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Oscillating Fubini instantons in curved space

Profile image of Wonwoo LeeWonwoo Lee

2015, Physical Review D

https://doi.org/10.1103/PHYSREVD.91.124044
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Abstract

A Fubini instanton is a bounce solution which describes the decay of a vacuum state located at the top of the tachyonic potential via the tunneling without a barrier. We investigate various types of Fubini instantons of a self-gravitating scalar field under a tachyonic quartic potential. With gravity taken into account, we show there exist various types of unexpected solutions including oscillating bounce solutions. We present numerically oscillating Fubini bounce solutions in anti-de Sitter and de Sitter spaces. We construct the parametric phase diagrams of the solutions, which is the extension of our previous work. Of particular significance is that there always exist solutions in all parameter spaces in anti-de Sitter space. The regions are divided depending on the number of oscillations. On the other hand, de Sitter space allows solutions with codimension-one in parameter spaces. We numerically evaluate semiclassical exponents which give the finite tunneling probabilities.

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References (65)

  1. S. Coleman, Phys. Rev. D 15, 2929 (1977); 16, 1248(E) (1977).
  2. C. G. Callan, Jr. and S. Coleman, Phys. Rev. D 16, 1762 (1977).
  3. R. Kallosh, A. D. Linde, S. Prokushkin, and M. Shmakova, Phys. Rev. D 66, 123503 (2002).
  4. R. Kallosh and A. D. Linde, Phys. Rev. D 67, 023510 (2003).
  5. A. H. Guth, Phys. Rev. D 23, 347 (1981).
  6. K. Sato, Mon. Not. R. Astron. Soc. 195, 467 (1981).
  7. A. D. Linde, Phys. Lett. B 108, 389 (1982).
  8. A. Albrecht and P. J. Steinhardt, Phys. Rev. Lett. 48, 1220 (1982).
  9. S. W. Hawking and I. G. Moss, Phys. Lett. B 110, 35 (1982).
  10. B.-H. Lee, C. H. Lee, W. Lee, and C. Oh, Phys. Rev. D 85, 024022 (2012).
  11. M. B. Voloshin, I. Yu. Kobzarev, and L. B. Okun, Yad. Fiz. 20, 1229 (1974)[Sov. J. Nucl. Phys. 20, 644 (1975)].
  12. S. Coleman and F. De Luccia, Phys. Rev. D 21, 3305 (1980).
  13. S. Parke, Phys. Lett. B 121, 313 (1983).
  14. B.-H. Lee and W. Lee, Classical Quantum Gravity 26, 225002 (2009).
  15. B.-H. Lee, C. H. Lee, W. Lee, and C. Oh, arXiv:1311.4279.
  16. K. Lee and E. J. Weinberg, Phys. Rev. D 36, 1088 (1987).
  17. J. C. Hackworth and E. J. Weinberg, Phys. Rev. D 71, 044014 (2005).
  18. B.-H. Lee, C. H. Lee, W. Lee, and C. Oh, Phys. Rev. D 82, 024019 (2010).
  19. J. Zinn-Justin, Path Integrals in Quantum Mechanics (Oxford University Press, Oxford, 2005).
  20. B.-H. Lee, W. Lee, and D.-h. Yeom, Int. J. Mod. Phys. A 28 1350082 (2013).
  21. L. Battarra, G. Lavrelashvili and J. L. Lehners, Phys. Rev. D 86, 124001 (2012).
  22. S. R. Coleman and E. J. Weinberg, Phys. Rev. D 7, 1888 (1973).
  23. Y.-l. Zhang, R. Saito, and M. Sasaki, J. Cosmol. Astropart. Phys. 02 (2013) 029.
