Journal of High Energy Physics

, 2019:75 | Cite as

Bounds on slow roll and the de Sitter Swampland

  • Sumit K. GargEmail author
  • Chethan Krishnan
Open Access
Regular Article - Theoretical Physics


The recently introduced swampland criterion for de Sitter [17] can be viewed as a (hierarchically large) bound on the smallness of the slow roll parameter 𝜖V. This leads us to consider the other slow roll parameter ηV more closely, and we are lead to conjecture that the bound is not necessarily on 𝜖V, but on slow roll itself. A natural refinement of the de Sitter swampland conjecture is therefore that slow roll is violated at \( \mathcal{O} \)(1) in Planck units in any UV complete theory. A corollary is that 𝜖V need not necesarily be \( \mathcal{O} \)(1), if \( {\eta}_V\lesssim -\mathcal{O}(1) \) holds. We consider various tachyonic tree level constructions of de Sitter in IIA/IIB string theory (as well as closely related models of inflation), which superficially violate [17], and show that they are consistent with this refined version of the bound. The phrasing in terms of slow roll makes it plausible why both versions of the conjecture run into trouble when the number of e-folds during inflation is high. We speculate that one way to evade the bound could be to have a large number of fields, like in N -flation.


Cosmology of Theories beyond the SM Superstring Vacua Flux compactifications 


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


  1. [1]
    J.M. Maldacena and C. NĂșñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys.A 16 (2001) 822 [hep-th/0007018] [INSPIRE].
  2. [2]
    U.H. Danielsson and T. Van Riet, What if string theory has no de Sitter vacua?, Int. J. Mod. Phys.D 27 (2018) 1830007 [arXiv:1804.01120] [INSPIRE].
  3. [3]
    T.D. Brennan, F. Carta and C. Vafa, The String Landscape, the Swampland and the Missing Corner, PoS(TASI2017)015 (2017) [arXiv:1711.00864] [INSPIRE].
  4. [4]
    S. Sethi, Supersymmetry Breaking by Fluxes, JHEP10 (2018) 022 [arXiv:1709.03554] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev.D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].
  6. [6]
    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].
  7. [7]
    J. Polchinski, Brane/antibrane dynamics and KKLT stability, arXiv:1509.05710 [INSPIRE].
  8. [8]
    V. Balasubramanian, P. Berglund, J.P. Conlon and F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP03 (2005) 007 [hep-th/0502058] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    A. Westphal, de Sitter string vacua from KĂ€hler uplifting, JHEP03 (2007) 102 [hep-th/0611332] [INSPIRE].
  10. [10]
    D. Cohen-Maldonado, J. Diaz, T. van Riet and B. Vercnocke, Observations on fluxes near anti-branes, JHEP01 (2016) 126 [arXiv:1507.01022] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    I. Bena, J. BlÄbÀck and D. Turton, Loop corrections to the antibrane potential, JHEP07 (2016) 132 [arXiv:1602.05959] [INSPIRE].
  12. [12]
    U.H. Danielsson, F.F. Gautason and T. Van Riet, Unstoppable brane-flux decay of \( \overline{\mathrm{D}6} \)branes, JHEP03 (2017) 141 [arXiv:1609.06529] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    M. Bertolini, D. Musso, I. Papadimitriou and H. Raj, A goldstino at the bottom of the cascade, JHEP11 (2015) 184 [arXiv:1509.03594] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    C. Krishnan, H. Raj and P.N. Bala Subramanian, On the KKLT Goldstino, JHEP06 (2018) 092 [arXiv:1803.04905] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    I. Bena, M. Graña and N. Halmagyi, On the Existence of Meta-stable Vacua in Klebanov-Strassler, JHEP09 (2010) 087 [arXiv:0912.3519] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  16. [16]
    E.A. Bergshoeff, K. Dasgupta, R. Kallosh, A. Van Proeyen and T. Wrase, \( \overline{\mathrm{D}3} \)and dS, JHEP05 (2015) 058 [arXiv:1502.07627] [INSPIRE].00000
  17. [17]
    G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, de Sitter Space and the Swampland, arXiv:1806.08362 [INSPIRE].
  18. [18]
