Skip to main content
Log in

Models of accelerating universe in supergravity and string theory

  • Review
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

We review models of the accelerating universe from the perspective of high-energy physics. Focusing on supergravity and the String Theory, we discuss the general framework for the construction of these models. We then go on to discuss explicit constructions.

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

Access this article

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

Notes

  1. The observed acceleration may also happen due to the modifications of gravity at cosmological distances.

  2. For earlier criticisms of dS in string theory, see, for example, [6,7,8].

  3. Note that in more realistic cases, this separation may not be possible, making the problem much worse.

  4. Note that in F-theory models the string coupling can be arbitrarily large, this tree-level analysis is not valid.

  5. See also [73] for \(N=1\) \(\mathcal {O}(\alpha '^2)\) corrections to K in heterotic strings which should get mapped to type IIB \(\mathcal {O}(g_s^2\alpha '^2)\) effects that have the extended no-scale cancellation.

  6. See also [82].

  7. Once challenge is to the field range to be suitably large [23, 24]. Various possible solutions have been proposed, see for e.g [9, 46, 137, 138] and the references there in.

References

  1. N. Aghanim et al. [Planck Collaboration], “Planck 2018 results. VI. Cosmological parameters,” arXiv:1807.06209 [astro-ph.CO]

  2. J. Martin, Everything you always wanted to know about the cosmological constant problem (but were afraid to ask). CR Phys. 13, 566–665 (2012). [arXiv:1205.3365 [astro-ph.CO]]

    ADS  Google Scholar 

  3. E. J. Copeland, M. Sami, S. Tsujikawa, Dynamics of dark energy. Int. J. Mod. Phys. D 15, 1753–1936 (2006) [arXiv:hep-th/0603057 [hep-th]]

  4. H. Ooguri, C. Vafa, On the geometry of the string landscape and the swampland. Nucl. Phys. B 766, 21 (2007). [hep-th/0605264]

    ADS  MathSciNet  MATH  Google Scholar 

  5. G. Obied, H. Ooguri, L. Spodyneiko, C. Vafa, De Sitter Space and the Swampland. arXiv:1806.08362 [hep-th]

  6. T. Banks, The top \(10^{500}\) reasons not to believe in the landscape. arXiv:1208.5715 [hep-th]

  7. S. Sethi, Supersymmetry breaking by fluxes. arXiv:1709.03554 [hep-th]

  8. I. Bena, M. Grana, N. Halmagyi, On the existence of meta-stable vacua in Klebanov-Strassler. JHEP 1009, 087 (2010). [arXiv:0912.3519 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  9. E. Palti, Fortsch. Phys. 67 (2019) no.6, 1900037 https://doi.org/10.1002/prop.201900037[arXiv:1903.06239 [hep-th]]

  10. C. Wetterich, Cosmology and the Fate of dilatation symmetry. Nucl. Phys. B 302, 668–696 (1988). [arXiv:1711.03844 [hep-th]]

    ADS  Google Scholar 

  11. B. Ratra, P.J.E. Peebles, Cosmological consequences of a rolling homogeneous scalar field. Phys. Rev. D 37, 3406 (1988)

    ADS  Google Scholar 

  12. R. R. Caldwell, R. Dave, P. J. Steinhardt, Cosmological imprint of an energy component with general equation of state. Phys. Rev. Lett. 80, 1582–1585 (1998) [arXiv:astro-ph/9708069 [astro-ph]]

  13. I. Zlatev, L. M. Wang, P. J. Steinhardt, Quintessence, cosmic coincidence, and the cosmological constant. Phys. Rev. Lett. 82, 896–899 (1999) [arXiv:astro-ph/9807002 [astro-ph]]

  14. R. R. Caldwell, E. V. Linder, The Limits of quintessence. Phys. Rev. Lett. 95, 141301 (2005) [arXiv:astro-ph/0505494 [astro-ph]]

  15. S. M. Carroll, Quintessence and the rest of the world. Phys. Rev. Lett. 81, 3067–3070 (1998) [arXiv:astro-ph/9806099 [astro-ph]]

