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Constant-rate inflation: primordial black holes from conformal weight transitions

A preprint version of the article is available at arXiv.

Abstract

Constant-rate inflation, including ultra-slow-roll inflation as a special case, has been widely applied to the formation of primordial black holes with a significant deviation from the standard slow-roll conditions at both the growing and decaying phases of the power spectrum. We derive analytic solutions for the curvature perturbations with respect to the late-time scaling dimensions (conformal weights) constrained by the dilatation symmetry of the de Sitter background and show that the continuity of conformal weights across different rolling phases is protected by the adiabatic condition of the inflaton perturbation. The temporal excitation of subleading states (with the next-to-lowest conformal weights), recorded as the “steepest growth” of the power spectrum, is triggered by the entropy production in the transition from the slow-roll to the constant-rate phases.

References

  1. B. Carr and F. Kuhnel, Primordial black holes as dark matter: recent developments, Ann. Rev. Nucl. Part. Sci. 70 (2020) 355 [arXiv:2006.02838] [INSPIRE].

    ADS  Google Scholar 

  2. A.M. Green and B.J. Kavanagh, Primordial black holes as a dark matter candidate, J. Phys. G 48 (2021) 043001 [arXiv:2007.10722] [INSPIRE].

  3. J. Yokoyama, Chaotic new inflation and formation of primordial black holes, Phys. Rev. D 58 (1998) 083510 [astro-ph/9802357] [INSPIRE].

  4. R. Saito, J. Yokoyama and R. Nagata, Single-field inflation, anomalous enhancement of superhorizon fluctuations, and non-Gaussianity in primordial black hole formation, JCAP 06 (2008) 024 [arXiv:0804.3470] [INSPIRE].

    ADS  Google Scholar 

  5. J. García-Bellido and E. Ruiz Morales, Primordial black holes from single field models of inflation, Phys. Dark Univ. 18 (2017) 47 [arXiv:1702.03901] [INSPIRE].

    Google Scholar 

  6. K. Kannike, L. Marzola, M. Raidal and H. Veermäe, Single field double inflation and primordial black holes, JCAP 09 (2017) 020 [arXiv:1705.06225] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  7. C. Germani and T. Prokopec, On primordial black holes from an inflection point, Phys. Dark Univ. 18 (2017) 6 [arXiv:1706.04226] [INSPIRE].

    Google Scholar 

  8. H. Motohashi and W. Hu, Primordial black holes and slow-roll violation, Phys. Rev. D 96 (2017) 063503 [arXiv:1706.06784] [INSPIRE].

  9. M. Cicoli, V.A. Diaz and F.G. Pedro, Primordial black holes from string inflation, JCAP 06 (2018) 034 [arXiv:1803.02837] [INSPIRE].

    ADS  Google Scholar 

  10. O. Özsoy, S. Parameswaran, G. Tasinato and I. Zavala, Mechanisms for primordial black hole production in string theory, JCAP 07 (2018) 005 [arXiv:1803.07626] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  11. C.T. Byrnes, P.S. Cole and S.P. Patil, Steepest growth of the power spectrum and primordial black holes, JCAP 06 (2019) 028 [arXiv:1811.11158] [INSPIRE].

    ADS  Google Scholar 

  12. S.-L. Cheng, W. Lee and K.-W. Ng, Superhorizon curvature perturbation in ultraslow-roll inflation, Phys. Rev. D 99 (2019) 063524 [arXiv:1811.10108] [INSPIRE].

  13. M. Biagetti, G. Franciolini, A. Kehagias and A. Riotto, Primordial black holes from inflation and quantum diffusion, JCAP 07 (2018) 032 [arXiv:1804.07124] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  14. V. Atal and C. Germani, The role of non-Gaussianities in primordial black hole formation, Phys. Dark Univ. 24 (2019) 100275 [arXiv:1811.07857] [INSPIRE].

  15. W.-T. Xu, J. Liu, T.-J. Gao and Z.-K. Guo, Gravitational waves from double-inflection-point inflation, Phys. Rev. D 101 (2020) 023505 [arXiv:1907.05213] [INSPIRE].

