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A smooth exit from eternal inflation?

Open Access
Regular Article - Theoretical Physics

Abstract

The usual theory of inflation breaks down in eternal inflation. We derive a dual description of eternal inflation in terms of a deformed Euclidean CFT located at the threshold of eternal inflation. The partition function gives the amplitude of different geometries of the threshold surface in the no-boundary state. Its local and global behavior in dual toy models shows that the amplitude is low for surfaces which are not nearly conformal to the round three-sphere and essentially zero for surfaces with negative curvature. Based on this we conjecture that the exit from eternal inflation does not produce an infinite fractal-like multiverse, but is finite and reasonably smooth.

Keywords

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

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    A. Vilenkin, The Birth of Inflationary Universes, Phys. Rev. D 27 (1983) 2848 [INSPIRE].ADSMathSciNetGoogle Scholar
  2. [2]
    A.D. Linde, D.A. Linde and A. Mezhlumian, Nonperturbative amplifications of inhomogeneities in a selfreproducing universe, Phys. Rev. D 54 (1996) 2504 [gr-qc/9601005] [INSPIRE].
  3. [3]
    S. Winitzki. Eternal inflation, World Scientific (2008).Google Scholar
  4. [4]
    P. Creminelli, S. Dubovsky, A. Nicolis, L. Senatore and M. Zaldarriaga, The Phase Transition to Slow-roll Eternal Inflation, JHEP 09 (2008) 036 [arXiv:0802.1067] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  5. [5]
    J. Hartle, S.W. Hawking and T. Hertog, The No-Boundary Measure in the Regime of Eternal Inflation, Phys. Rev. D 82 (2010) 063510 [arXiv:1001.0262] [INSPIRE].
  6. [6]
    C.M. Hull, Timelike T duality, de Sitter space, large N gauge theories and topological field theory, JHEP 07 (1998) 021 [hep-th/9806146] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    V. Balasubramanian, J. de Boer and D. Minic, Mass, entropy and holography in asymptotically de Sitter spaces, Phys. Rev. D 65 (2002) 123508 [hep-th/0110108] [INSPIRE].
  8. [8]
    A. Strominger, The dS/CFT correspondence, JHEP 10 (2001) 034 [hep-th/0106113] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    R. Brout, F. Englert and E. Gunzig, The Creation of the Universe as a Quantum Phenomenon, Annals Phys. 115 (1978) 78 [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    J.B. Hartle and S.W. Hawking, Wave Function of the Universe, Phys. Rev. D 28 (1983) 2960 [INSPIRE].ADSMathSciNetMATHGoogle Scholar
  11. [11]
    J.B. Hartle, S.W. Hawking and T. Hertog, The Classical Universes of the No-Boundary Quantum State, Phys. Rev. D 77 (2008) 123537 [arXiv:0803.1663] [INSPIRE].
  12. [12]
    J.B. Hartle, S.W. Hawking and T. Hertog, No-Boundary Measure of the Universe, Phys. Rev. Lett. 100 (2008) 201301 [arXiv:0711.4630] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    J. Hartle, S.W. Hawking and T. Hertog, Local Observation in Eternal inflation, Phys. Rev. Lett. 106 (2011) 141302 [arXiv:1009.2525] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [INSPIRE].
  15. [15]
    P. McFadden and K. Skenderis, Holography for Cosmology, Phys. Rev. D 81 (2010) 021301 [arXiv:0907.5542] [INSPIRE].
  16. [16]
    D. Harlow and D. Stanford, Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT, arXiv:1104.2621 [INSPIRE].
  17. [17]
    J. Maldacena, Einstein Gravity from Conformal Gravity, arXiv:1105.5632 [INSPIRE].
  18. [18]
    T. Hertog and J. Hartle, Holographic No-Boundary Measure, JHEP 05 (2012) 095 [arXiv:1111.6090] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    D. Anninos, T. Hartman and A. Strominger, Higher Spin Realization of the dS/CFT Correspondence, Class. Quant. Grav. 34 (2017) 015009 [arXiv:1108.5735] [INSPIRE].
  20. [20]
