Natural inflation with and without modulations in type IIB string theory

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Regular Article - Theoretical Physics


We propose a mechanism for the natural inflation with and without modulation in the framework of type IIB string theory on toroidal orientifold or orbifold. We explicitly construct the stabilization potential of complex structure, dilaton and Kähler moduli, where one of the imaginary component of complex structure moduli becomes light which is identified as the inflaton. The inflaton potential is generated by the gaugino-condensation term which receives the one-loop threshold corrections determined by the field value of complex structure moduli and the axion decay constant of inflaton is enhanced by the inverse of one-loop factor. We also find the threshold corrections can also induce the modulations to the original scalar potential for the natural inflation. Depending on these modulations, we can predict several sizes of tensor-to-scalar ratio as well as the other cosmological observables reported by WMAP, Planck and/or BICEP2 collaborations.


Cosmology of Theories beyond the SM Supergravity Models 


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  1. [1]
    BICEP2 collaboration, P.A.R. Ade et al., Detection of B-mode polarization at degree angular scales by BICEP2, Phys. Rev. Lett. 112 (2014) 241101 [arXiv:1403.3985] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    Planck collaboration, R. Adam et al., Planck intermediate results. XXX. The angular power spectrum of polarized dust emission at intermediate and high galactic latitudes, arXiv:1409.5738 [INSPIRE].
  3. [3]
    BICEP2 and Planck collaborations, P. Ade et al., Joint analysis of BICEP2/Keck Array and Planck data, Phys. Rev. Lett. 114 (2015) 101301 [arXiv:1502.00612] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    K. Freese, J.A. Frieman and A.V. Olinto, Natural inflation with pseudo-Nambu-Goldstone bosons, Phys. Rev. Lett. 65 (1990) 3233 [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    Planck collaboration, P.A.R. Ade et al., Planck 2013 results. XXII. Constraints on inflation, Astron. Astrophys. 571 (2014) A22 [arXiv:1303.5082] [INSPIRE].CrossRefGoogle Scholar
  6. [6]
    Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XX. Constraints on inflation, arXiv:1502.02114 [INSPIRE].
  7. [7]
    K. Freese and W.H. Kinney, Natural inflation: consistency with cosmic microwave background observations of Planck and BICEP2, JCAP 03 (2015) 044 [arXiv:1403.5277] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    J.E. Kim, H.P. Nilles and M. Peloso, Completing natural inflation, JCAP 01 (2005) 005 [hep-ph/0409138] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    R. Kallosh, On inflation in string theory, Lect. Notes Phys. 738 (2008) 119 [hep-th/0702059] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  10. [10]
    M. Czerny, T. Higaki and F. Takahashi, Multi-natural inflation in supergravity, JHEP 05 (2014) 144 [arXiv:1403.0410] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    M. Czerny, T. Higaki and F. Takahashi, Multi-natural inflation in supergravity and BICEP2, Phys. Lett. B 734 (2014) 167 [arXiv:1403.5883] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  12. [12]
    K. Choi, H. Kim and S. Yun, Natural inflation with multiple sub-Planckian axions, Phys. Rev. D 90 (2014) 023545 [arXiv:1404.6209] [INSPIRE].ADSGoogle Scholar
  13. [13]
    S.-H. Henry Tye and S.S.C. Wong, Helical inflation and cosmic strings, arXiv:1404.6988 [INSPIRE].
  14. [14]
    R. Kappl, S. Krippendorf and H.P. Nilles, Aligned natural inflation: monodromies of two axions, Phys. Lett. B 737 (2014) 124 [arXiv:1404.7127] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  15. [15]
    I. Ben-Dayan, F.G. Pedro and A. Westphal, Hierarchical axion inflation, Phys. Rev. Lett. 113 (2014) 261301 [arXiv:1404.7773] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    C. Long, L. McAllister and P. McGuirk, Aligned natural inflation in string theory, Phys. Rev. D 90 (2014) 023501 [arXiv:1404.7852] [INSPIRE].ADSGoogle Scholar
  17. [17]
    T. Li, Z. Li and D.V. Nanopoulos, Aligned natural inflation and moduli stabilization from anomalous U(1) gauge symmetries, JHEP 11 (2014) 012 [arXiv:1407.1819] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    Z. Kenton and S. Thomas, D-brane potentials in the warped resolved conifold and natural inflation, JHEP 02 (2015) 127 [arXiv:1409.1221] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    T. Ali, S.S. Haque and V. Jejjala, Natural inflation from near alignment in heterotic string theory, Phys. Rev. D 91 (2015) 083516 [arXiv:1410.4660] [INSPIRE].ADSMathSciNetGoogle Scholar
  20. [20]
    N. Arkani-Hamed, H.-C. Cheng, P. Creminelli and L. Randall, Extra natural inflation, Phys. Rev. Lett. 90 (2003) 221302 [hep-th/0301218] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  21. [21]