  16. H. Motohashi, S. Mukohyama and M. Oliosi, Constant roll and primordial black holes, JCAP 03 (2020) 002 [arXiv:1910.13235] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  17. N. Bhaumik and R.K. Jain, Primordial black holes dark matter from inflection point models of inflation and the effects of reheating, JCAP 01 (2020) 037 [arXiv:1907.04125] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  18. J. Liu, Z.-K. Guo and R.-G. Cai, Analytical approximation of the scalar spectrum in the ultraslow-roll inflationary models, Phys. Rev. D 101 (2020) 083535 [arXiv:2003.02075] [INSPIRE].

  19. G. Ballesteros, J. Rey, M. Taoso and A. Urbano, Primordial black holes as dark matter and gravitational waves from single-field polynomial inflation, JCAP 07 (2020) 025 [arXiv:2001.08220] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  20. H.V. Ragavendra, P. Saha, L. Sriramkumar and J. Silk, Primordial black holes and secondary gravitational waves from ultraslow roll and punctuated inflation, Phys. Rev. D 103 (2021) 083510 [arXiv:2008.12202] [INSPIRE].

  21. M. Taoso and A. Urbano, Non-Gaussianities for primordial black hole formation, JCAP 08 (2021) 016 [arXiv:2102.03610] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  22. J. Yokoyama, Formation of MACHO primordial black holes in inflationary cosmology, Astron. Astrophys. 318 (1997) 673 [astro-ph/9509027] [INSPIRE].

  23. M. Kawasaki, A. Kusenko and T.T. Yanagida, Primordial seeds of supermassive black holes, Phys. Lett. B 711 (2012) 1 [arXiv:1202.3848] [INSPIRE].

    ADS  Google Scholar 

  24. S. Clesse and J. García-Bellido, Massive primordial black holes from hybrid inflation as dark matter and the seeds of Galaxies, Phys. Rev. D 92 (2015) 023524 [arXiv:1501.07565] [INSPIRE].

  25. M. Kawasaki, A. Kusenko, Y. Tada and T.T. Yanagida, Primordial black holes as dark matter in supergravity inflation models, Phys. Rev. D 94 (2016) 083523 [arXiv:1606.07631] [INSPIRE].

  26. S.-L. Cheng, W. Lee and K.-W. Ng, Production of high stellar-mass primordial black holes in trapped inflation, JHEP 02 (2017) 008 [arXiv:1606.00206] [INSPIRE].

    ADS  MATH  Google Scholar 

  27. S. Pi, Y.-l. Zhang, Q.-G. Huang and M. Sasaki, Scalaron from R2-gravity as a heavy field, JCAP 05 (2018) 042 [arXiv:1712.09896] [INSPIRE].

  28. S.-L. Cheng, W. Lee and K.-W. Ng, Primordial black holes and associated gravitational waves in axion monodromy inflation, JCAP 07 (2018) 001 [arXiv:1801.09050] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  29. O. Özsoy, Synthetic gravitational waves from a rolling axion monodromy, JCAP 04 (2021) 040 [arXiv:2005.10280] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  30. J. Fumagalli, S. Renaux-Petel, J.W. Ronayne and L.T. Witkowski, Turning in the landscape: a new mechanism for generating Primordial Black Holes, arXiv:2004.08369 [INSPIRE].

  31. G.A. Palma, S. Sypsas and C. Zenteno, Seeding primordial black holes in multifield inflation, Phys. Rev. Lett. 125 (2020) 121301 [arXiv:2004.06106] [INSPIRE].

  32. M. Braglia, D.K. Hazra, F. Finelli, G.F. Smoot, L. Sriramkumar and A.A. Starobinsky, Generating PBHs and small-scale GWs in two-field models of inflation, JCAP 08 (2020) 001 [arXiv:2005.02895] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  33. O. Özsoy and Z. Lalak, Primordial black holes as dark matter and gravitational waves from bumpy axion inflation, JCAP 01 (2021) 040 [arXiv:2008.07549] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  34. L. Anguelova, On primordial black holes from rapid turns in two-field models, JCAP 06 (2021) 004 [arXiv:2012.03705] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  35. J. Fumagalli, S. Renaux-Petel and L.T. Witkowski, Oscillations in the stochastic gravitational wave background from sharp features and particle production during inflation, JCAP 08 (2021) 030 [arXiv:2012.02761] [INSPIRE].

    MathSciNet  Google Scholar 

  36. N.C. Tsamis and R.P. Woodard, Improved estimates of cosmological perturbations, Phys. Rev. D 69 (2004) 084005 [astro-ph/0307463] [INSPIRE].