    R. Dijkgraaf, B. Heidenreich, P. Jefferson and C. Vafa, Negative Branes, Supergroups and the Signature of Spacetime, JHEP 02 (2018) 050 [arXiv:1603.05665] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    E.A. Bergshoeff, J. Hartong, A. Ploegh, J. Rosseel and D. Van den Bleeken, Pseudo-supersymmetry and a tale of alternate realities, JHEP 07 (2007) 067 [arXiv:0704.3559] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    K. Skenderis, P.K. Townsend and A. Van Proeyen, Domain-wall/cosmology correspondence in AdS/dS supergravity, JHEP 08 (2007) 036 [arXiv:0704.3918] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  23. [23]
    J.B. Hartle, S.W. Hawking and T. Hertog, Quantum Probabilities for Inflation from Holography, JCAP 01 (2014) 015 [arXiv:1207.6653] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    A. Strominger, Inflation and the dS/CFT correspondence, JHEP 11 (2001) 049 [hep-th/0110087] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  25. [25]
    A. Bzowski, P. McFadden and K. Skenderis, Holography for inflation using conformal perturbation theory, JHEP 04 (2013) 047 [arXiv:1211.4550] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    J.M. Maldacena and G.L. Pimentel, On graviton non-Gaussianities during inflation, JHEP 09 (2011) 045 [arXiv:1104.2846] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  27. [27]
    J. Garriga, K. Skenderis and Y. Urakawa, Multi-field inflation from holography, JCAP 01 (2015) 028 [arXiv:1410.3290] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    N. Afshordi, C. Corianò, L. Delle Rose, E. Gould and K. Skenderis, From Planck data to Planck era: Observational tests of Holographic Cosmology, Phys. Rev. Lett. 118 (2017) 041301 [arXiv:1607.04878] [INSPIRE].
  29. [29]
    J. Maldacena, Vacuum decay into Anti de Sitter space, arXiv:1012.0274 [INSPIRE].
  30. [30]
    D.L. Jafferis, The Exact Superconformal R-Symmetry Extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  31. [31]
    I.R. Klebanov, S.S. Pufu and B.R. Safdi, F-Theorem without Supersymmetry, JHEP 10 (2011) 038 [arXiv:1105.4598] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  32. [32]
    N. Bobev, P. Bueno and Y. Vreys, Comments on Squashed-sphere Partition Functions, JHEP 07 (2017) 093 [arXiv:1705.00292] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  33. [33]
    S. Fischetti and T. Wiseman, On universality of holographic results for (2 + 1)-dimensional CFTs on curved spacetimes, JHEP 12 (2017) 133 [arXiv:1707.03825] [INSPIRE].
  34. [34]
    I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N ) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].
  35. [35]
    S.A. Hartnoll and S.P. Kumar, The O(N) model on a squashed S 3 and the Klebanov-Polyakov correspondence, JHEP 06 (2005) 012 [hep-th/0503238] [INSPIRE].
  36. [36]
    N. Bobev, T. Hertog and Y. Vreys, The NUTs and Bolts of Squashed Holography, JHEP 11 (2016) 140 [arXiv:1610.01497] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  37. [37]
    D. Anninos, F. Denef and D. Harlow, Wave function of Vasiliev’s universe: A few slices thereof, Phys. Rev. D 88 (2013) 084049 [arXiv:1207.5517] [INSPIRE].
  38. [38]
    G. Conti, T. Hertog and Y. Vreys, Squashed Holography with Scalar Condensates, arXiv:1707.09663 [INSPIRE].
  39. [39]
    D. Anninos, F. Denef, G. Konstantinidis and E. Shaghoulian, Higher Spin de Sitter Holography from Functional Determinants, JHEP 02 (2014) 007 [arXiv:1305.6321] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    B.L. Hu, Scalar Waves in the Mixmaster Universe. I. The Helmholtz Equation in a Fixed Background, Phys. Rev. D 8 (1973) 1048 [INSPIRE].
  41. [41]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  42. [42]
    R. Schoen, Conformal deformation of a Riemannian metric to constant scalar curvature, J. Diff. Geom. 20 (1984) 479.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.DAMTP, CMSCambridgeU.K.
  2. 2.Institute for Theoretical PhysicsUniversity of LeuvenLeuvenBelgium

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