Hybrid Natural Inflation

  • Graham G. Ross
  • Gabriel Germán
  • J. Alberto Vázquez
Open Access
Regular Article - Theoretical Physics

Abstract

We construct two simple effective field theory versions of Hybrid Natural Inflation (HNI) that illustrate the range of its phenomenological implications. The resulting inflationary sector potential, V = Δ4(1 + acos(ϕ/f)), arises naturally, with the inflaton field a pseudo-Nambu-Goldstone boson. The end of inflation is triggered by a waterfall field and the conditions for this to happen are determined. Also of interest is the fact that the slow-roll parameter ϵ (and hence the tensor r) is a non-monotonic function of the field with a maximum where observables take universal values that determines the maximum possible tensor to scalar ratio r. In one of the models the inflationary scale can be as low as the electroweak scale. We explore in detail the associated HNI phenomenology, taking account of the constraints from Black Hole production, and perform a detailed fit to the Planck 2015 temperature and polarisation data.

Keywords

Effective field theories Spontaneous Symmetry Breaking 

References

  1. [1]
    A.H. Guth, The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems, Phys. Rev. D 23 (1981) 347 [INSPIRE].ADSGoogle Scholar
  2. [2]
    A.D. Linde, A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems, Phys. Lett. B 108 (1982) 389 [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  3. [3]
    A. Albrecht and P.J. Steinhardt, Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking, Phys. Rev. Lett. 48 (1982) 1220 [INSPIRE].CrossRefADSGoogle 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].
  5. [5]
    D.H. Lyth and A.R. Liddle, The primordial density perturbation: Cosmology, inflation and the origin of structure, Cambridge University Press, Cambridge, U.K. (2009), pg. 497.Google Scholar
  6. [6]
    D. Baumann, Inflation, arXiv:0907.5424 [INSPIRE].
  7. [7]
    K. Freese, J.A. Frieman and A.V. Olinto, Natural inflation with pseudo-Nambu-Goldstone bosons, Phys. Rev. Lett. 65 (1990) 3233 [INSPIRE].CrossRefADSGoogle Scholar
  8. [8]
    F.C. Adams, J.R. Bond, K. Freese, J.A. Frieman and A.V. Olinto, Natural inflation: Particle physics models, power law spectra for large scale structure and constraints from COBE, Phys. Rev. D 47 (1993) 426 [hep-ph/9207245] [INSPIRE].
  9. [9]
    K. Freese, C. Savage and W.H. Kinney, Natural Inflation: The Status after WMAP 3-year data, Int. J. Mod. Phys. D 16 (2008) 2573 [arXiv:0802.0227] [INSPIRE].ADSGoogle Scholar
  10. [10]
    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].CrossRefADSGoogle Scholar
  11. [11]
    Planck collaboration, P.A.R. Ade et al., Planck 2013 results. XXII. Constraints on inflation, Astron. Astrophys. 571 (2014) A22 [arXiv:1303.5082] [INSPIRE].
  12. [12]
    J.E. Kim, H.P. Nilles and M. Peloso, Completing natural inflation, JCAP 01 (2005) 005 [hep-ph/0409138] [INSPIRE].
  13. [13]
    S. Dimopoulos, S. Kachru, J. McGreevy and J.G. Wacker, N-flation, JCAP 08 (2008) 003 [hep-th/0507205] [INSPIRE].CrossRefADSGoogle Scholar
  14. [14]
    E. Palti, On Natural Inflation and Moduli Stabilisation in String Theory, JHEP 10 (2015) 188 [arXiv:1508.00009] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  15. [15]
    F. Baume and E. Palti, Backreacted Axion Field Ranges in String Theory, arXiv:1602.06517 [INSPIRE].
  16. [16]
    G.G. Ross and G. German, Hybrid natural inflation from non Abelian discrete symmetry, Phys. Lett. B 684 (2010) 199 [arXiv:0902.4676] [INSPIRE].CrossRefADSGoogle Scholar
  17. [17]
    G.G. Ross and G. German, Hybrid Natural Low Scale Inflation, Phys. Lett. B 691 (2010) 117 [arXiv:1002.0029] [INSPIRE].CrossRefADSGoogle Scholar
  18. [18]
    J.A. Vázquez, M. Carrillo-González, G. Germán, A. Herrera-Aguilar and J.C. Hidalgo, Constraining Hybrid Natural Inflation with recent CMB data, JCAP 02 (2015) 039 [arXiv:1411.6616] [INSPIRE].CrossRefGoogle Scholar