  16. E. G. Adelberger, B. R. Heckel, A. E. Nelson, Tests of the gravitational inverse square law. Ann. Rev. Nucl. Part. Sci. 53, 77–121 (2003) [arXiv:hep-ph/0307284 [hep-ph]]

  17. C. J. A. P. Martins, The status of varying constants: a review of the physics, searches and implications. [arXiv:1709.02923 [astro-ph.CO]]

  18. J. Khoury, A. Weltman, Chameleon fields: awaiting surprises for tests of gravity in space. Phys. Rev. Lett. 93, 171104 (2004) [arXiv:astro-ph/0309300 [astro-ph]]

  19. K. Hinterbichler, J. Khoury, Symmetron fields: screening long-range forces through local symmetry restoration. Phys. Rev. Lett. 104, 231301 (2010). [arXiv:1001.4525 [hep-th]]

    ADS  Google Scholar 

  20. J. A. Frieman, C. T. Hill, A. Stebbins, I. Waga, Cosmology with ultralight pseudo Nambu-Goldstone bosons. Phys. Rev. Lett. 75, 2077–2080 (1995) [arXiv:astro-ph/9505060 [astro-ph]]

  21. K. Dutta, L. Sorbo, Confronting pNGB quintessence with data. Phys. Rev. D 75, 063514 (2007) [arXiv:astro-ph/0612457 [astro-ph]]

  22. D. Adak, K. Dutta, Viable dark energy models using pseudo-Nambu-Goldstone bosons. Phys. Rev. D 90(4), 043502 (2014) [arXiv:1404.1570 [astro-ph.CO]]

  23. T. Banks, M. Dine, P. J. Fox, E. Gorbatov, On the possibility of large axion decay constants. JCAP 06, 001 (2003) [arXiv:hep-th/0303252 [hep-th]]

  24. N. Arkani-Hamed, L. Motl, A. Nicolis, C. Vafa, JHEP 06 (2007), 060 https://doi.org/10.1088/1126-6708/2007/06/060[arXiv:hep-th/0601001 [hep-th]]

  25. P. Binetruy, Models of dynamical supersymmetry breaking and quintessence. Phys. Rev. D 60, 063502 (1999) [arXiv:hep-ph/9810553 [hep-ph]]

  26. A. Masiero, M. Pietroni, F. Rosati, SUSY QCD and quintessence. Phys. Rev. D 61, 023504 (2000) [arXiv:hep-ph/9905346 [hep-ph]]

  27. P. Brax, J. Martin, Quintessence and supergravity. Phys. Lett. B 468, 40–45 (1999) [arXiv:astro-ph/9905040 [astro-ph]]

  28. P. Brax, J. Martin, The Robustness of quintessence. Phys. Rev. D 61, 103502 (2000) [arXiv:astro-ph/9912046 [astro-ph]]

  29. E.J. Copeland, N.J. Nunes, F. Rosati, Phys. Rev. D 62, 123503 (2000). [arXiv:hep-ph/0005222 [hep-ph]]

    ADS  Google Scholar 

  30. C. F. Kolda, D. H. Lyth, Quintessential difficulties. Phys. Lett. B 458, 197–201 (1999) [arXiv:hep-ph/9811375 [hep-ph]]

