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Journal of High Energy Physics

, 2019:96 | Cite as

Kerr-NUT-de Sitter as an inhomogeneous non-singular bouncing cosmology

  • Andrés AnabalónEmail author
  • Sebastian F. Bramberger
  • Jean-Luc Lehners
Open Access
Regular Article - Theoretical Physics
  • 38 Downloads

Abstract

We present exact non-singular bounce solutions of general relativity in the presence of a positive cosmological constant and an electromagnetic field, without any exotic matter. The solutions are distinguished by being spatially inhomogeneous in one direction while they can also contain non-trivial electromagnetic field lines. The inhomogeneity may be substantial, for instance there can be one bounce in one region of the universe, and two bounces elsewhere. Since the bounces are followed by a phase of accelerated expansion, the metrics described here also permit the study of (geodesically complete) models of inflation with inhomogeneous “initial” conditions. Our solutions admit two Killing vectors, and may be re-interpreted as the pathology-free interior regions of Kerr-de Sitter black holes with non-trivial NUT charge. Remarkably enough, within this cosmological context the NUT parameter does not introduce any string singularity nor closed timelike curves but renders the geometry everywhere regular, eliminating the Big-Bang singularity by means of a bounce.

Keywords

Classical Theories of Gravity Spacetime Singularities Black Holes 

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]
    S.W. Hawking and R. Penrose, The Singularities of gravitational collapse and cosmology, Proc. Roy. Soc. Lond. A 314 (1970) 529.Google Scholar
  2. [2]
    R.H. Brandenberger and C. Vafa, Superstrings in the Early Universe, Nucl. Phys. B 316 (1989) 391 [INSPIRE].
  3. [3]
    J.B. Hartle and S.W. Hawking, Wave Function of the Universe, Phys. Rev. D 28 (1983) 2960 [INSPIRE].
  4. [4]
    T. Qiu, J. Evslin, Y.-F. Cai, M. Li and X. Zhang, Bouncing Galileon Cosmologies, JCAP 10 (2011) 036 [arXiv:1108.0593] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    D.A. Easson, I. Sawicki and A. Vikman, G-Bounce, JCAP 11 (2011) 021 [arXiv:1109.1047] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    M. Koehn, J.-L. Lehners and B.A. Ovrut, Cosmological super-bounce, Phys. Rev. D 90 (2014) 025005 [arXiv:1310.7577] [INSPIRE].
  7. [7]
    A. Ijjas and P.J. Steinhardt, Classically stable nonsingular cosmological bounces, Phys. Rev. Lett. 117 (2016) 121304 [arXiv:1606.08880] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    J. Magueijo, T.G. Zlosnik and T.W.B. Kibble, Cosmology with a spin, Phys. Rev. D 87 (2013) 063504 [arXiv:1212.0585] [INSPIRE].
  9. [9]
    S. Farnsworth, J.-L. Lehners and T. Qiu, Spinor driven cosmic bounces and their cosmological perturbations, Phys. Rev. D 96 (2017) 083530 [arXiv:1709.03171] [INSPIRE].
  10. [10]
    S. Hawking, The occurrence of singularities in cosmology. III. Causality and singularities, Proc. Roy. Soc. Lond. A 300 (1967) 187.Google Scholar
  11. [11]
    D.M. Scolnic et al., The Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample, Astrophys. J. 859 (2018) 101 [arXiv:1710.00845] [INSPIRE].
  12. [12]
    A. Anabalón and J. Oliva, Four-dimensional Traversable Wormholes and Bouncing Cosmologies in Vacuum, JHEP 04 (2019) 106 [arXiv:1811.03497] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    S.F. Bramberger and J.-L. Lehners, Nonsingular bounces catalyzed by dark energy, Phys. Rev. D 99 (2019) 123523 [arXiv:1901.10198] [INSPIRE].
  14. [14]
    A.H. Taub, Empty space-times admitting a three parameter group of motions, Ann. Math. 53 (1951) 472.ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    E. Newman, L. Tamburino and T. Unti, Empty space generalization of the Schwarzschild metric, J. Math. Phys. 4 (1963) 915 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    B. Carter, Hamilton-Jacobi and Schrödinger separable solutions of Einsteins equations, Commun. Math. Phys. 10 (1968) 280 [INSPIRE].
  17. [17]
