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A gravitino-rich universe

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Abstract

The gravitino may well play an important role in cosmology, not only because its interactions are Planck-suppressed and therefore long-lived, but also because it is copiously produced via various processes such as particle scatterings in thermal plasma, and (pseudo) modulus and inflaton decays. We study a possibility that the early Universe was gravitino-rich from various aspects. In particular, a viable cosmology is possible, if high-scale supersymmetry is realized in nature as suggested by the recent discovery of the standard-model like Higgs boson of mass about 125-126 GeV. We find that the Universe can be even gravitino-dominated, in which case there will be an entropy dilution by the gravitino decay. If the gravitino abundance is proportional to the reheating temperature, both the maximal baryon asymmetry in leptogenesis and the dark matter from the gravitino decay become independent of the reheating temperature. The dark matter candidate is the Wino-like neutralino, whose mass is suppressed compared to the anomaly-mediation relation.

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References

  1. ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].

    ADS  Google Scholar 

  2. CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].

    ADS  Google Scholar 

  3. Y. Okada, M. Yamaguchi and T. Yanagida, Renormalization group analysis on the Higgs mass in the softly broken supersymmetric standard model, Phys. Lett. B 262 (1991) 54 [INSPIRE].

    Article  ADS  Google Scholar 

  4. Y. Okada, M. Yamaguchi and T. Yanagida, Upper bound of the lightest Higgs boson mass in the minimal supersymmetric standard model, Prog. Theor. Phys. 85 (1991) 1 [INSPIRE].

    Article  ADS  Google Scholar 

  5. J.R. Ellis, G. Ridolfi and F. Zwirner, Radiative corrections to the masses of supersymmetric Higgs bosons, Phys. Lett. B 257 (1991) 83 [INSPIRE].

    Article  ADS  Google Scholar 

  6. H.E. Haber and R. Hempfling, Can the mass of the lightest Higgs boson of the minimal supersymmetric model be larger than m(Z)?, Phys. Rev. Lett. 66 (1991) 1815 [INSPIRE].

    Article  ADS  Google Scholar 

  7. G.F. Giudice and A. Strumia, Probing High-Scale and Split Supersymmetry with Higgs Mass Measurements, Nucl. Phys. B 858 (2012) 63 [arXiv:1108.6077] [INSPIRE].

    Article  ADS  Google Scholar 

  8. G. Degrassi, S. Di Vita, J. Elias-Miro, J.R. Espinosa, G.F. Giudice, et al., Higgs mass and vacuum stability in the Standard Model at NNLO, JHEP 08 (2012) 098 [arXiv:1205.6497] [INSPIRE].

    Article  ADS  Google Scholar 

  9. F. Bezrukov, M.Y. Kalmykov, B.A. Kniehl and M. Shaposhnikov, Higgs Boson Mass and New Physics, JHEP 10 (2012) 140 [arXiv:1205.2893] [INSPIRE].

    Article  ADS  Google Scholar 

  10. M. Bolz, A. Brandenburg and W. Buchmüller, Thermal production of gravitinos, Nucl. Phys. B 606 (2001) 518 [Erratum ibid. B 790 (2008) 336–337] [hep-ph/0012052] [INSPIRE].

    Article  ADS  Google Scholar 

  11. J. Pradler and F.D. Steffen, Thermal gravitino production and collider tests of leptogenesis, Phys. Rev. D 75 (2007) 023509 [hep-ph/0608344] [INSPIRE].

    ADS  Google Scholar 

  12. J. Pradler and F.D. Steffen, Constraints on the Reheating Temperature in Gravitino Dark Matter Scenarios, Phys. Lett. B 648 (2007) 224 [hep-ph/0612291] [INSPIRE].

    Article  ADS  Google Scholar 

  13. V.S. Rychkov and A. Strumia, Thermal production of gravitinos, Phys. Rev. D 75 (2007) 075011 [hep-ph/0701104] [INSPIRE].

