Skip to main content
SpringerLink
Log in

Pre-inflation and trans-Planckian censorship

  • Article
  • Published:
Science China Physics, Mechanics & Astronomy Aims and scope Submit manuscript

Abstract

We investigate the implication of trans-Planckian censorship conjecture (TCC) for the initial state of primordial perturbations. It is possible to set the state of perturbation modes in the infinite past as the Minkowski vacuum, only if the pre-inflationary era is past-complete. We calculate the evolution of the perturbation modes in such a pre-inflationary era and show that at the beginning of inflation the perturbation modes with wavelengths much shorter than the Hubble scale (but still larger than the Planck length scale) will behave as they are in the Bunch-Davis state. Therefore, a past-complete pre-inflationary evolution may automatically prepare the initial state required for the inflationary perturbations at the CMB window while obeying the TCC.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. H. Guth, Phys. Rev. D 23, 347 (1981).

    ADS  Google Scholar 

  2. A. D. Linde, Phys. Lett. B 108, 389 (1982).

    ADS  Google Scholar 

  3. A. Albrecht, and P. J. Steinhardt, Phys. Rev. Lett. 48, 1220 (1982).

    ADS  Google Scholar 

  4. A. A. Starobinsky, Phys. Lett. B 91, 99 (1980).

    ADS  Google Scholar 

  5. P. A. R. Ade, et al. (Planck Collaboration), Astron. Astrophys. 594, A13 (2016), arXiv: 1502.01589.

    Google Scholar 

  6. P. A. R. Ade, et al. (Planck Collaboration), Astron. Astrophys. 594, A20 (2016), arXiv: 1502.02114.

    Google Scholar 

  7. A. Borde, and A. Vilenkin, Phys. Rev. Lett. 72, 3305 (1994), arXiv: gr-qc/9312022.

    ADS  Google Scholar 

  8. A. Borde, A. H. Guth, and A. Vilenkin, Phys. Rev. Lett. 90, 151301 (2003), arXiv: gr-qc/0110012.

    ADS  Google Scholar 

  9. T. S. Bunch, and P. C. W. Davies, Proc. R. Soc. Lond. A 360, 117 (1978).

    ADS  Google Scholar 

  10. R. H. Brandenberger, and J. R. M. Martin, Mod. Phys. Lett. A 16, 999 (2001), arXiv: astro-ph/0005432.

    ADS  Google Scholar 

  11. J. Martin, and R. H. Brandenberger, Phys. Rev. D 63, 123501 (2001), arXiv: hep-th/0005209.

    ADS  Google Scholar 

  12. A. Ashoorioon, A. Kempf, and R. B. Mann, Phys. Rev. D 71, 023503 (2005), arXiv: astro-ph/0410139.

    ADS  Google Scholar 

  13. A. Ashoorioon, J. L. Hovdebo, and R. B. Mann, Nucl. Phys. B 727, 63 (2005), arXiv: gr-qc/0504135.

    ADS  Google Scholar 

  14. X. Chen, and Y. Wang, J. Cosmol. Astropart. Phys. 2014, 004 (2014), arXiv: 1306.0609.

    Google Scholar 

  15. A. Ashoorioon, K. Dimopoulos, M. M. Sheikh-Jabbari, and G. Shiu, J. Cosmol. Astropart. Phys. 2014, 025 (2014), arXiv: 1306.4914.