    J.F. Plebanski and M. Demianski, Rotating, charged and uniformly accelerating mass in general relativity, Annals Phys. 98 (1976) 98 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    D. Finkelstein, Past-Future Asymmetry of the Gravitational Field of a Point Particle, Phys. Rev. 110 (1958) 965 [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  19. [19]
    M.D. Kruskal, Maximal extension of Schwarzschild metric, Phys. Rev. 119 (1960) 1743 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    W. Kinnersley and M. Walker, Uniformly accelerating charged mass in general relativity, Phys. Rev. D 2 (1970) 1359 [INSPIRE].
  21. [21]
    K. Subramanian, The origin, evolution and signatures of primordial magnetic fields, Rept. Prog. Phys. 79 (2016) 076901 [arXiv:1504.02311] [INSPIRE].
  22. [22]
    K. Schwarzschild, On the gravitational field of a mass point according to Einsteins theory, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys. ) 1916 (1916) 189 [physics/9905030] [INSPIRE].
  23. [23]
    R. Kantowski and R.K. Sachs, Some spatially homogeneous anisotropic relativistic cosmological models, J. Math. Phys. 7 (1966) 443 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    J.B. Griffiths and J. Podolsky, A New look at the Plebanski-Demianski family of solutions, Int. J. Mod. Phys. D 15 (2006) 335 [gr-qc/0511091] [INSPIRE].
  25. [25]
    R.L. Arnowitt, S. Deser and C.W. Misner, The Dynamics of general relativity, Gen. Rel. Grav. 40 (2008) 1997 [gr-qc/0405109] [INSPIRE].
  26. [26]
    A. Vilenkin, Creation of Universes from Nothing, Phys. Lett. B 117 (1982) 25.Google Scholar
  27. [27]
    A. Di Tucci and J.-L. Lehners, No-Boundary Proposal as a Path Integral with Robin Boundary Conditions, Phys. Rev. Lett. 122 (2019) 201302 [arXiv:1903.06757] [INSPIRE].
  28. [28]
    L. Battarra and J.-L. Lehners, On the Creation of the Universe via Ekpyrotic Instantons, Phys. Lett. B 742 (2015) 167 [arXiv:1406.5896] [INSPIRE].
  29. [29]
    L. Battarra and J.-L. Lehners, On the No-Boundary Proposal for Ekpyrotic and Cyclic Cosmologies, JCAP 12 (2014) 023 [arXiv:1407.4814] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    S.F. Bramberger, T. Hertog, J.-L. Lehners and Y. Vreys, Quantum Transitions Through Cosmological Singularities, JCAP 07 (2017) 007 [arXiv:1701.05399] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  31. [31]
    P. Creminelli, L. Senatore and A. Vasy, Asymptotic Behavior of Cosmologies with Λ > 0 in 2+1 Dimensions,arXiv:1902.00519[INSPIRE].
  32. [32]
    W.E. East, M. Kleban, A. Linde and L. Senatore, Beginning inflation in an inhomogeneous universe, JCAP 09 (2016) 010 [arXiv:1511.05143] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    K. Clough, E.A. Lim, B.S. DiNunno, W. Fischler, R. Flauger and S. Paban, Robustness of Inflation to Inhomogeneous Initial Conditions, JCAP 09 (2017) 025 [arXiv:1608.04408] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  34. [34]
    R.H. Dicke and P.J.E. Peebles, The big bang cosmology: Enigmas and nostrums, in General Relativity: An Einstein Centenary Survey, Cambridge University Press, Cambridge U.K. (1979).Google Scholar
  35. [35]
    A.H. Guth, The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems, Phys. Rev. D 23 (1981) 347 [INSPIRE].
  36. [36]
    L. Smolin, The lifetime of the cosmos, Oxford University Press, New York U.S.A. (1997).Google Scholar
  37. [37]
    T. Buchert and J. Ehlers, Averaging inhomogeneous Newtonian cosmologies, Astron. Astrophys. 320 (1997) 1 [astro-ph/9510056] [INSPIRE].
  38. [38]
    J.-L. Lehners, Ekpyrotic and Cyclic Cosmology, Phys. Rept. 465 (2008) 223 [arXiv:0806.1245] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Andrés Anabalón
    • 1
    Email author
  • Sebastian F. Bramberger
    • 2
  • Jean-Luc Lehners
    • 2
  1. 1.Departamento de Ciencias, Facultad de Artes LiberalesUniversidad Adolfo IbáñezViña del MarChile
  2. 2.Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute)PotsdamGermany

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