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Journal of High Energy Physics

, 2019:161 | Cite as

From Minkowski to de Sitter in multifield no-scale models

  • John Ellis
  • Balakrishnan Nagaraj
  • Dimitri V. Nanopoulos
  • Keith A. Olive
  • Sarunas VernerEmail author
Open Access
Regular Article - Theoretical Physics
  • 39 Downloads

ABSTRACT

We show the uniqueness of superpotentials leading to Minkowski vacua of single-field no-scale supergravity models, and the construction of dS/AdS solutions using pairs of these single-field Minkowski superpotentials. We then extend the construction to two- and multifield no-scale supergravity models, providing also a geometrical interpretation. We also consider scenarios with additional twisted or untwisted moduli fields, and discuss how inflationary models can be constructed in this framework.

KEYWORDS

Supergravity Models Superstring Vacua 

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]
    PARTICLE DATA GROUP collaboration, Review of particle physics, Phys. Rev.D 98 (2018) 030001 [INSPIRE].Google Scholar
  2. [2]
    K.A. Olive, Inflation, Phys. Rept.190 (1990) 307 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    A.D. Linde, Particl e physics and inflationary cosmology, Harwood, Chur, Switzerland (1990).CrossRefGoogle Scholar
  4. [4]
    D.H. Lyth and A. Riotto, Particle physics models of inflation and the cosmological density perturbation, Phys. Rept.314 (1999) 1 [hep-ph/9807278] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    J. Martin, C. Ringeval and V. Vennin, Encyclop(Edia inflationaris), Phys. Dark Univ.5-6 (2014) 75 [arXiv:1303.3787] [INSPIRE].CrossRefGoogle Scholar
  6. [6]
    J. Martin, C. Ringeval, R. Trotta and V. Vennin, The best inflationary models after Planck, JCAP03 (2014) 039 [arXiv:1312.3529] [INSPIRE].ADSMathSciNetGoogle Scholar
  7. [7]
    J. Martin, The observational status of cosmic inflation after Planck, Astrophys. Space Sci. Proc.45 (2016) 41 [arXiv:1502.05733], [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    H.P. Nilles, Supersymmetry, supergravity and particle physics, Phys. Rept.110 (1984) 1 [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    H.E. Haber and G.L. Kane, The search for supersymmetry: probing physics beyond the Standard Model, Phys. Rept.117 (1985) 75 [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    J.R. Ellis, D.V. Nanopoulos, K.A. Olive and K. Tamvakis, Cosmological inflation cries out for supersymmetry, Phys. Lett.B 118 (1982) 335 [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    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].ADSGoogle Scholar
  12. [12]
    E.D. Stewart, Inflation, supergravity and superstrings, Phys. Rev.D 51 (1995) 6847 [hep-ph/9405389] [INSPIRE].ADSGoogle Scholar
  13. [13]
    D.H. Lyth and A. Riotto, Particle physics models of inflation and the cosmological density perturbation, Phys. Rept.314 (1999) 1 [hep-ph/9807278] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    E. Cremmer, S. Ferrara, C. Kounnas and D.V. Nanopoulos, Naturally va nishing cosmological constant in N = 1 supergravity, Phys. Lett.B 133 (1983) 61 [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    J.R. Ellis, A.B. Lahanas, D.V. Nanopoulos and K. Tamvakis, No-scale supersymmetric Standard Model, Phys. Lett.B 134 (1984) 429 [INSPIRE]. ADSCrossRefGoogle Scholar
  16. [16]
    A.B. Lahanas and D.V. Nanopoulos, The road to no scale supergravity, Phys. Rept.145 (1987) 1 [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    J.R. Ellis, C. Kounnas and D.V. Nanopoulos, Phenomenological SU(1,1) supergravity, Nucl. Phys.B 241 (1984) 406 [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    J. Ellis, B. Nagaraj, D.V. Nanopoulos and K.A. Olive, De Sitter vacua in no-scale supergravity, JHEP11 (2018) 110 [arXiv:1809.10114] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  19. [19]