    Google Scholar 

  16. A. Ashoorioon, K. Dimopoulos, M. M. Sheikh-Jabbari, and G. Shiu, Phys. Lett. B 737, 98 (2014), arXiv: 1403.6099.

    ADS  Google Scholar 

  17. A. Ashoorioon, Phys. Lett. B 790, 568 (2019), arXiv: 1810.04001.

    ADS  Google Scholar 

  18. A. Bedroya, and C. Vafa, arXiv: 1909.11063.

  19. A. Bedroya, R. Brandenberger, M. Loverde and C. Vafa, arXiv: 1909.11106.

  20. A. Di Tucci, J. Feldbrugge, J. L. Lehners, and N. Turok, Phys. Rev. D 100, 063517 (2019), arXiv: 1906.09007.

    ADS  MathSciNet  Google Scholar 

  21. Y. S. Piao, B. Feng, and X. Zhang, Phys. Rev. D 69, 103520 (2004), arXiv: hep-th/0310206

    ADS  Google Scholar 

  22. Y. S. Piao, Phys. Rev. D 71, 087301 (2005), arXiv: astro-ph/0502343

    ADS  Google Scholar 

  23. Y. S. Piao, Phys. Rev. D 70, 101302 (2004), arXiv: hep-th/0407258.

    ADS  Google Scholar 

  24. Z. G. Liu, Z. K. Guo, and Y. S. Piao, Phys. Rev. D 88, 063539 (2013), arXiv: 1304.6527.

    ADS  Google Scholar 

  25. T. Qiu, and Y. T. Wang, J. High Energ. Phys. 2015, 130 (2015).

    Google Scholar 

  26. M. Libanov, S. Mironov, and V. Rubakov, J. Cosmol. Astropart. Phys. 2016, 037 (2016), arXiv: 1605.05992.

    Google Scholar 

  27. T. Kobayashi, Phys. Rev. D 94, 043511 (2016), arXiv: 1606.05831.

    ADS  MathSciNet  Google Scholar 

  28. A. Ijjas, and P. J. Steinhardt, Phys. Lett. B 764, 289 (2017), arXiv: 1609.01253.

    ADS  Google Scholar 

  29. D. A. Dobre, A. V. Frolov, J. T. G. Ghersi, S. Ramazanov, and A. Vikman, J. Cosmol. Astropart. Phys. 2018, 020 (2018), arXiv: 1712.10272.

    Google Scholar 

  30. Y. Cai, Y. Wan, H. G. Li, T. Qiu, and Y. S. Piao, J. High Energ. Phys. 2017, 90 (2017).

    Google Scholar 

  31. P. Creminelli, D. Pirtskhalava, L. Santoni, and E. Trincherini, J. Cosmol. Astropart. Phys. 2016, 047 (2016), arXiv: 1610.04207.

    Google Scholar 

  32. Y. Cai, H. G. Li, T. Qiu, and Y. S. Piao, Eur. Phys. J. C 77, 369 (2017), arXiv: 1701.04330.

    ADS  Google Scholar 

  33. Y. Cai, and Y. S. Piao, J. High Energ. Phys. 2017, 27 (2017).

    Google Scholar 

  34. R. Kolevatov, S. Mironov, N. Sukhov, and V. Volkova, J. Cosmol. Astropart. Phys. 2017, 038 (2017), arXiv: 1705.06626.

    Google Scholar 

  35. A. Ijjas, and P. J. Steinhardt, Phys. Rev. Lett. 117, 121304 (2016), arXiv: 1606.08880.

    ADS  MathSciNet  Google Scholar 

  36. R. Kolevatov, and S. Mironov, Phys. Rev. D 94, 123516 (2016), arXiv: 1607.04099.

    ADS  MathSciNet  Google Scholar 

  37. G. Ye, and Y. S. Piao, Phys. Rev. D 99, 084019 (2019), arXiv: 1901.08283.

    ADS  MathSciNet  Google Scholar 

  38. G. Ye, and Y. S. Piao, Commun. Theor. Phys. 71, 427 (2019), arXiv: 1901.02202.

    ADS  Google Scholar 

  39. S. Mironov, V. Rubakov, and V. Volkova, J. Cosmol. Astropart. Phys. 2018, 050 (2018), arXiv: 1807.08361.

    Google Scholar 

  40. S. S. Boruah, H. J. Kim, M. Rouben, and G. Geshnizjani, J. Cosmol. Astropart. Phys. 2018, 031 (2018), arXiv: 1802.06818.