    ADS  Google Scholar 

  14. M. Endo, K. Hamaguchi and F. Takahashi, Moduli-induced gravitino problem, Phys. Rev. Lett. 96 (2006) 211301 [hep-ph/0602061] [INSPIRE].

    Article  ADS  Google Scholar 

  15. S. Nakamura and M. Yamaguchi, Gravitino production from heavy moduli decay and cosmological moduli problem revived, Phys. Lett. B 638 (2006) 389 [hep-ph/0602081] [INSPIRE].

    Article  ADS  Google Scholar 

  16. M. Dine, R. Kitano, A. Morisse and Y. Shirman, Moduli decays and gravitinos, Phys. Rev. D 73 (2006) 123518 [hep-ph/0604140] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  17. M. Endo, K. Hamaguchi and F. Takahashi, Moduli/Inflaton Mixing with Supersymmetry Breaking Field, Phys. Rev. D 74 (2006) 023531 [hep-ph/0605091] [INSPIRE].

    ADS  Google Scholar 

  18. M. Kawasaki, F. Takahashi and T. Yanagida, Gravitino overproduction in inflaton decay, Phys. Lett. B 638 (2006) 8 [hep-ph/0603265] [INSPIRE].

    Article  ADS  Google Scholar 

  19. M. Kawasaki, F. Takahashi and T. Yanagida, The Gravitino-overproduction problem in inflationary universe, Phys. Rev. D 74 (2006) 043519 [hep-ph/0605297] [INSPIRE].

    ADS  Google Scholar 

  20. T. Asaka, S. Nakamura and M. Yamaguchi, Gravitinos from heavy scalar decay, Phys. Rev. D 74 (2006) 023520 [hep-ph/0604132] [INSPIRE].

    ADS  Google Scholar 

  21. M. Endo, M. Kawasaki, F. Takahashi and T. Yanagida, Inflaton decay through supergravity effects, Phys. Lett. B 642 (2006) 518 [hep-ph/0607170] [INSPIRE].

    Article  ADS  Google Scholar 

  22. M. Endo, F. Takahashi and T. Yanagida, Anomaly-induced inflaton decay and gravitino-overproduction problem, Phys. Lett. B 658 (2008) 236 [hep-ph/0701042] [INSPIRE].

    Article  ADS  Google Scholar 

  23. M. Endo, F. Takahashi and T. Yanagida, Inflaton Decay in Supergravity, Phys. Rev. D 76 (2007) 083509 [arXiv:0706.0986] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  24. S. Weinberg, Cosmological Constraints on the Scale of Supersymmetry Breaking, Phys. Rev. Lett. 48 (1982) 1303 [INSPIRE].

    Article  ADS  Google Scholar 

  25. J.R. Ellis, A.D. Linde and D.V. Nanopoulos, Inflation Can Save the Gravitino, Phys. Lett. B 118 (1982) 59 [INSPIRE].

    Article  ADS  Google Scholar 

  26. L.M. Krauss, New Constraints on Ino Masses from Cosmology. 1. Supersymmetric Inos, Nucl. Phys. B 227 (1983) 556 [INSPIRE].

    Article  ADS  Google Scholar 

  27. M. Kawasaki, K. Kohri and N. Sugiyama, Cosmological constraints on late time entropy production, Phys. Rev. Lett. 82 (1999) 4168 [astro-ph/9811437] [INSPIRE].

    Article  ADS  Google Scholar 

  28. M. Kawasaki, K. Kohri and N. Sugiyama, MeV scale reheating temperature and thermalization of neutrino background, Phys. Rev. D 62 (2000) 023506 [astro-ph/0002127] [INSPIRE].

    ADS  Google Scholar 

  29. S. Hannestad, What is the lowest possible reheating temperature?, Phys. Rev. D 70 (2004) 043506 [astro-ph/0403291] [INSPIRE].