  31. J. E. Kim, H. P. Nilles, Phys. Lett. B 553, 1–6 (2003) [arXiv:hep-ph/0210402 [hep-ph]]

  32. Y. Nomura, T. Watari, T. Yanagida, Phys. Lett. B 484, 103–111 (2000) [arXiv:hep-ph/0004182 [hep-ph]]

  33. L.J. Hall, Y. Nomura, S.J. Oliver, Phys. Rev. Lett. 95, 141302 (2005). [arXiv:astro-ph/0503706 [astro-ph]]

    ADS  Google Scholar 

  34. Z. Chacko, L.J. Hall, Y. Nomura, JCAP 10, 011 (2004). [arXiv:astro-ph/0405596 [astro-ph]]

    ADS  Google Scholar 

  35. R. Barbieri, L.J. Hall, S.J. Oliver, A. Strumia, Phys. Lett. B 625, 189–195 (2005). [arXiv:hep-ph/0505124 [hep-ph]]

    ADS  Google Scholar 

  36. P.Q. Hung, Nucl. Phys. B 747, 55–87 (2006). [arXiv:hep-ph/0512282 [hep-ph]]

    ADS  Google Scholar 

  37. K. Choi, Phys. Rev. D 62, 043509 (2000). [arXiv:hep-ph/9902292 [hep-ph]]

    ADS  Google Scholar 

  38. C. I. Chiang, H. Murayama, [arXiv:1808.02279 [hep-th]]

  39. R. Kallosh, A.D. Linde, S. Prokushkin, M. Shmakova, Phys. Rev. D 66, 123503 (2002). [arXiv:hep-th/0208156 [hep-th]]

    ADS  MathSciNet  Google Scholar 

  40. P. Fre, M. Trigiante, A. Van Proeyen, Class. Quant. Grav. 19, 4167–4194 (2002). [arXiv:hep-th/0205119 [hep-th]]

    ADS  Google Scholar 

  41. P. Brax, J. Martin, Phys. Rev. D 75, 083507 (2007). [arXiv:hep-th/0605228 [hep-th]]

    ADS  Google Scholar 

  42. P. Brax, J. Martin, JCAP 11, 008 (2006). [arXiv:astro-ph/0606306 [astro-ph]]

    ADS  Google Scholar 

  43. P. Brax, C. van de Bruck, J. Martin, A.C. Davis, JCAP 09, 032 (2009). [arXiv:0904.3471 [hep-th]]

    ADS  Google Scholar 

  44. M. Dine, N. Seiberg, Is the superstring weakly coupled? Phys. Lett. 162B, 299 (1985)

    ADS  MathSciNet  Google Scholar 

  45. S. Kachru, S.P. Trivedi, Fortsch. Phys. 67(1–2), 1800086 (2019). https://doi.org/10.1002/prop.201800086 [arXiv:1808.08971 [hep-th]]

    Article  ADS  Google Scholar 

  46. M. Cicoli, S. De. Alwis, A. Maharana, F. Muia, F. Quevedo, Fortsch. Phys. 67(1–2), 1800079 (2019). https://doi.org/10.1002/prop.201800079 [arXiv:1808.08967 [hep-th]]

    Article  ADS  Google Scholar 

  47. S. Gukov, C. Vafa, E. Witten, CFT’s from Calabi-Yau fourfolds. Nucl. Phys. B 584 (2000) 69 Erratum: [Nucl. Phys. B 608 (2001) 477] [hep-th/9906070]

  48. K. Dasgupta, G. Rajesh, S. Sethi, M theory, orientifolds and G-flux. JHEP 9908, 023 (1999). [hep-th/9908088]

    ADS  MathSciNet  MATH  Google Scholar 

  49. S.B. Giddings, S. Kachru, J. Polchinski, Hierarchies from fluxes in string compactifications. Phys. Rev. D 66, 106006 (2002). [hep-th/0105097]

    ADS  MathSciNet  Google Scholar 

  50. R. Blumenhagen, M. Cvetic, S. Kachru, T. Weigand, D-Brane instantons in type II orientifolds. Ann. Rev. Nucl. Part. Sci. 59, 269 (2009). [arXiv:0902.3251 [hep-th]]

    ADS  Google Scholar 

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

    ADS  MathSciNet  MATH  Google Scholar 

  52. V. Balasubramanian, P. Berglund, J.P. Conlon, F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications. JHEP 0503, 007 (2005). [hep-th/0502058]

    ADS  MathSciNet  Google Scholar 

  53. J.P. Conlon, F. Quevedo, K. Suruliz, Large-volume flux compactifications: moduli spectrum and D3/D7 soft supersymmetry breaking. JHEP 0508, 007 (2005). [hep-th/0505076]

    ADS  MathSciNet  Google Scholar 

  54. M. Cicoli, J.P. Conlon, F. Quevedo, General analysis of LARGE volume scenarios with string loop moduli stabilisation. JHEP 0810, 105 (2008). [arXiv:0805.1029 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  55. M. Demirtas, M. Kim, L. Mcallister, J. Moritz, Phys. Rev. Lett. 124(21), 211603 (2020). https://doi.org/10.1103/PhysRevLett.124.211603 [arXiv:1912.10047 [hep-th]]