    E. Witten, Dimensional reduction of superstring models, Phys. Lett.B 155 (1985) 151 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    S. Ferrara and R. Kallosh, Seven-disk manifold, a-attractors and B modes, Phys. Rev.D 94 (2016) 126015 [arXiv:1610.04163] [INSPIRE].ADSMathSciNetGoogle Scholar
  21. [21]
    PLANCK collaboration, Planck 2018 results. VI. Cosmological parameters, arXiv: 1807.06209 [INSPIRE].
  22. [22]
    PLANCK collaboration, Planck 2018 results. X Constraints on inflation, arXiv: 1807.06211 [INSPIRE].
  23. [23]
    BICEP2 and KECK ARRAY collaborations, BICEP2 / Keck Array X: constraints on primordial gravitational waves using Planck , WMAP and new BICEP2/ Keck observations through the 2015 season, Phys. Rev. Lett.121 (2018) 221301 [arXiv:1810.05216] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    A.A. Starobinsky, A new type of isotropic cosmological models without singularity, Phys. Lett.B 91 (1980) 99 [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  25. [25]
    J. Ellis, D.V. Nanopoulos and K.A. Olive, No-scale supergravity realization of the Starobinsky model of inflation, Phys. Rev. Lett.111 (2013) 111301 [ Erratum ibid.111(2013) 129902] [arXiv:1305.1247] [INSPIRE].
  26. [26]
    A.S. Goncharov and A.D. Linde, A simple realization of the inflationary universe scenario in SU(1, 1) supergravity, Class. Quant. Grav.1 (1984) L75 [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    C. Kounnas and M. Quiros, A maximally symmetric no scale inflationary universe, Phys. Lett.B 151 (1985) 189 [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    J.R. Ellis, K. Enqvist, D.V. Nanopoulos, K.A. Olive and M. Srednicki, SU(N, 1) inflation, Phys. Lett.B 152 (1985) 175 [Erratum ibid.B 156 (1985) 452] [INSPIRE].
  29. [29]
    K. Enqvist, D.V. Nanopoulos and M. Quiros, Inflation from a ripple on a vanishing potential, Phys. Lett.B 159 (1985) 249 [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    P. Binetruy and M.K. Gaillard, Candidates for the inflaton field in superstring models, Phys. Rev.D 34 (1986) 3069 [INSPIRE].ADSGoogle Scholar
  31. [31]
    H. Murayama, H. Suzuki, T. Yanagida and J. Yokoyama, Chaotic inflation and baryogenesis in supergravity, Phys. Rev.D 50 (1994) R2356 [hep-ph/9311326] [INSPIRE].ADSGoogle Scholar
  32. [32]
    S.C. Davis and M. Postma, SUGRA chaotic inflation and moduli stabilisation, JCAP03 (2008) 015 [arXiv:0801.4696] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    S. Antusch, M. Bastero-Gil, K. Dutta, S.F. King and P.M. Kostka, Solving the η-problem in hybrid inflation with Heisenberg symmetry and stabilized modulus, JCAP01 (2009) 040 [arXiv: 0808.2425] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    S. Antusch, M. Bastero-Gil, K. Dutta, S.F. King and P.M. Kostka, Chaotic inflation in supergravity with Heisenberg symmetry, Ph ys. Lett.B 679 (2009) 428 [arXiv:0905.0905] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    R. Kallosh and A. Linde, New models of chaotic inflation in supergravity, JCAP11 (2010) 011 [arXiv:1008.3375] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  36. [36]
    R. Kallosh, A. Linde and T. Rube, General inflaton potentials in supergravity, Phys. Rev.D 83 (2011) 043507 [arXiv:1011.5945] [INSPIRE].ADSGoogle Scholar
  37. [37]
    S. Antusch, K. Dutta, J. Erdmenger and S. Halter, Towards matter inflation in heterotic string theory, JHEP04 (2011) 065 [arXiv: 1102.0093] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  38. [38]
    R. Kallosh, A. Linde, K.A. Olive and T. Rube, Chaotic inflation and supersymmetry breaking, Phys. Rev.D 84 (2011) 083519 [arXiv:1106.6025] [INSPIRE].ADSGoogle Scholar
  39. [39]
    T. Li, Z. Li and D.V. Nanopoulos, Supergravity inflation with broken shift symmetry and large tensor-to-scalar ratio, J CAP02 (2014) 028 [arXiv:1311.6770] [INSPIRE].ADSMathSciNetGoogle Scholar
  40. [40]
    W. Buchmuller, C. Wieck and M.W. Winkler, Supersymmetric moduli stabilization and high-scale inflation, Phys. Lett.B 736 (2014) 237 [arXiv:1404.2275] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  41. [41]