    Google Scholar 

  41. S. Mironov, V. Rubakov, and V. Volkova, arXiv: 1906.12139.

  42. S. Akama, S. Hirano, and T. Kobayashi, arXiv: 1908.10663.

  43. D. Langlois, Int. J. Mod. Phys. D 28, 1942006 (2019), arXiv: 1811.06271.

    ADS  Google Scholar 

  44. T. Kobayashi, Rep. Prog. Phys. 82, 086901 (2019), arXiv: 1901.07183.

    ADS  Google Scholar 

  45. Y. F. Cai, T. Qiu, X. Zhang, Y. S. Piao, and M. Li, J. High Energy Phys. 2007, 071 (2007), arXiv: 0704.1090.

    Google Scholar 

  46. Y. F. Cai, T. Qiu, R. Brandenberger, and X. Zhang, Phys. Rev. D 80, 023511 (2009), arXiv: 0810.4677.

    ADS  Google Scholar 

  47. T. Qiu, J. Evslin, Y. F. Cai, M. Li, and X. Zhang, J. Cosmol. Astropart. Phys. 2011, 036 (2011), arXiv: 1108.0593.

    Google Scholar 

  48. D. A. Easson, I. Sawicki, and A. Vikman, J. Cosmol. Astropart. Phys. 2011, 021 (2011), arXiv: 1109.1047.

    ADS  Google Scholar 

  49. Y. F. Cai, D. A. Easson, and R. Brandenberger, J. Cosmol. Astropart. Phys. 2012, 020 (2012), arXiv: 1206.2382.

    Google Scholar 

  50. Y. F. Cai, E. McDonough, F. Duplessis, and R. H. Brandenberger, J. Cosmol. Astropart. Phys. 2013, 024 (2013), arXiv: 1305.5259.

    Google Scholar 

  51. T. Qiu, X. Gao, and E. N. Saridakis, Phys. Rev. D 88, 043525 (2013), arXiv: 1303.2372.

    ADS  Google Scholar 

  52. M. Koehn, J. L. Lehners, and B. A. Ovrut, Phys. Rev. D 90, 025005 (2014), arXiv: 1310.7577.

    ADS  Google Scholar 

  53. L. Battarra, M. Koehn, J. L. Lehners, and B. A. Ovrut, J. Cosmol. Astropart. Phys. 2014, 007 (2014), arXiv: 1404.5067.

    Google Scholar 

  54. Y. Wan, T. Qiu, F. P. Huang, Y. F. Cai, H. Li, and X. Zhang, J. Cosmol. Astropart. Phys. 2015, 019 (2015), arXiv: 1509.08772.

    Google Scholar 

  55. M. Koehn, J. L. Lehners, and B. Ovrut, Phys. Rev. D 93, 103501 (2016), arXiv: 1512.03807.

    ADS  Google Scholar 

  56. S. D. Odintsov, and V. K. Oikonomou, Phys. Rev. D 90, 124083 (2014), arXiv: 1410.8183

    ADS  Google Scholar 

  57. S. Nojiri, S. D. Odintsov, and V. K. Oikonomou, Phys. Rev. D 93, 084050 (2016), arXiv: 1601.04112.

    ADS  MathSciNet  Google Scholar 

  58. S. Banerjee, and E. N. Saridakis, Phys. Rev. D 95, 063523 (2017), arXiv: 1604.06932.

    ADS  MathSciNet  Google Scholar 

  59. P. Creminelli, M. A. Luty, A. Nicolis, and L. Senatore, J. High Energy Phys. 2006, 080 (2006), arXiv: hep-th/0606090.