    Article  ADS  MathSciNet  Google Scholar 

  56. J. Louis, M. Rummel, R. Valandro, A. Westphal, Building an explicit de Sitter. JHEP 1210, 163 (2012). [arXiv:1208.3208 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  57. M. Cicoli, D. Klevers, S. Krippendorf, C. Mayrhofer, F. Quevedo, R. Valandro, Explicit de Sitter flux vacua for global string models with chiral matter. JHEP 1405, 001 (2014). [arXiv:1312.0014 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  58. S.P. de Alwis, On potentials from fluxes. Phys. Rev. D 68, 126001 (2003). [hep-th/0307084]

    ADS  MathSciNet  Google Scholar 

  59. S.B. Giddings, A. Maharana, Dynamics of warped compactifications and the shape of the warped landscape. Phys. Rev. D 73, 126003 (2006). [hep-th/0507158]

    ADS  MathSciNet  Google Scholar 

  60. A.R. Frey, A. Maharana, JHEP 08, 021 (2006). https://doi.org/10.1088/1126-6708/2006/08/021 [arXiv:hep-th/0603233 [hep-th]]

    Article  ADS  Google Scholar 

  61. C.P. Burgess, P.G. Camara, S.P. de Alwis, S.B. Giddings, A. Maharana, F. Quevedo, K. Suruliz, JHEP 04, 053 (2008). https://doi.org/10.1088/1126-6708/2008/04/053 [arXiv:hep-th/0610255 [hep-th]]

    Article  ADS  Google Scholar 

  62. G. Shiu, G. Torroba, B. Underwood, M.R. Douglas, Dynamics of warped flux compactifications. JHEP 0806, 024 (2008). [arXiv:0803.3068 [hep-th]]

    ADS  MathSciNet  Google Scholar 

  63. A.R. Frey, G. Torroba, B. Underwood, M.R. Douglas, The universal Kahler modulus in warped compactifications. JHEP 0901, 036 (2009). [arXiv:0810.5768 [hep-th]]

    ADS  MATH  Google Scholar 

  64. L. Martucci, On moduli and effective theory of \(N=1\) warped flux compactifications. JHEP 0905, 027 (2009). [arXiv:0902.4031 [hep-th]]

    ADS  MathSciNet  Google Scholar 

  65. L. Martucci, Warping the Kahler potential of F-theory/IIB flux compactifications. JHEP 1503, 067 (2015). [arXiv:1411.2623 [hep-th]]

    ADS  MATH  Google Scholar 

  66. I. Broeckel, M. Cicoli, A. Maharana, K. Singh, K. Sinha, JHEP 10, 015 (2020). https://doi.org/10.1007/JHEP10(2020)015 [arXiv:2007.04327 [hep-th]]

    Article  ADS  Google Scholar 

  67. K. Becker, M. Becker, M. Haack, J. Louis, Supersymmetry breaking and alpha-prime corrections to flux induced potentials. JHEP 0206, 060 (2002). [hep-th/0204254]

    ADS  Google Scholar 

  68. M. Berg, M. Haack, B. Kors, String loop corrections to Kahler potentials in orientifolds. JHEP 0511, 030 (2005). [hep-th/0508043]

    ADS  Google Scholar 

  69. M. Berg, M. Haack, E. Pajer, Jumping through loops: on soft terms from large volume compactifications. JHEP 0709, 031 (2007). [arXiv:0704.0737 [hep-th]]

    ADS  MathSciNet  Google Scholar 

  70. M. Cicoli, J.P. Conlon, F. Quevedo, Systematics of string loop corrections in type IIB Calabi-Yau flux compactifications. JHEP 0801, 052 (2008). [arXiv:0708.1873 [hep-th]]