  37. W.H. Kinney, Horizon crossing and inflation with large eta, Phys. Rev. D 72 (2005) 023515 [gr-qc/0503017] [INSPIRE].

  38. J. Martin, H. Motohashi and T. Suyama, Ultra slow-roll inflation and the non-Gaussianity consistency relation, Phys. Rev. D 87 (2013) 023514 [arXiv:1211.0083] [INSPIRE].

  39. H. Motohashi, A.A. Starobinsky and J. Yokoyama, Inflation with a constant rate of roll, JCAP 09 (2015) 018 [arXiv:1411.5021] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  40. L. Anguelova, P. Suranyi and L.C.R. Wijewardhana, Systematics of Constant Roll Inflation, JCAP 02 (2018) 004 [arXiv:1710.06989] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  41. O. Özsoy and G. Tasinato, On the slope of the curvature power spectrum in non-attractor inflation, JCAP 04 (2020) 048 [arXiv:1912.01061] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  42. G. Ballesteros, J. Rey, M. Taoso and A. Urbano, Stochastic inflationary dynamics beyond slow-roll and consequences for primordial black hole formation, JCAP 08 (2020) 043 [arXiv:2006.14597] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  43. V. Vennin, Stochastic inflation and primordial black holes, arXiv:2009.08715 [INSPIRE].

  44. C. Pattison, V. Vennin, D. Wands and H. Assadullahi, Ultra-slow-roll inflation with quantum diffusion, JCAP 04 (2021) 080 [arXiv:2101.05741] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  45. K. Ando and V. Vennin, Power spectrum in stochastic inflation, JCAP 04 (2021) 057 [arXiv:2012.02031] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  46. C. Pattison, Inflation: a quantum laboratory on cosmological scales, arXiv:2102.01030 [INSPIRE].

  47. P. Carrilho, K.A. Malik and D.J. Mulryne, Dissecting the growth of the power spectrum for primordial black holes, Phys. Rev. D 100 (2019) 103529 [arXiv:1907.05237] [INSPIRE].

  48. M. Braglia, X. Chen and D.K. Hazra, Probing primordial features with the stochastic gravitational wave background, JCAP 03 (2021) 005 [arXiv:2012.05821] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  49. I. Antoniadis, P.O. Mazur and E. Mottola, Conformal invariance, dark energy, and CMB non-Gaussianity, JCAP 09 (2012) 024 [arXiv:1103.4164] [INSPIRE].

    ADS  Google Scholar 

  50. J.M. Maldacena and G.L. Pimentel, On graviton non-Gaussianities during inflation, JHEP 09 (2011) 045 [arXiv:1104.2846] [INSPIRE].

    ADS  MATH  Google Scholar 

  51. P. Creminelli, Conformal invariance of scalar perturbations in inflation, Phys. Rev. D 85 (2012) 041302 [arXiv:1108.0874] [INSPIRE].

  52. K. Hinterbichler, L. Hui and J. Khoury, Conformal symmetries of adiabatic modes in cosmology, JCAP 08 (2012) 017 [arXiv:1203.6351] [INSPIRE].

    ADS  Google Scholar 

  53. N. Arkani-Hamed and J. Maldacena, Cosmological collider physics, arXiv:1503.08043 [INSPIRE].

  54. N. Arkani-Hamed, D. Baumann, H. Lee and G.L. Pimentel, The cosmological bootstrap: inflationary correlators from symmetries and singularities, JHEP 04 (2020) 105 [arXiv:1811.00024] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  55. A. Strominger, The dS/CFT correspondence, JHEP 10 (2001) 034 [hep-th/0106113] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  56. G.S. Ng and A. Strominger, State/operator correspondence in higher-spin dS/CFT, Class. Quant. Grav. 30 (2013) 104002 [arXiv:1204.1057] [INSPIRE].

  57. D.L. Jafferis, A. Lupsasca, V. Lysov, G.S. Ng and A. Strominger, Quasinormal quantization in de Sitter spacetime, JHEP 01 (2015) 004 [arXiv:1305.5523] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  58. A.R. Brown, Hyperbolic inflation, Phys. Rev. Lett. 121 (2018) 251601 [arXiv:1705.03023] [INSPIRE].