    Google Scholar 

  60. D. Pirtskhalava, L. Santoni, E. Trincherini, and P. Uttayarat, J. High Energ. Phys. 2014, 151 (2014).

    ADS  Google Scholar 

  61. T. Kobayashi, M. Yamaguchi, and J. Yokoyama, J. Cosmol. Astropart. Phys. 2015, 017 (2015), arXiv: 1504.05710.

    Google Scholar 

  62. Z. G. Liu, H. Li, and Y. S. Piao, Phys. Rev. D 90, 083521 (2014), arXiv: 1405.1188.

    ADS  Google Scholar 

  63. Y. Wang, Commun. Theor. Phys. 62, 109 (2014), arXiv: 1303.1523.

    ADS  Google Scholar 

  64. L. H. Ford, arXiv: gr-qc/9707062.

  65. A. Ashoorioon, R. Casadio, M. Cicoli, G. Geshnizjani, and H. J. Kim, J. High Energ. Phys. 2018, 172 (2018).

    Google Scholar 

  66. G. Obied, H. Ooguri, L. Spodyneiko, and C. Vafa, arXiv: 1806.08362.

  67. P. Agrawal, G. Obied, P. J. Steinhardt, and C. Vafa, Phys. Lett. B 784, 271 (2018), arXiv: 1806.09718.

    ADS  Google Scholar 

  68. S. K. Garg, and C. Krishnan, arXiv: 1807.05193.

  69. H. Ooguri, E. Palti, G. Shiu, and C. Vafa, Phys. Lett. B 788, 180 (2019), arXiv: 1810.05506.

    ADS  MathSciNet  Google Scholar 

  70. C. Armendariz-Picon, J. Cosmol. Astropart. Phys. 2007, 031 (2007), arXiv: astro-ph/0612288.

    Google Scholar 

  71. H. Jiang, and Y. Wang, Phys. Lett. B 760, 202 (2016), arXiv: 1507.05193.

    ADS  Google Scholar 

  72. H. Jiang, Y. Wang, and S. Zhou, J. Cosmol. Astropart. Phys. 2016, 041 (2016), arXiv: 1601.01179.

    Google Scholar 

  73. S. M. Carroll, Spacetime and Geometry (Addison-Wesley, San Francisco, 2004). p. 513.

    MATH  Google Scholar 

  74. Y. Cai, Y. T. Wang, and Y. S. Piao, Phys. Rev. D 92, 023518 (2015), arXiv: 1501.01730.

    ADS  Google Scholar 

  75. J. Khoury, B. A. Ovrut, P. J. Steinhardt, and N. Turok, Phys. Rev. D 64, 123522 (2001), arXiv: hep-th/0103239.

    ADS  MathSciNet  Google Scholar 

  76. Z. G. Liu, J. Zhang, and Y. S. Piao, Phys. Rev. D 84, 063508 (2011), arXiv: 1105.5713.

    ADS  Google Scholar 

  77. Y. Cai, Y. T. Wang, J. Y. Zhao, and Y. S. Piao, Phys. Rev. D 97, 103535 (2018), arXiv: 1709.07464.

    ADS  MathSciNet  Google Scholar 

  78. S. Ni, H. Li, T. Qiu, W. Zheng, and X. Zhang, Eur. Phys. J. C 78, 608 (2018), arXiv: 1707.05570.

    ADS  Google Scholar 

  79. S. Mizuno, S. Mukohyama, S. Pi, and Y. Zhang, arXiv: 1910.02979.

  80. A. Vilenkin, Phys. Lett. B 117, 25 (1982).

    ADS  MathSciNet  Google Scholar 

  81. J. B. Hartle, and S. W. Hawking, Phys. Rev. D 28, 2960 (1983).

    ADS  MathSciNet  Google Scholar 

  82. J. Feldbrugge, J. L. Lehners, and N. Turok, Phys. Rev. Lett. 119, 171301 (2017), arXiv: 1705.00192.

    ADS  Google Scholar 

  83. J. D. Dorronsoro, J. J. Halliwell, J. B. Hartle, T. Hertog, and O. Janssen, Phys. Rev. D 96, 043505 (2017).

    ADS  MathSciNet  Google Scholar 

  84. A. Vilenkin, and M. Yamada, Phys. Rev. D 98, 066003 (2018), arXiv: 1808.02032.

    ADS  MathSciNet  Google Scholar 

  85. M. Bojowald, and S. Brahma, Phys. Rev. Lett. 121, 201301 (2018), arXiv: 1810.09871.

    ADS  Google Scholar 

  86. A. Di Tucci, and J. L. Lehners, Phys. Rev. Lett. 122, 201302 (2019), arXiv: 1903.06757.

    ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Physics, University of Chinese Academy of Sciences, Beijing, 100049, China

    Yong Cai & YunSong Piao

  2. Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China

    YunSong Piao

Authors
  1. Yong Cai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. YunSong Piao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Yong Cai or YunSong Piao.

Additional information

Yong Cai was suppoerted by the China Postdoctoral Science Foundation (Grant No. 2019M650810), and the National Natural Science Foundation of China (Grant No. 11905224). YunSong Piao was supported by the National Natural Science Foundation of China (Grant Nos. 11575188, and 11690021). This work was supported by the University of Chinese Academy of Sciences.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cai, Y., Piao, Y. Pre-inflation and trans-Planckian censorship. Sci. China Phys. Mech. Astron. 63, 110411 (2020). https://doi.org/10.1007/s11433-020-1573-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11433-020-1573-5

Keywords

Search

Navigation