    ADS  MathSciNet  Google Scholar 

  71. T.W. Grimm, R. Savelli, M. Weissenbacher, On \(\alpha ^{\prime }\) corrections in \(N=1\) F-theory compactifications. Phys. Lett. B 725, 431 (2013). [arXiv:1303.3317 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  72. R. Minasian, T.G. Pugh, R. Savelli, F-theory at order \(\alpha ^{\prime 3}\). JHEP 1510, 050 (2015). [arXiv:1506.06756 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  73. L. Anguelova, C. Quigley, S. Sethi, The leading quantum corrections to stringy Kahler potentials. JHEP 1010, 065 (2010). [arXiv:1007.4793 [hep-th]]

    ADS  MATH  Google Scholar 

  74. F. Bonetti, M. Weissenbacher, The Euler characteristic correction to the Kahler potential—revisited. JHEP 1701, 003 (2017). [arXiv:1608.01300 [hep-th]]

    ADS  MATH  Google Scholar 

  75. D. Ciupke, J. Louis, A. Westphal, Higher-derivative supergravity and Moduli stabilization. JHEP 1510, 094 (2015). [arXiv:1505.03092 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  76. T.W. Grimm, K. Mayer, M. Weissenbacher, Higher derivatives in type II and M-theory on Calabi-Yau threefolds. JHEP 1802, 127 (2018). [arXiv:1702.08404 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  77. B.J. Broy, D. Ciupke, F.G. Pedro, A. Westphal, Starobinsky-type inflation from \(\alpha ^{\prime }\)-corrections. JCAP 1601, 001 (2016). [arXiv:1509.00024 [hep-th]]

    ADS  Google Scholar 

  78. M. Cicoli, D. Ciupke, S. de Alwis, F. Muia, \(\alpha ^{\prime }\) Inflation: moduli stabilisation and observable tensors from higher derivatives. JHEP 1609, 026 (2016). [arXiv:1607.01395 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  79. M. Berg, M. Haack, J.U. Kang, S. Sjors, Towards the one-loop Kahler metric of Calabi-Yau orientifolds. JHEP 1412, 077 (2014). [arXiv:1407.0027 [hep-th]]

    ADS  MATH  Google Scholar 

  80. M. Haack, J.U. Kang, One-loop Einstein-Hilbert term in minimally supersymmetric type IIB orientifolds. JHEP 1602, 160 (2016). [arXiv:1511.03957 [hep-th]]

    ADS  MATH  Google Scholar 

  81. M. Haack, J.U. Kang, Field redefinitions and Kahler potential in string theory at 1-loop. JHEP 1808, 019 (2018). [arXiv:1805.00817 [hep-th]]

    ADS  MATH  Google Scholar 

  82. I. Antoniadis, Y. Chen, G. K. Leontaris, Perturbative moduli stabilisation in type IIB/F-theory framework. arXiv:1803.08941 [hep-th]

  83. C.P. Burgess, A. Maharana, F. Quevedo, Uber-naturalness: unexpectedly light scalars from supersymmetric extra dimensions. JHEP 1105, 010 (2011). [arXiv:1005.1199 [hep-th]]

    ADS  MATH  Google Scholar 

  84. J.P. Conlon, Moduli stabilisation and applications in IIB string theory. Fortsch. Phys. 55, 287 (2007). [hep-th/0611039]

    ADS  MathSciNet  MATH  Google Scholar 

  85. C.P. Burgess, C. Escoda, F. Quevedo, Nonrenormalization of flux superpotentials in string theory. JHEP 0606, 044 (2006). [hep-th/0510213]

    ADS  MathSciNet  Google Scholar 

  86. E. Witten, New issues in manifolds of SU(3) holonomy. Nucl. Phys. B 268, 79 (1986)

    ADS  MathSciNet  Google Scholar 

  87. C.P. Burgess, A. Font, F. Quevedo, Low-energy effective action for the superstring. Nucl. Phys. B 272, 661 (1986)

    ADS  MathSciNet  Google Scholar 

  88. M. Dine, N. Seiberg, Nonrenormalization theorems in superstring theory. Phys. Rev. Lett. 57, 2625 (1986)

    ADS  MathSciNet  Google Scholar 

  89. M. Cicoli, J.P. Conlon, A. Maharana, F. Quevedo, A note on the magnitude of the flux superpotential. JHEP 1401, 027 (2014). [arXiv:1310.6694 [hep-th]]