  19. [19]
    M. Carrillo-González, G. Germán, A. Herrera-Aguilar, J.C. Hidalgo and R. Sussman, Testing Hybrid Natural Inflation with BICEP2, Phys. Lett. B 734 (2014) 345 [arXiv:1404.1122] [INSPIRE].CrossRefADSGoogle Scholar
  20. [20]
    A.D. Linde, Hybrid inflation, Phys. Rev. D 49 (1994) 748 [astro-ph/9307002] [INSPIRE].
  21. [21]
    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].
  22. [22]
    A.D. Linde, Inflationary Cosmology, Lect. Notes Phys. 738 (2008) 1 [arXiv:0705.0164] [INSPIRE].MathSciNetCrossRefADSMATHGoogle Scholar
  23. [23]
    M. Shaposhnikov, Baryogenesis, J. Phys. Conf. Ser. 171 (2009) 012005 [INSPIRE].CrossRefADSGoogle Scholar
  24. [24]
    W.E. East, M. Kleban, A. Linde and L. Senatore, Beginning inflation in an inhomogeneous universe, arXiv:1511.05143 [INSPIRE].
  25. [25]
    S.W. Hawking and N. Turok, Open inflation without false vacua, Phys. Lett. B 425 (1998) 25 [hep-th/9802030] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  26. [26]
    A. Vilenkin, Singular instantons and creation of open universes, Phys. Rev. D 57 (1998) 7069 [hep-th/9803084] [INSPIRE].MathSciNetADSGoogle Scholar
  27. [27]
    A.D. Linde, Quantum creation of an open inflationary universe, Phys. Rev. D 58 (1998) 083514 [gr-qc/9802038] [INSPIRE].MathSciNetADSGoogle Scholar
  28. [28]
    N. Turok and S.W. Hawking, Open inflation, the four form and the cosmological constant, Phys. Lett. B 432 (1998) 271 [hep-th/9803156] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  29. [29]
    N. Turok, Before inflation, astro-ph/0011195 [INSPIRE].
  30. [30]
    A. Vilenkin, Creation of Universes from Nothing, Phys. Lett. B 117 (1982) 25 [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  31. [31]
    A. Vilenkin, The Birth of Inflationary Universes, Phys. Rev. D 27 (1983) 2848 [INSPIRE].MathSciNetADSGoogle Scholar
  32. [32]
    A. Vilenkin, Quantum Creation of Universes, Phys. Rev. D 30 (1984) 509 [INSPIRE].MathSciNetADSGoogle Scholar
  33. [33]
    A.D. Linde, Quantum creation of an inflationary universe, Sov. Phys. JETP 60 (1984) 211 [INSPIRE].MathSciNetGoogle Scholar
  34. [34]
    V.A. Rubakov, Particle creation in a tunneling universe, JETP Lett. 39 (1984) 107 [INSPIRE].ADSGoogle Scholar
  35. [35]
    Ya. B. Zeldovich and A.A. Starobinsky, Quantum creation of a universe in a nontrivial topology, Sov. Astron. Lett. 10 (1984) 135 [INSPIRE].
  36. [36]
    A. Vilenkin, Topological inflation, Phys. Rev. Lett. 72 (1994) 3137 [hep-th/9402085] [INSPIRE].CrossRefADSGoogle Scholar
  37. [37]
    R. Brandenberger, Initial Conditions for Inflation — A Short Review, arXiv:1601.01918 [INSPIRE].
  38. [38]
    L. Kofman, A.D. Linde and A.A. Starobinsky, Reheating after inflation, Phys. Rev. Lett. 73 (1994) 3195 [hep-th/9405187] [INSPIRE].CrossRefADSGoogle Scholar
  39. [39]
    Y. Shtanov, J.H. Traschen and R.H. Brandenberger, Universe reheating after inflation, Phys. Rev. D 51 (1995) 5438 [hep-ph/9407247] [INSPIRE].
  40. [40]
    L. Kofman, A.D. Linde and A.A. Starobinsky, Towards the theory of reheating after inflation, Phys. Rev. D 56 (1997) 3258 [hep-ph/9704452] [INSPIRE].
  41. [41]
    G.N. Felder, J. Garc´ıa-Bellido, P.B. Greene, L. Kofman, A.D. Linde and I. Tkachev, Dynamics of symmetry breaking and tachyonic preheating, Phys. Rev. Lett. 87 (2001) 011601 [hep-ph/0012142] [INSPIRE].
  42. [42]
    G.N. Felder, L. Kofman and A.D. Linde, Tachyonic instability and dynamics of spontaneous symmetry breaking, Phys. Rev. D 64 (2001) 123517 [hep-th/0106179] [INSPIRE].ADSGoogle Scholar
  43. [43]
    M. Desroche, G.N. Felder, J.M. Kratochvil and A.D. Linde, Preheating in new inflation, Phys. Rev. D 71 (2005) 103516 [hep-th/0501080] [INSPIRE].ADSGoogle Scholar
  44. [44]