  59. X. Chen and Y. Wang, Large non-Gaussianities with intermediate shapes from quasi-single field inflation, Phys. Rev. D 81 (2010) 063511 [arXiv:0909.0496] [INSPIRE].

  60. X. Chen and Y. Wang, Quasi-single field inflation and non-Gaussianities, JCAP 04 (2010) 027 [arXiv:0911.3380] [INSPIRE].

    ADS  Google Scholar 

  61. T. Noumi, M. Yamaguchi and D. Yokoyama, Effective field theory approach to quasi-single field inflation and effects of heavy fields, JHEP 06 (2013) 051 [arXiv:1211.1624] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  62. X. Chen and Y. Wang, Quasi-single field inflation with large mass, JCAP 09 (2012) 021 [arXiv:1205.0160] [INSPIRE].

    ADS  Google Scholar 

  63. S. Pi and M. Sasaki, Curvature perturbation spectrum in two-field inflation with a turning trajectory, JCAP 10 (2012) 051 [arXiv:1205.0161] [INSPIRE].

    ADS  Google Scholar 

  64. J.-O. Gong, S. Pi and M. Sasaki, Equilateral non-Gaussianity from heavy fields, JCAP 11 (2013) 043 [arXiv:1306.3691] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  65. H. Lee, D. Baumann and G.L. Pimentel, Non-Gaussianity as a particle detector, JHEP 12 (2016) 040 [arXiv:1607.03735] [INSPIRE].

    ADS  MATH  Google Scholar 

  66. Y. Wang, Y.-P. Wu, J. Yokoyama and S. Zhou, Hybrid quasi-single field inflation, JCAP 07 (2018) 068 [arXiv:1804.07541] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  67. Y.-P. Wu, Higgs as heavy-lifted physics during inflation, JHEP 04 (2019) 125 [arXiv:1812.10654] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  68. R.K. Jain, P. Chingangbam, J.-O. Gong, L. Sriramkumar and T. Souradeep, Punctuated inflation and the low CMB multipoles, JCAP 01 (2009) 009 [arXiv:0809.3915] [INSPIRE].

    ADS  Google Scholar 

  69. R.K. Jain, P. Chingangbam, L. Sriramkumar and T. Souradeep, The tensor-to-scalar ratio in punctuated inflation, Phys. Rev. D 82 (2010) 023509 [arXiv:0904.2518] [INSPIRE].

  70. R. Allahverdi, K. Enqvist, J. García-Bellido, A. Jokinen and A. Mazumdar, MSSM flat direction inflation: slow roll, stability, fine tunning and reheating, JCAP 06 (2007) 019 [hep-ph/0610134] [INSPIRE].

  71. Y. Tada and S. Yokoyama, Primordial black hole tower: dark matter, earth-mass, and LIGO black holes, Phys. Rev. D 100 (2019) 023537 [arXiv:1904.10298] [INSPIRE].

  72. Y.-F. Cai, X. Chen, M.H. Namjoo, M. Sasaki, D.-G. Wang and Z. Wang, Revisiting non-Gaussianity from non-attractor inflation models, JCAP 05 (2018) 012 [arXiv:1712.09998] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  73. T. Suyama, Y. Tada and M. Yamaguchi, Revisiting non-Gaussianity in non-attractor inflation models in the light of the cosmological soft theorem, PTEP 2021 (2021) 073E02 [arXiv:2101.10682] [INSPIRE].

  74. S.M. Leach, M. Sasaki, D. Wands and A.R. Liddle, Enhancement of superhorizon scale inflationary curvature perturbations, Phys. Rev. D 64 (2001) 023512 [astro-ph/0101406] [INSPIRE].

  75. S.M. Leach and A.R. Liddle, Inflationary perturbations near horizon crossing, Phys. Rev. D 63 (2001) 043508 [astro-ph/0010082] [INSPIRE].

  76. C. Gordon, D. Wands, B.A. Bassett and R. Maartens, Adiabatic and entropy perturbations from inflation, Phys. Rev. D 63 (2000) 023506 [astro-ph/0009131] [INSPIRE].

  77. J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [INSPIRE].

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Ng, KW., Wu, YP. Constant-rate inflation: primordial black holes from conformal weight transitions. J. High Energ. Phys. 2021, 76 (2021). https://doi.org/10.1007/JHEP11(2021)076

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Keywords

  • Cosmology of Theories beyond the SM
  • Space-Time Symmetries
  • Conformal Field Theory