    ADS  Google Scholar 

  90. M. Cicoli, F. Quevedo, R. Valandro, De Sitter from T-branes. JHEP 1603, 141 (2016). [arXiv:1512.04558 [hep-th]]

    ADS  Google Scholar 

  91. A. Westphal, De Sitter string vacua from Kahler uplifting. JHEP 0703, 102 (2007). [hep-th/0611332]

    ADS  MathSciNet  MATH  Google Scholar 

  92. M. Cicoli, A. Maharana, F. Quevedo, C.P. Burgess, De Sitter string vacua from Dilaton-dependent non-perturbative effects. JHEP 1206, 011 (2012). [arXiv:1203.1750 [hep-th]]

    ADS  MATH  Google Scholar 

  93. D. Gallego, M.C.D. Marsh, B. Vercnocke, T. Wrase, A new class of de Sitter Vacua in type IIB large volume compactifications. JHEP 1710, 193 (2017). [arXiv:1707.01095 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  94. J. Biablack, D. Roest, I. Zavala, De Sitter Vacua from nonperturbative flux compactifications. Phys. Rev. D 90(2), 024065 (2014). [arXiv:1312.5328 [hep-th]]

    ADS  Google Scholar 

  95. M. Cicoli, S. de Alwis, A. Westphal, Heterotic Moduli stabilisation. JHEP 1310, 199 (2013). [arXiv:1304.1809 [hep-th]]

    ADS  Google Scholar 

  96. S.L. Parameswaran, S. Ramos-Sanchez, I. Zavala, On Moduli stabilisation and de Sitter Vacua in MSSM heterotic orbifolds. JHEP 1101, 071 (2011). [arXiv:1009.3931 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  97. J.P. Conlon, A. Maharana, F. Quevedo, JHEP 05, 109 (2009). https://doi.org/10.1088/1126-6708/2009/05/109 [arXiv:0810.5660 [hep-th]]

    Article  ADS  Google Scholar 

  98. S. Krippendorf, M.J. Dolan, A. Maharana, F. Quevedo, JHEP 06, 092 (2010). https://doi.org/10.1007/JHEP06(2010)092 [arXiv:1002.1790 [hep-th]]

    Article  ADS  Google Scholar 

  99. M. Cicoli, C. Mayrhofer, R. Valandro, Moduli stabilisation for Chiral Global Models. JHEP 1202, 062 (2012). [arXiv:1110.3333 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  100. M. Cicoli, S. Krippendorf, C. Mayrhofer, F. Quevedo, R. Valandro, D-Branes at del Pezzo singularities: global embedding and Moduli stabilisation. JHEP 1209, 019 (2012). [arXiv:1206.5237 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  101. M. Cicoli, S. Krippendorf, C. Mayrhofer, F. Quevedo, R. Valandro, D3/D7 branes at singularities: constraints from global embedding and Moduli stabilisation. JHEP 1307, 150 (2013). [arXiv:1304.0022 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  102. M. Cicoli, F. Muia, P. Shukla, Global embedding of fibre inflation models. JHEP 1611, 182 (2016). [arXiv:1611.04612 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  103. M. Cicoli, I. Garcia-Etxebarria, C. Mayrhofer, F. Quevedo, P. Shukla, R. Valandro, Global orientifolded quivers with inflation. JHEP 1711, 134 (2017). [arXiv:1706.06128 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  104. M. Cicoli, D. Ciupke, V.A. Diaz, V. Guidetti, F. Muia, P. Shukla, Chiral global embedding of fibre inflation models. JHEP 1711, 207 (2017). [arXiv:1709.01518 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  105. L. Aparicio, M. Cicoli, S. Krippendorf, A. Maharana, F. Muia, F. Quevedo, JHEP 11, 071 (2014). https://doi.org/10.1007/JHEP11(2014)071 [arXiv:1409.1931 [hep-th]]

    Article  ADS  Google Scholar 

  106. L. Aparicio, M. Cicoli, B. Dutta, S. Krippendorf, A. Maharana, F. Muia, F. Quevedo, JHEP 05, 098 (2015). https://doi.org/10.1007/JHEP05(2015)098 [arXiv:1502.05672 [hep-ph]]

