXiv:1612.05861] [INSPIRE].
  68. [68]
    P. Kraus, H. Ooguri and S. Shenker, Inside the horizon with AdS/CFT, Phys. Rev. D 67 (2003) 124022 [hep-th/0212277] [INSPIRE].
  69. [69]
    L. Fidkowski, V. Hubeny, M. Kleban and S. Shenker, The black hole singularity in AdS/CFT, JHEP 02 (2004) 014 [hep-th/0306170] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  70. [70]
    N. Engelhardt and G.T. Horowitz, Entanglement entropy near cosmological singularities, JHEP 06 (2013) 041 [arXiv:1303.4442] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  71. [71]
    V.A. Belinskii, E.M. Lifshitz and I.M. Khalatnikov, Oscillatory approach to the singular point in relativistic cosmology, Sov. Phys. Usp. 13 (1971) 745.CrossRefGoogle Scholar

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Institute for Theoretical PhysicsUniversity of RegensburgRegensburgGermany

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