  24. M. Sasaki, D.-h. Yeom, and Y.-l. Zhang, Classical Quantum Gravity 30, 232001 (2013).
  25. Y.-l. Zhang, R. Saito, D.-h. Yeom, and M. Sasaki, J. Cosmol. Astropart. Phys. 02 (2014) 022.
  26. S. Fubini, Nuovo Cimento A 34, 521 (1976).
  27. L. N. Lipatov, Sov. Phys. JETP 45, 216 (1977).
  28. A. D. Linde, Nucl. Phys. B 216, 421 (1983); 223, 544(E) (1983).
  29. I. Affleck, Nucl. Phys. B 191, 429 (1981).
  30. J. Garriga, X. Montes, M. Sasaki, and T. Tanaka, Nucl. Phys. B 551, 317 (1999).
  31. S. Khlebnikov, Nucl. Phys. B 631, 307 (2002).
  32. F. Loran, Mod. Phys. Lett. A 22, 2217 (2007).
  33. K. Lee and E. J. Weinberg, Nucl. Phys. B 267, 181 (1986).
  34. K. Lee, Nucl. Phys. B 282, 509 (1987).
  35. L. G. Jensen and P. J. Steinhardt, Nucl. Phys. B 317, 693 (1989).
  36. S. Kanno, M. Sasaki, and J. Soda, Classical Quantum Gravity 29, 075010 (2012).
  37. B.-H. Lee, W. Lee, C. Oh, D. Ro, and D.-h. Yeom, J. High Energy Phys. 06 (2013) 003.
  38. B.-H. Lee, W. Lee, D. Ro, and D.-h. Yeom, J. Korean Phys. Soc. 65, 884 (2014).
  39. L. Battarra, G. Lavrelashvili, and J.-L. Lehners, Phys. Rev. D 88, 104012 (2013).
  40. R. Bousso, B. Freivogel, and M. Lippert, Phys. Rev. D 74, 046008 (2006).
  41. A. D. Linde, Nonsingular regenerating inflationary universe, Cambridge University Report No. 82-0554.
  42. A. Vilenkin, Phys. Rev. D 27, 2848 (1983).
  43. A. D. Linde, Phys. Lett. B 175, 395 (1986).
  44. A. H. Guth, Phys. Rep. 333-334, 555 (2000).
  45. R. Bousso and J. Polchinski, J. High Energy Phys. 06 (2000) 006.
  46. L. Susskind, arXiv:hep-th/0302219.
  47. S. Kachru, R. Kallosh, A. Linde, and S. P. Trivedi, Phys. Rev. D 68, 046005 (2003).
  48. C. Hull, Classical Quantum Gravity 2, 343 (1985).
  49. R. Kallosh, A. D. Linde, S. Prokushkin, and M. Shmakova, Phys. Rev. D 65, 105016 (2002).
  50. S. de Haro and A. C. Petkou, J. High Energy Phys. 12 (2006) 076.
  51. S. de Haro, I. Papadimitriou, and A. C. Petkou, Phys. Rev. Lett. 98, 231601 (2007).
  52. J. L. F. Barbon and E. Rabinivici, J. High Energy Phys. 04 (2010) 123; 04 (2011) 044.
  53. E. J. Weinberg, Phys. Rev. D 47, 4614 (1993).
  54. J. Baacke and G. Lavrelashvili, Phys. Rev. D 69, 025009 (2004).
  55. G. V. Dunne and H. Min, Phys. Rev. D 72, 125004 (2005).
  56. J. W. York, Jr., Phys. Rev. Lett. 28, 1082 (1972).
  57. G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15, 2752 (1977).
  58. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W. H. Freeman and Company, New York, 1973).
  59. G. Lavrelashvili, Phys. Rev. D 73, 083513 (2006).
  60. B.-H. Lee, W. Lee, D. Ro, and D.-h. Yeom, arXiv:1409.3728.
  61. S. Kanno, M. Sasaki, and J. Soda, Prog. Theor. Phys. 128, 213 (2012).
  62. T. Hertog and J. Hartle, J. High Energy Phys. 05 (2012) 095.
  63. A. R. Brown and E. J. Weinberg, Phys. Rev. D 76, 064003 (2007).
  64. P. Breitenlohner and D. Z. Freedman, Ann. Phys. (N.Y.) 144, 249 (1982).
  65. P. Breitenlohner and D. Z. Freedman, Phys. Lett. B 115, 197 (1982).

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