    J. Ellis, D.V. Nanopoulos and K.A. Olive, Starobinsky-like inflationary models as avatars of no-scale supergravity, JCAP10 (2013) 009 [arXiv:1307.3537] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    J. Ellis, D.V. Nanopoulos and K.A. Olive, From R2gravity to no-scale supergravity, Phys. Rev.D 97 (2018) 043530 [arXiv:1711.11051] [INSPIRE].ADSGoogle Scholar
  43. [43]
    J. Ellis, D.V. Nanopoulos, K.A. Olive and S. Verner, A general classification of Starobinsky-like inflationary avatars of SU (2, 1) /SU (2) X U (1) no-scale supergravity, JHEP03 (2019) 099 [arXiv:1812.02192] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  44. [44]
    J. Ellis, D.V. Nanopoulos, K.A. Olive and S. Verner, Unified no-scale model of modulus fixing, inflation, supersymmetry breaking and dark energy, Phys. Rev.D 100 (2019) 025009 [arXiv:1903.05267] [INSPIRE].ADSGoogle Scholar
  45. [45]
    J. Ellis, D.V. Nanopoulos, K.A. Olive and S. Verner, Unified no-scale attractors, JCAP09 (2019) 040 [arXiv: 1906.10176] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    M.C. Romao and S.F. King, Starobinsky-like inflation in no-scale supergravity Wess-Zumino model with Polonyi term, JHEP07 (2017) 033 [arXiv:1703.08333] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  47. [47]
    S.F. King and E. Perdomo, Starobinsky-like inflation and soft-SUSY breaking, JHEP 05 (2019) 211 [arXiv:1903.08448] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  48. [48]
    R. Kallosh and A. Linde, Superconformal generalizations of the Starobinsky model, JCAP06 (2013) 028 [arXiv: 1306.3214] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  49. [49]
    F. Farakos, A. Kehagias and A. Riotto, On the Starobinsky model of inflation from supergravity, Nucl. Phys.B 876 (2013) 187 [arXiv:1307.1137] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  50. [50]
    S. Ferrara, A. Kehagias and A. Riotto, The imaginary Starobinsky model, Fortsch. Phys.62 (2014) 573 [arXiv:1403.5531] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  51. [51]
    S. Ferrara, A. Kehagias and A. Riotto, The imaginary Starobinsky model and higher curvature corrections, Fortsch. Phys.63 (2015) 2 [arXiv:1405.2353] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  52. [52]
    R. Kallosh, A. Linde, B. Vercnocke and W. Chemissany, Is imaginary Starobinsky model real?, JCAP07 (2014) 053 [arXiv:1403.7189] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    K. Hamaguchi, T. Moroi and T. Terada, Complexified Starobinsky inflation in supergravity in the light of recent BICEP2 result, Phys. Lett.B 733 (2014) 305 [arXiv:1403.7521] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  54. [54]
    J. Ellis, M.A.G. Garcia, D.V. Nanopoulos and K.A. Olive, Resurrecting quadratic inflation in no-scale supergravity in light of BICEP2, JCAP 05 (2014) 037 [arXiv:1403.7518] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    J. Ellis, M.A.G. Garcia, D.V. Nanopoulos and K.A. Olive, A no-scale inflationary model to fit them all, JCAP08 (2014) 044 [arXiv:1405.0271] [INSPIRE].ADSGoogle Scholar
  56. [56]
    T. Li, Z. Li and D.V. Nanopoulos, No-scale ripple inflation revisited, JCAP04 (2014) 018 [arXiv:1310.3331] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    J. Ellis, D.V. Nanopoulos and K.A. Olive, A no-scale supergravity framework for sub-Planckian physics, Phys. Rev.D 89 (2014) 043502 [arXiv:1310.4770] [INSPIRE].ADSGoogle Scholar
  58. [58]
    C.P. Burgess, M. Cicoli and F. Quevedo, String inflation after Planck 2013, JCAP11 (2013) 003 [arXiv:1306.3512] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    S. Ferrara, R. Kallosh, A. Linde and M. Porrati, Minimal supergravity models of inflation, Phys. Rev.D 88 (2013) 085038 [arXiv:1307.7696] [INSPIRE].ADSGoogle Scholar
  60. [60]
    W. Buchmuller, V. Domcke and C. Wieck, No-scale D-term inflation with stabilized moduli, Phys. Lett.B 730 (2014) 155 [arXiv:1309.3122] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  61. [61]