    ADS  Google Scholar 

  30. K. Ichikawa, M. Kawasaki and F. Takahashi, The Oscillation effects on thermalization of the neutrinos in the Universe with low reheating temperature, Phys. Rev. D 72 (2005) 043522 [astro-ph/0505395] [INSPIRE].

    ADS  Google Scholar 

  31. S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, de Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  32. M. Endo, F. Takahashi and T. Yanagida, Retrofitted gravity mediation without the gravitino-overproduction problem, Phys. Rev. D 76 (2007) 083508 [hep-ph/0702247] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  33. WMAP collaboration, E. Komatsu et al., Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation, Astrophys. J. Suppl. 192 (2011) 18 [arXiv:1001.4538] [INSPIRE].

    Article  ADS  Google Scholar 

  34. J. Dunkley, R. Hlozek, J. Sievers, V. Acquaviva, P. Ade, et al., The Atacama Cosmology Telescope: Cosmological Parameters from the 2008 Power Spectra, Astrophys. J. 739 (2011) 52 [arXiv:1009.0866] [INSPIRE].

    Article  ADS  Google Scholar 

  35. K. Ichikawa, M. Kawasaki, K. Nakayama, M. Senami and F. Takahashi, Increasing effective number of neutrinos by decaying particles, JCAP 05 (2007) 008 [hep-ph/0703034] [INSPIRE].

    Article  ADS  Google Scholar 

  36. J. Jaeckel, J. Redondo and A. Ringwald, Signatures of a hidden cosmic microwave background, Phys. Rev. Lett. 101 (2008) 131801 [arXiv:0804.4157] [INSPIRE].

    Article  ADS  Google Scholar 

  37. K. Nakayama, F. Takahashi and T.T. Yanagida, A theory of extra radiation in the Universe, Phys. Lett. B 697 (2011) 275 [arXiv:1010.5693] [INSPIRE].

    Article  ADS  Google Scholar 

  38. T. Kobayashi, F. Takahashi, T. Takahashi and M. Yamaguchi, Dark Radiation from Modulated Reheating, JCAP 03 (2012) 036 [arXiv:1111.1336] [INSPIRE].

    Article  ADS  Google Scholar 

  39. K.S. Jeong and F. Takahashi, Light Higgsino from Axion Dark Radiation, JHEP 08 (2012) 017 [arXiv:1201.4816] [INSPIRE].

    Article  ADS  Google Scholar 

  40. K. Choi, K.-Y. Choi and C.S. Shin, Dark radiation and small-scale structure problems with decaying particles, Phys. Rev. D 86 (2012) 083529 [arXiv:1208.2496] [INSPIRE].

    ADS  Google Scholar 

  41. M. Cicoli, J.P. Conlon and F. Quevedo, Dark Radiation in LARGE Volume Models, arXiv:1208.3562 [INSPIRE].

  42. T. Higaki and F. Takahashi, Dark Radiation and Dark Matter in Large Volume Compactifications, JHEP 11 (2012) 125 [arXiv:1208.3563] [INSPIRE].

    Article  ADS  Google Scholar 

  43. K. Nakayama, F. Takahashi and T.T. Yanagida, On the Adiabatic Solution to the Polonyi/Moduli Problem, Phys. Rev. D 84 (2011) 123523 [arXiv:1109.2073] [INSPIRE].

    ADS  Google Scholar 

  44. R. Kallosh and A.D. Linde, Landscape, the scale of SUSY breaking and inflation, JHEP 12 (2004) 004 [hep-th/0411011] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  45. W. Buchmüller, K. Hamaguchi, O. Lebedev and M. Ratz, Dilaton destabilization at high temperature, Nucl. Phys. B 699 (2004) 292 [hep-th/0404168] [INSPIRE].