    Article  ADS  Google Scholar 

  107. A. Maloney, E. Silverstein, A. Strominger, De Sitter space in noncritical string theory. hep-th/0205316

  108. E. Silverstein, Simple de Sitter solutions. Phys. Rev. D 77, 106006 (2008). [arXiv:0712.1196 [hep-th]]

    ADS  MathSciNet  Google Scholar 

  109. S. de Alwis, K. Givens, Physical Vacua in IIB compactifications with a single Kahler modulus. JHEP 1110, 109 (2011). [arXiv:1106.0759 [hep-th]]

    ADS  MATH  Google Scholar 

  110. M. Rummel, A. Westphal, A sufficient condition for de Sitter vacua in type IIB string theory. JHEP 1201, 020 (2012). [arXiv:1107.2115 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  111. B.S. Acharya, K. Bobkov, G. Kane, P. Kumar, D. Vaman, An M theory solution to the hierarchy problem. Phys. Rev. Lett. 97, 191601 (2006). [hep-th/0606262]

    ADS  MathSciNet  MATH  Google Scholar 

  112. B.S. Acharya, K. Bobkov, G.L. Kane, P. Kumar, J. Shao, Explaining the electroweak scale and stabilizing Moduli in M theory. Phys. Rev. D 76, 126010 (2007). [hep-th/0701034]

    ADS  MathSciNet  Google Scholar 

  113. C. Caviezel, P. Koerber, S. Kors, D. Lust, T. Wrase, M. Zagermann, On the cosmology of type IIA compactifications on SU(3)-structure manifolds. JHEP 0904, 010 (2009). [arXiv:0812.3551 [hep-th]]

    ADS  MathSciNet  Google Scholar 

  114. R. Flauger, S. Paban, D. Robbins, T. Wrase, Searching for slow-roll moduli inflation in massive type IIA supergravity with metric fluxes. Phys. Rev. D 79, 086011 (2009). [arXiv:0812.3886 [hep-th]]

    ADS  Google Scholar 

  115. U.H. Danielsson, S.S. Haque, G. Shiu, T. Van Riet, Towards classical de Sitter solutions in string theory. JHEP 0909, 114 (2009). [arXiv:0907.2041 [hep-th]]

    ADS  MathSciNet  Google Scholar 

  116. C. Caviezel, T. Wrase, M. Zagermann, Moduli stabilization and cosmology of type IIB on SU(2)-structure orientifolds. JHEP 1004, 011 (2010). [arXiv:0912.3287 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  117. U.H. Danielsson, P. Koerber, T. Van Riet, Universal de Sitter solutions at tree-level. JHEP 1005, 090 (2010). [arXiv:1003.3590 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  118. U.H. Danielsson, S.S. Haque, P. Koerber, G. Shiu, T. Van Riet, T. Wrase, De Sitter hunting in a classical landscape. Fortsch. Phys. 59, 897 (2011). [arXiv:1103.4858 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  119. D. Andriot, New constraints on classical de Sitter: flirting with the swampland. arXiv:1807.09698 [hep-th]

  120. B.S. Acharya, F. Benini, R. Valandro, Fixing moduli in exact type IIA flux vacua. JHEP 0702, 018 (2007). [hep-th/0607223]

    ADS  MathSciNet  MATH  Google Scholar 

  121. J. McOrist, S. Sethi, M-theory and type IIA flux compactifications. JHEP 1212, 122 (2012). [arXiv:1208.0261 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  122. B. de Carlos, A. Guarino, J.M. Moreno, Flux moduli stabilisation, supergravity algebras and no-go theorems. JHEP 1001, 012 (2010). [arXiv:0907.5580 [hep-th]]

    MathSciNet  MATH  Google Scholar 

  123. U. Danielsson, G. Dibitetto, On the distribution of stable de Sitter vacua. JHEP 1303, 018 (2013). [arXiv:1212.4984 [hep-th]]

    ADS  Google Scholar 

  124. J. Blabäck, U. Danielsson, G. Dibitetto, Fully stable dS vacua from generalised fluxes. JHEP 1308, 054 (2013). [arXiv:1301.7073 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  125. C. Damian, L.R. Diaz-Barron, O. Loaiza-Brito, M. Sabido, Slow-roll inflation in non-geometric flux compactification. JHEP 1306, 109 (2013). [arXiv:1302.0529 [hep-th]]