    C. Pallis, Linking Starobinsky-type inflation in no-scale supergravity to MSSM, JCAP04 (2014) 024 [Erratum ibid.07 (2017) E01] [arXiv:1312.3623] [INSPIRE].
  62. [62]
    C. Pallis, Induced-gravity inflation in no-scale supergravity and beyond, JCAP08 (2014) 057 [arXiv:1403.5486] [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    I. Antoniadis, E. Dudas, S. Ferrara and A. Sagnotti, The Volkov-Akulov-Starobinsky supergravity, Phys. Lett.B 733 (2014) 32 [arXiv:1403.3269] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  64. [64]
    T. Li, Z. Li and D.V. Nanopoulos, Chaotic inflation in no-scale supergravity with string inspired moduli stabilization, Eur. Phys. J. C 75 (2015) 55 [arXiv:1405.0197] [INSPIRE].ADSCrossRefGoogle Scholar
  65. [65]
    W. Buchmuller, E. Dudas, L. Heurtier and C. Wieck, Large-field inflation and supersymmetry breaking, JHEP09 (2014) 053 [arXiv:1407.0253] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  66. [66]
    J. Ellis, M.A.G. Garcia, D.V. Nanopoulos and K.A. Olive, Two-field analysis of no-scale supergravity inflation, JCAP01 (2015) 010 [arXiv:1409.8197] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  67. [67]
    T. Terada, Y. Watanabe, Y. Yamada and J. Yokoyama, Reheating processes after Starobinsky inflation in old-minimal supergravity, JHEP02 (2015) 105 [arXiv:1411.6746] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  68. [68]
    W. Buchmuller, E. Dudas, L. Heurtier, A. Westphal, C. Wieck and M.W. Winkler, Challenges for large-field inflation and moduli stabilization, JHEP04 (2015) 058 [arXiv:1501.05812] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  69. [69]
    A.B. Lahanas and K. Tamvakis, Inflation in no-scale supergravity, Phys. Rev.D 91 (2015) 085001 [arXiv:1501.06547] [INSPIRE].ADSMathSciNetGoogle Scholar
  70. [70]
    D. Roest and M. Scalisi, Cosmological attractors from a-scale supergravity, Phys. Rev.D 92 (2015) 043525 [arXiv:1503.07909] [INSPIRE].ADSMathSciNetGoogle Scholar
  71. [71]
    J. Ellis, M.A.G. Garcia, D.V. Nanopoulos and K.A. Olive, Phenomenological aspects of no-scale inflation models, JCAP 10 (2015) 003 [arXiv:1503.08867] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  72. [72]
    J. Ellis, M.A.G. Garcia, D.V. Nanopoulos and K.A. Olive, Calculations of inflaton decays and reheating: with applications to no-scale inflation models, JCAP 07 (2015) 050 [arXiv:1505.06986] [INSPIRE].ADSCrossRefGoogle Scholar
  73. [73]
    I. Dalianis and F. Farakos, On the initial conditions for inflation with plateau potentials: the R + R 2(super)gravity case, JCAP 07 (2015) 044 [arXiv:1502.01246] [INSPIRE].ADSCrossRefGoogle Scholar
  74. [74]
    I. Garg and S. Mohanty, No scale SU GRA SO(lO) derived Starobinsky model of inflation, Phys. Lett.B 751 (2015) 7 [arXiv:1504.07725] [INSPIRE].ADSCrossRefGoogle Scholar
  75. [75]
    E. Dudas and C. Wieck, Moduli backreaction and supersymmetry breaking in string-inspired inflation models, JHEP10 (2015) 062 [arXiv:1506.01253] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  76. [76]
    M. Scalisi, Cosmological o:-attractors and de Sitter landscape, JHEP12 (2015) 134 [arXiv:1506.01368] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  77. [77]
    S. Ferrara, A. Kehagias and M. Porrati, R 2supergravity, JHEP08 (2015) 001 [arXiv:1506.01566] [INSPIRE].ADSCrossRefGoogle Scholar
  78. [78]
    J. Ellis, M.A.G. Garcia, D.V. Nanopoulos and K.A. Olive, No-scale inflation, Class. Quant. Grav.33 (2016) 094001 [arXiv:1507.02308] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  79. [79]
    A. Addazi and M. Yu. Khlopov, Dark matter and inflation in R + ζR2supergravity, Phys. Lett.B 766 (2017) 17 [arXiv:1612.06417] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  80. [80]
    C. Pallis and N. Toumbas, Starobinsky inflation: from non-SUSY to SUGRA realizations, Adv. High E nergy Phys. 2017 (2017) 6759267 [arXiv:1612.09202] [INSPIRE].zbMATHGoogle Scholar
  81. [81]