    Article  ADS  Google Scholar 

  46. T. Higaki, K. Kamada and F. Takahashi, Higgs, Moduli Problem, Baryogenesis and Large Volume Compactifications, JHEP 09 (2012) 043 [arXiv:1207.2771] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  47. M. Graña, Flux compactifications in string theory: A Comprehensive review, Phys. Rept. 423 (2006) 91 [hep-th/0509003] [INSPIRE].

    Article  ADS  Google Scholar 

  48. M.R. Douglas and S. Kachru, Flux compactification, Rev. Mod. Phys. 79 (2007) 733 [hep-th/0610102] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  49. R. Blumenhagen, B. Körs, D. Lüst and S. Stieberger, Four-dimensional String Compactifications with D-branes, Orientifolds and Fluxes, Phys. Rept. 445 (2007) 1 [hep-th/0610327] [INSPIRE].

    Article  ADS  Google Scholar 

  50. K. Nakayama, F. Takahashi and T.T. Yanagida, Eluding the Gravitino Overproduction in Inflaton Decay, Phys. Lett. B 718 (2012) 526 [arXiv:1209.2583] [INSPIRE].

    Article  ADS  Google Scholar 

  51. T. Asaka, K. Hamaguchi, M. Kawasaki and T. Yanagida, Leptogenesis in inflationary universe, Phys. Rev. D 61 (2000) 083512 [hep-ph/9907559] [INSPIRE].

    ADS  Google Scholar 

  52. V.N. Senoguz and Q. Shafi, New inflation, preinflation and leptogenesis, Phys. Lett. B 596 (2004) 8 [hep-ph/0403294] [INSPIRE].

    Article  ADS  Google Scholar 

  53. K. Nakayama and F. Takahashi, Low-scale Supersymmetry from Inflation, JCAP 10 (2011) 033 [arXiv:1108.0070] [INSPIRE].

    Article  ADS  Google Scholar 

  54. K. Nakayama and F. Takahashi, PeV-scale Supersymmetry from New Inflation, JCAP 05 (2012) 035 [arXiv:1203.0323] [INSPIRE].

    Article  ADS  Google Scholar 

  55. E.J. Copeland, A.R. Liddle, D.H. Lyth, E.D. Stewart and D. Wands, False vacuum inflation with Einstein gravity, Phys. Rev. D 49 (1994) 6410 [astro-ph/9401011] [INSPIRE].

    ADS  Google Scholar 

  56. G.R. Dvali, Q. Shafi and R.K. Schaefer, Large scale structure and supersymmetric inflation without fine tuning, Phys. Rev. Lett. 73 (1994) 1886 [hep-ph/9406319] [INSPIRE].

    Article  ADS  Google Scholar 

  57. A.D. Linde and A. Riotto, Hybrid inflation in supergravity, Phys. Rev. D 56 (1997) 1841 [hep-ph/9703209] [INSPIRE].

    ADS  Google Scholar 

  58. G. Lazarides and C. Panagiotakopoulos, Smooth hybrid inflation, Phys. Rev. D 52 (1995) 559 [hep-ph/9506325] [INSPIRE].

    ADS  Google Scholar 

  59. M. Kawasaki, M. Yamaguchi and T. Yanagida, Natural chaotic inflation in supergravity, Phys. Rev. Lett. 85 (2000) 3572 [hep-ph/0004243] [INSPIRE].

    Article  ADS  Google Scholar 

  60. M. Kawasaki, M. Yamaguchi and T. Yanagida, Natural chaotic inflation in supergravity and leptogenesis, Phys. Rev. D 63 (2001) 103514 [hep-ph/0011104] [INSPIRE].

    ADS  Google Scholar 

  61. W. Buchmüller, L. Covi and D. Delepine, Inflation and supersymmetry breaking, Phys. Lett. B 491 (2000) 183 [hep-ph/0006168] [INSPIRE].

    Article  ADS  Google Scholar 

  62. K. Nakayama, F. Takahashi and T.T. Yanagida, Constraint on the gravitino mass in hybrid inflation, JCAP 12 (2010) 010 [arXiv:1007.5152] [INSPIRE].