    ADS  MathSciNet  MATH  Google Scholar 

  126. C. Damian, O. Loaiza-Brito, More stable de Sitter vacua from S-dual nongeometric fluxes. Phys. Rev. D 88(4), 046008 (2013). [arXiv:1304.0792 [hep-th]]

    ADS  Google Scholar 

  127. B.S. Acharya, A. Maharana, F. Muia, JHEP 03, 048 (2019). https://doi.org/10.1007/JHEP03(2019)048 [arXiv:1811.10633 [hep-th]]

    Article  ADS  Google Scholar 

  128. K. Choi, String or M-theory axion as a quintessence. Phys. Rev. D 62, 043509 (2000). ([hep-ph/9902292])

    ADS  Google Scholar 

  129. N. Kaloper, L. Sorbo, Where in the String landscape is quintessence. Phys. Rev. D 79, 043528 (2009). [arXiv:0810.5346 [hep-th]]

    ADS  Google Scholar 

  130. S. Panda, Y. Sumitomo, S.P. Trivedi, Axions as quintessence in string theory. Phys. Rev. D 83, 083506 (2011). [arXiv:1011.5877 [hep-th]]

    ADS  Google Scholar 

  131. M. Cicoli, F.G. Pedro, G. Tasinato, Natural quintessence in string theory. JCAP 1207, 044 (2012). [arXiv:1203.6655 [hep-th]]

    ADS  Google Scholar 

  132. J. Blabäck, U. Danielsson, G. Dibitetto, JCAP 03, 003 (2014). https://doi.org/10.1088/1475-7516/2014/03/003 [arXiv:1310.8300 [hep-th]]

    Article  ADS  Google Scholar 

  133. G. D’Amico, N. Kaloper, A. Lawrence, Phys. Rev. D 100(10), 103504 (2019). https://doi.org/10.1103/PhysRevD.100.103504 [arXiv:1809.05109 [hep-th]]

  134. Y. Olguin-Trejo, S. L. Parameswaran, G. Tasinato, I. Zavala, Runaway quintessence, out of the Swampland. arXiv:1810.08634 [hep-th]

  135. M. Cicoli, G. Dibitetto, F.G. Pedro, JHEP 10, 035 (2020). https://doi.org/10.1007/JHEP10(2020)035 [arXiv:2007.11011 [hep-th]]

    Article  ADS  Google Scholar 

  136. A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper, J. March-Russell, Phys. Rev. D 81, 123530 (2010). https://doi.org/10.1103/PhysRevD.81.123530 [arXiv:0905.4720 [hep-th]]

    Article  ADS  Google Scholar 

  137. S. Dimopoulos, S. Kachru, J. McGreevy, J.G. Wacker, JCAP 08, 003 (2008). https://doi.org/10.1088/1475-7516/2008/08/003 [arXiv:hep-th/0507205 [hep-th]]

    Article  ADS  Google Scholar 

  138. L. McAllister, E. Silverstein, A. Westphal, Phys. Rev. D 82, 046003 (2010). https://doi.org/10.1103/PhysRevD.82.046003 [arXiv:0808.0706 [hep-th]]

    Article  ADS  Google Scholar 

  139. Ruchika, K. Dutta, A. Mukherjee, A. A. Sen, Observational constraints on axion(s) with a cosmological constant. [arXiv:2005.08813 [astro-ph.CO]]

Download references

Acknowledgements

KD is partially supported in part by the Grant MTR/2019/000395 and Indo-Russian project Grant DST/INT/RUS/RSF/P-21, both funded by the DST, Govt of India. AM is supported in part by the SERB, DST, Government of India, by the Grant MTR/2019/000267.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Koushik Dutta.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dutta, K., Maharana, A. Models of accelerating universe in supergravity and string theory. Eur. Phys. J. Spec. Top. 230, 2111–2122 (2021). https://doi.org/10.1140/epjs/s11734-021-00195-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjs/s11734-021-00195-w

Navigation