    T. Kobayashi, O. Seto and T.H. Tatsuishi, Toward pole inflation and attractors in supergravity: chiral matter field inflation, PTEP2017 (2017) 123B04 [arXiv:1703.09960] [INSPIRE].Google Scholar
  82. [82]
    E. Dudas, T. Gherghetta, Y. Mambrini and K.A. Olive, Inflation and high-scale supersymmetry with an EeV gravitino, Phys. Rev.D 96 (2017) 115032 [arXiv:1710.07341] [INSPIRE].ADSGoogle Scholar
  83. [83]
    I. Garg and S. Mohanty, No-scale SUGRA inflation and type-I seesaw, Int. J. Mod. Phys.A 33 (2018) 1850127 [arXiv:1711.01979] [INSPIRE].ADSCrossRefGoogle Scholar
  84. [84]
    W. Ahmed and A. Karozas, Inflation from a no-scale supersymmetric SU(4)c x SU(2)L x SU(2)Rmodel, Phys. Rev.D 98 (2018) 023538 [arXiv:1804.04822] [INSPIRE].ADSGoogle Scholar
  85. [85]
    Y. Cai, R. Deen, B.A. Ovrut and A. Purves, Perturbative reheating in Sneutrino-Higgs cosmology, JHEP09 (2018) 001 [arXiv:1804.07848] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  86. [86]
    S. Khalil, A. Moursy, A.K. Saha and A. Sil, U(1)R inspired inflation model in no-scale supergravity, Phys. Rev.D 99 (2019) 095022 [arXiv:1810.06408] [INSPIRE].ADSMathSciNetGoogle Scholar
  87. [87]
    J. Ellis, M.A.G. Garcia, N. Nagata, D.V. Nanopoulos and K.A. Olive, Starobinsky-lik e inflation and neutrino masses in a no-scale 80(10) model, JCAP11 (2016) 018 [arXiv:1609.05849] [INSPIRE].ADSCrossRefGoogle Scholar
  88. [88]
    J. Ellis, M.A.G. Garcia, N. Nagata, D.V. Nanopoulos and K.A. Olive, Starobinsky-lik e inflation, supercosmology and neutrino masses in no-scale flipped SU(5), JCAP 07 (2017) 006 [arXiv:1704.07331] [INSPIRE].ADSCrossRefGoogle Scholar
  89. [89]
    J. Ellis, M.A.G. Garcia, N. Nagata, D.V. Nanopoulos and K.A. Olive, Symmetry breaking and reheating after inflation in no-scale flipped SU(5), JCAP 04 (2019) 009 [arXiv:1812.08184] [INSPIRE].ADSCrossRefGoogle Scholar
  90. [90]
    J.R. Ellis, C. Kounnas and D.V. Nanopoulos, No scale supersymmetric GUTs, Nucl. Phys.B 247 (1984) 373 [INSPIRE].ADSCrossRefGoogle Scholar
  91. [91]
    R. Kallosh, A. Linde and D. Roest, Superconformal inflationary cx-attractors, JHEP11 (2013) 198 [arXiv:1311.0472] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  92. [92]
    A. Linde, Single-field cx-attractors, JCAP05 (2015) 003 [arXiv:1504.00663] [INSPIRE].ADSCrossRefGoogle Scholar
  93. [93]
    J.R. Ellis, C. Kounnas and D.V. Nanopoulos, No scale supergravity models with a Planck mass gravitino, Phys. Lett.B 143 (1984) 410 [INSPIRE].ADSCrossRefGoogle Scholar
  94. [94]
    J. Ellis, M.A.G. Garcia, N. Nagata, D.V. Nanopoulos and K.A. Olive, Cosmology with a master coupling in flipped SU(5) X U(1): the λ6 universe, Phys. Lett.B 797 (2019) 134864 [arXiv:1906.08483] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  95. [95]
    J. Ellis, M.A.G. García, N. Nagata, D.V. Nanopoulos and K.A. Olive, Phenomenological aspects of the λ6 universe in flipped SU(5) X U(1), in preparation.Google Scholar
  96. [96]
    G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, De Sitter space and the swampland, arXiv:1806.08362 [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • John Ellis
    • 1
    • 2
    • 3
  • Balakrishnan Nagaraj
    • 4
  • Dimitri V. Nanopoulos
    • 4
    • 5
    • 6
  • Keith A. Olive
    • 7
  • Sarunas Verner
    • 7
    Email author
  1. 1.Theoretical Particle Physics and Cosmology Group, Department of Physics, King’s College LondonLondonU.K.
  2. 2.Theoretical Physics Department, CERNGeneva 23Switzerland
  3. 3.National Institute of Chemical Physics & BiophysicsTallinnEstonia
  4. 4.George P. and Cynthia W. Mitchell Institute for Fundamental Phyffics and AstronomyTexas A &M UniversityCollege StationU.S.A.
  5. 5.Astroparticle Physics Group, Houston Advanced Research Center (HARC)WoodlandsU.S.A.
  6. 6.Academy of Athens, Division of Natural SciencesAthensGreece
  7. 7.William I. Fine Theoretical Physics Institute, School of Physics and Astronomy, University of MinnesotaMinneapolisU.S.A.

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