    ADS  Google Scholar 

  63. M. Fujii and K. Hamaguchi, Higgsino and wino dark matter from Q ball decay, Phys. Lett. B 525 (2002) 143 [hep-ph/0110072] [INSPIRE].

    Article  ADS  Google Scholar 

  64. N. Arkani-Hamed, S. Dimopoulos, G. Giudice and A. Romanino, Aspects of split supersymmetry, Nucl. Phys. B 709 (2005) 3 [hep-ph/0409232] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  65. K.S. Jeong, M. Shimosuka and M. Yamaguchi, Light Higgsino in Heavy Gravitino Scenario with Successful Electroweak Symmetry Breaking, JHEP 09 (2012) 050 [arXiv:1112.5293] [INSPIRE].

    Article  ADS  Google Scholar 

  66. M. Ibe and T.T. Yanagida, The Lightest Higgs Boson Mass in Pure Gravity Mediation Model, Phys. Lett. B 709 (2012) 374 [arXiv:1112.2462] [INSPIRE].

    Article  ADS  Google Scholar 

  67. W. Buchmüller, V. Domcke and K. Schmitz, WIMP Dark Matter from Gravitino Decays and Leptogenesis, Phys. Lett. B 713 (2012) 63 [arXiv:1203.0285] [INSPIRE].

    Article  ADS  Google Scholar 

  68. J. Hisano, S. Matsumoto and M.M. Nojiri, Explosive dark matter annihilation, Phys. Rev. Lett. 92 (2004) 031303 [hep-ph/0307216] [INSPIRE].

    Article  ADS  Google Scholar 

  69. J. Hisano, S. Matsumoto, M.M. Nojiri and O. Saito, Non-perturbative effect on dark matter annihilation and gamma ray signature from galactic center, Phys. Rev. D 71 (2005) 063528 [hep-ph/0412403] [INSPIRE].

    ADS  Google Scholar 

  70. M. Fukugita and T. Yanagida, Baryogenesis Without Grand Unification, Phys. Lett. B 174 (1986) 45 [INSPIRE].

    Article  ADS  Google Scholar 

  71. T. Yanagida, Horizontal Symmetry and Masses of Neutrinos, Prog. Theor. Phys. 64 (1980) 1103 [INSPIRE].

    Article  ADS  Google Scholar 

  72. M. Gell-Mann, P. Ramond and R. Slansky, in Supergravity, North-Holland, Amsterdam, (1979) D.Z. Freedom and P. van Nieuwenhuizen eds., Print-80-0576 (CERN).

  73. P. Minkowski, μeγ at a Rate of One Out of 1-Billion Muon Decays?, Phys. Lett. B 67 (1977) 421 [INSPIRE].

    Article  ADS  Google Scholar 

  74. W. Buchmüller, P. Di Bari and M. Plümacher, Leptogenesis for pedestrians, Annals Phys. 315 (2005) 305 [hep-ph/0401240] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  75. W. Buchmüller, R. Peccei and T. Yanagida, Leptogenesis as the origin of matter, Ann. Rev. Nucl. Part. Sci. 55 (2005) 311 [hep-ph/0502169] [INSPIRE].

    Article  ADS  Google Scholar 

  76. S. Davidson, E. Nardi and Y. Nir, Leptogenesis, Phys. Rept. 466 (2008) 105 [arXiv:0802.2962] [INSPIRE].

    Article  ADS  Google Scholar 

  77. K.S. Jeong and F. Takahashi, Anarchy and Leptogenesis, JHEP 07 (2012) 170 [arXiv:1204.5453] [INSPIRE].

    Article  ADS  Google Scholar 

  78. L. Randall and R. Sundrum, Out of this world supersymmetry breaking, Nucl. Phys. B 557 (1999) 79 [hep-th/9810155] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  79. J.A. Bagger, T. Moroi and E. Poppitz, Anomaly mediation in supergravity theories, JHEP 04 (2000) 009 [hep-th/9911029] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  80. G.F. Giudice, M.A. Luty, H. Murayama and R. Rattazzi, Gaugino mass without singlets, JHEP 12 (1998) 027 [hep-ph/9810442] [INSPIRE].