    K.A. Intriligator, N. Seiberg and D. Shih, Dynamical SUSY breaking in meta-stable vacua, JHEP04 (2006) 021 [hep-th/0602239] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    W. Fischler, V. Kaplunovsky, C. Krishnan, L. Mannelli and M.A.C. Torres, Meta-Stable Supersymmetry Breaking in a Cooling Universe, JHEP03 (2007) 107 [hep-th/0611018] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    S.K. Garg, C. Krishnan and M. Zaid Zaz, Bounds on Slow Roll at the Boundary of the Landscape, JHEP03 (2019) 029 [arXiv:1810.09406] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    A.R. Liddle and D.H. Lyth, Cosmological Inflation and Large-Scale Structure, Cambridge (2000) [INSPIRE].
  22. [22]
    M.P. Hertzberg, S. Kachru, W. Taylor and M. Tegmark, Inflationary Constraints on Type IIA String Theory, JHEP12 (2007) 095 [arXiv:0711.2512] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    T. Wrase and M. Zagermann, On Classical de Sitter Vacua in String Theory, Fortsch. Phys.58 (2010) 906 [arXiv:1003.0029] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    P. Agrawal, G. Obied, P.J. Steinhardt and C. Vafa, On the Cosmological Implications of the String Swampland, Phys. Lett.B 784 (2018) 271 [arXiv:1806.09718] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    D. Andriot, On the de Sitter swampland criterion, Phys. Lett.B 785 (2018) 570 [arXiv:1806.10999] [INSPIRE].
  26. [26]
    S. Banerjee, U. Danielsson, G. Dibitetto, S. Giri and M. Schillo, Emergent de Sitter Cosmology from Decaying Anti-de Sitter Space, Phys. Rev. Lett.121 (2018) 261301 [arXiv:1807.01570] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    L. Aalsma, M. Tournoy, J.P. Van Der Schaar and B. Vercnocke, Supersymmetric embedding of antibrane polarization, Phys. Rev.D 98 (2018) 086019 [arXiv:1807.03303] [INSPIRE].
  28. [28]
    A. AchĂșcarro and G.A. Palma, The string swampland constraints require multi-field inflation, JCAP02 (2019) 041 [arXiv:1807.04390] [INSPIRE].
  29. [29]
    G. Shiu and Y. Sumitomo, Stability Constraints on Classical de Sitter Vacua, JHEP09 (2011) 052 [arXiv:1107.2925] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    R. Flauger, S. Paban, D. Robbins and T. Wrase, Searching for slow-roll moduli inflation in massive type IIA supergravity with metric fluxes, Phys. Rev.D 79 (2009) 086011 [arXiv:0812.3886] [INSPIRE].
  31. [31]
    J. BlÄbÀck, U. Danielsson and G. Dibitetto, Accelerated Universes from type IIA Compactifications, JCAP03 (2014) 003 [arXiv:1310.8300] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    U.H. Danielsson, S.S. Haque, P. Koerber, G. Shiu, T. Van Riet and T. Wrase, de Sitter hunting in a classical landscape, Fortsch. Phys.59 (2011) 897 [arXiv:1103.4858] [INSPIRE].
  33. [33]
    T. Van Riet, On classical de Sitter solutions in higher dimensions, Class. Quant. Grav.29 (2012) 055001 [arXiv:1111.3154] [INSPIRE].
  34. [34]
    J. Blaback, U.H. Danielsson, D. Junghans, T. Van Riet, T. Wrase and M. Zagermann, The problematic backreaction of SUSY-breaking branes, JHEP08 (2011) 105 [arXiv:1105.4879] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    D. Junghans and M. Zagermann, A Universal Tachyon in Nearly No-scale de Sitter Compactifications, JHEP07 (2018) 078 [arXiv:1612.06847] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  36. [36]
    S. Dimopoulos, S. Kachru, J. McGreevy and J.G. Wacker, N-flation, JCAP08 (2008) 003 [hep-th/0507205] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    A.R. Liddle, A. Mazumdar and F.E. Schunck, Assisted inflation, Phys. Rev.D 58 (1998) 061301 [astro-ph/9804177] [INSPIRE].
  38. [38]
    E.J. Copeland, A. Mazumdar and N.J. Nunes, Generalized assisted inflation, Phys. Rev.D 60 (1999) 083506 [astro-ph/9904309] [INSPIRE].
  39. [39]
    W. Fischler, A. Kashani-Poor, R. McNees and S. Paban, The Acceleration of the universe, a challenge for string theory, JHEP07 (2001) 003 [hep-th/0104181] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  40. [40]
    S. Hellerman, N. Kaloper and L. Susskind, String theory and quintessence, JHEP06 (2001) 003 [hep-th/0104180] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  41. [41]
    E. Farhi and A.H. Guth, An Obstacle to Creating a Universe in the Laboratory, Phys. Lett.B 183 (1987) 149 [INSPIRE].
  42. [42]
    D. Andriot, New constraints on classical de Sitter: flirting with the swampland, Fortsch. Phys.67 (2019) 1800103 [arXiv:1807.09698] [INSPIRE].MathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of PhysicsCMR UniversityBengaluruIndia
  2. 2.Center for High Energy PhysicsIndian Institute of ScienceBangaloreIndia

Personalised recommendations