    H. Abe and H. Otsuka, Moduli inflation in five-dimensional supergravity models, JCAP 11 (2014) 027 [arXiv:1405.6520] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    H. Abe, T. Kobayashi and H. Otsuka, Towards natural inflation from weakly coupled heterotic string theory, arXiv:1409.8436 [INSPIRE].
  23. [23]
    N.V. Krasnikov, On supersymmetry breaking in superstring theories, Phys. Lett. B 193 (1987) 37 [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    T.R. Taylor, Dilaton, gaugino condensation and supersymmetry breaking, Phys. Lett. B 252 (1990) 59 [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    J.A. Casas, Z. Lalak, C. Muñoz and G.G. Ross, Hierarchical supersymmetry breaking and dynamical determination of compactification parameters by nonperturbative effects, Nucl. Phys. B 347 (1990) 243 [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    B. de Carlos, J.A. Casas and C. Muñoz, Supersymmetry breaking and determination of the unification gauge coupling constant in string theories, Nucl. Phys. B 399 (1993) 623 [hep-th/9204012] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    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].ADSMathSciNetMATHGoogle Scholar
  28. [28]
    D. Lüst and S. Stieberger, Gauge threshold corrections in intersecting brane world models, Fortsch. Phys. 55 (2007) 427 [hep-th/0302221] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    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].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    L.J. Dixon, V. Kaplunovsky and J. Louis, Moduli dependence of string loop corrections to gauge coupling constants, Nucl. Phys. B 355 (1991) 649 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  31. [31]
    J.P. Conlon and E. Palti, Gauge threshold corrections for local orientifolds, JHEP 09 (2009) 019 [arXiv:0906.1920] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  32. [32]
    J.P. Conlon and E. Palti, On gauge threshold corrections for local IIB/F-theory GUTs, Phys. Rev. D 80 (2009) 106004 [arXiv:0907.1362] [INSPIRE].ADSGoogle Scholar
  33. [33]
    N. Akerblom, R. Blumenhagen, D. Lüst and M. Schmidt-Sommerfeld, Instantons and holomorphic couplings in intersecting D-brane models, JHEP 08 (2007) 044 [arXiv:0705.2366] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  34. [34]
    S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].ADSMathSciNetGoogle Scholar
  35. [35]
    R. Blumenhagen, D. Herschmann and E. Plauschinn, The challenge of realizing F-term axion monodromy inflation in string theory, JHEP 01 (2015) 007 [arXiv:1409.7075] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    E. Dudas, C. Papineau and S. Pokorski, Moduli stabilization and uplifting with dynamically generated F-terms, JHEP 02 (2007) 028 [hep-th/0610297] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  37. [37]
    H. Abe, T. Higaki, T. Kobayashi and Y. Omura, Moduli stabilization, F-term uplifting and soft supersymmetry breaking terms, Phys. Rev. D 75 (2007) 025019 [hep-th/0611024] [INSPIRE].ADSGoogle Scholar
  38. [38]
    R. Kallosh and A.D. Linde, OKKLT, JHEP 02 (2007) 002 [hep-th/0611183] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  39. [39]
    H. Abe, T. Higaki and T. Kobayashi, More about F-term uplifting, Phys. Rev. D 76 (2007) 105003 [arXiv:0707.2671] [INSPIRE].ADSGoogle Scholar
  40. [40]
    T. Kobayashi and F. Takahashi, Running spectral index from inflation with modulations, JCAP 01 (2011) 026 [arXiv:1011.3988] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    M. Czerny, T. Kobayashi and F. Takahashi, Running spectral index from large-field inflation with modulations revisited, Phys. Lett. B 735 (2014) 176 [arXiv:1403.4589] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    T. Kobayashi, O. Seto and Y. Yamaguchi, Axion monodromy inflation with sinusoidal corrections, Prog. Theor. Exp. Phys. 2014 (2014) 103E01 [arXiv:1404.5518] [INSPIRE].CrossRefGoogle Scholar
  43. [43]
    T. Higaki, T. Kobayashi, O. Seto and Y. Yamaguchi, Axion monodromy inflation with multi-natural modulations, JCAP 10 (2014) 025 [arXiv:1405.0775] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    P.G. Harris et al., New experimental limit on the electric dipole moment of the neutron, Phys. Rev. Lett. 82 (1999) 904 [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    C.A. Baker et al., An improved experimental limit on the electric dipole moment of the neutron, Phys. Rev. Lett. 97 (2006) 131801 [hep-ex/0602020] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    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

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Department of PhysicsWaseda UniversityTokyoJapan
  2. 2.Department of PhysicsHokkaido UniversitySapporoJapan

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