    Article  ADS  Google Scholar 

  81. K. Choi and H.P. Nilles, The Gaugino code, JHEP 04 (2007) 006 [hep-ph/0702146] [INSPIRE].

    Article  ADS  Google Scholar 

  82. N. Okada, Positively deflected anomaly mediation, Phys. Rev. D 65 (2002) 115009 [hep-ph/0202219] [INSPIRE].

    ADS  Google Scholar 

  83. R. Peccei and H.R. Quinn, CP Conservation in the Presence of Instantons, Phys. Rev. Lett. 38 (1977) 1440 [INSPIRE].

    Article  ADS  Google Scholar 

  84. J.E. Kim, Light Pseudoscalars, Particle Physics and Cosmology, Phys. Rept. 150 (1987) 1 [INSPIRE].

    Article  ADS  Google Scholar 

  85. H.-Y. Cheng, The Strong CP Problem Revisited, Phys. Rept. 158 (1988) 1 [INSPIRE].

    Article  ADS  Google Scholar 

  86. T. Gherghetta, G.F. Giudice and J.D. Wells, Phenomenological consequences of supersymmetry with anomaly induced masses, Nucl. Phys. B 559 (1999) 27 [hep-ph/9904378] [INSPIRE].

    Article  ADS  Google Scholar 

  87. J.L. Feng, T. Moroi, L. Randall, M. Strassler and S.-f. Su, Discovering supersymmetry at the Tevatron in wino LSP scenarios, Phys. Rev. Lett. 83 (1999) 1731 [hep-ph/9904250] [INSPIRE].

    Article  ADS  Google Scholar 

  88. M. Ibe, S. Matsumoto and T.T. Yanagida, Pure Gravity Mediation with m 3/2 = 10–100 TeV, Phys. Rev. D 85 (2012) 095011 [arXiv:1202.2253] [INSPIRE].

    ADS  Google Scholar 

  89. J.M. Cline and S. Raby, Gravitino induced baryogenesis: A Problem made a virtue, Phys. Rev. D 43 (1991) 1781 [INSPIRE].

    ADS  Google Scholar 

  90. R.J. Scherrer, J.M. Cline, S. Raby and D. Seckel, Gravitino induced baryogenesis, primordial nucleosynthesis and the Tremaine-Gunn limit, Phys. Rev. D 44 (1991) 3760 [INSPIRE].

    ADS  Google Scholar 

  91. I. Affleck and M. Dine, A New Mechanism for Baryogenesis, Nucl. Phys. B 249 (1985) 361 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  92. M. Dine, L. Randall and S.D. Thomas, Baryogenesis from flat directions of the supersymmetric standard model, Nucl. Phys. B 458 (1996) 291 [hep-ph/9507453] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  93. M. Kawasaki, T. Moroi and T. Yanagida, Can decaying particles raise the upper bound on the Peccei-Quinn scale?, Phys. Lett. B 383 (1996) 313 [hep-ph/9510461] [INSPIRE].

    Article  ADS  Google Scholar 

  94. A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper and J. March-Russell, String Axiverse, Phys. Rev. D 81 (2010) 123530 [arXiv:0905.4720] [INSPIRE].

    ADS  Google Scholar 

  95. F. Takahashi and T.T. Yanagida, Why have supersymmetric particles not been observed?, Phys. Lett. B 698 (2011) 408 [arXiv:1101.0867] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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Jeong, K.S., Takahashi, F. A gravitino-rich universe. J. High Energ. Phys. 2013, 173 (2013). https://doi.org/10.1007/JHEP01(2013)173

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