    A.R. Liddle, P. Parsons and J.D. Barrow, Formalizing the slow roll approximation in inflation, Phys. Rev. D 50 (1994) 7222 [astro-ph/9408015] [INSPIRE].
  45. [45]
    A.R. Liddle and D.H. Lyth, Cosmological Inflation and Large-Scale Structure, Cambridge University Press (2000).Google Scholar
  46. [46]
    Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XIII. Cosmological parameters, arXiv:1502.01589 [INSPIRE].
  47. [47]
    A. Lewis, A. Challinor and A. Lasenby, Efficient computation of CMB anisotropies in closed FRW models, Astrophys. J. 538 (2000) 473 [astro-ph/9911177] [INSPIRE].
  48. [48]
    A. Lewis and S. Bridle, Cosmological parameters from CMB and other data: A Monte Carlo approach, Phys. Rev. D 66 (2002) 103511 [astro-ph/0205436] [INSPIRE].
  49. [49]
    BICEP2, 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].
  50. [50]
    G. German, A. Herrera-Aguilar, J.C. Hidalgo and R.A. Sussman, Canonical single field slow-roll inflation with a non-monotonic tensor, arXiv:1512.03105 [INSPIRE].
  51. [51]
    K. Kohri, D.H. Lyth and A. Melchiorri, Black hole formation and slow-roll inflation, JCAP 04 (2008) 038 [arXiv:0711.5006] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  52. [52]
    A.S. Josan, A.M. Green and K.A. Malik, Generalised constraints on the curvature perturbation from primordial black holes, Phys. Rev. D 79 (2009) 103520 [arXiv:0903.3184] [INSPIRE].MathSciNetADSGoogle Scholar
  53. [53]
    B.J. Carr, K. Kohri, Y. Sendouda and J. Yokoyama, New cosmological constraints on primordial black holes, Phys. Rev. D 81 (2010) 104019 [arXiv:0912.5297] [INSPIRE].ADSGoogle Scholar
  54. [54]
    S. Clesse, Hybrid inflation along waterfall trajectories, Phys. Rev. D 83 (2011) 063518 [arXiv:1006.4522] [INSPIRE].ADSGoogle Scholar
  55. [55]
    S. Clesse, B. Garbrecht and Y. Zhu, Non-Gaussianities and Curvature Perturbations from Hybrid Inflation, Phys. Rev. D 89 (2014) 063519 [arXiv:1304.7042] [INSPIRE].ADSGoogle Scholar
  56. [56]
    H. Kodama, K. Kohri and K. Nakayama, On the waterfall behavior in hybrid inflation, Prog. Theor. Phys. 126 (2011) 331 [arXiv:1102.5612] [INSPIRE].CrossRefADSMATHGoogle Scholar
  57. [57]
    S. Clesse and B. Garbrecht, Slow Roll during the Waterfall Regime: The Small Coupling Window for SUSY Hybrid Inflation, Phys. Rev. D 86 (2012) 023525 [arXiv:1204.3540] [INSPIRE].ADSGoogle Scholar
  58. [58]
    D. Mulryne, S. Orani and A. Rajantie, Non-Gaussianity from the hybrid potential, Phys. Rev. D 84 (2011) 123527 [arXiv:1107.4739] [INSPIRE].ADSGoogle Scholar
  59. [59]
    B.J. Carr and S.W. Hawking, Black holes in the early Universe, Mon. Not. Roy. Astron. Soc. 168 (1974) 399 [INSPIRE].CrossRefADSGoogle Scholar
  60. [60]
    M. Yu. Khlopov, Primordial Black Holes, Res. Astron. Astrophys. 10 (2010) 495 [arXiv:0801.0116] [INSPIRE].CrossRefADSGoogle Scholar
  61. [61]
    P.H. Frampton, M. Kawasaki, F. Takahashi and T.T. Yanagida, Primordial Black Holes as All Dark Matter, JCAP 04 (2010) 023 [arXiv:1001.2308] [INSPIRE].CrossRefADSGoogle Scholar
  62. [62]
    D. Blais, C. Kiefer and D. Polarski, Can primordial black holes be a significant part of dark matter?, Phys. Lett. B 535 (2002) 11 [astro-ph/0203520] [INSPIRE].
  63. [63]
    S. Clesse and J. Garc´ıa-Bellido, Massive Primordial Black Holes from Hybrid Inflation as Dark Matter and the seeds of Galaxies, Phys. Rev. D 92 (2015) 023524 [arXiv:1501.07565] [INSPIRE].
  64. [64]
    M. Kawasaki and Y. Tada, Can massive primordial black holes be produced in mild waterfall hybrid inflation?, arXiv:1512.03515 [INSPIRE].
  65. [65]
    D.H. Lyth, Contribution of the hybrid inflation waterfall to the primordial curvature perturbation, JCAP 07 (2011) 035 [arXiv:1012.4617] [INSPIRE].CrossRefADSGoogle Scholar
  66. [66]
    D.H. Lyth, Primordial black hole formation and hybrid inflation, arXiv:1107.1681 [INSPIRE].
  67. [67]
    D.H. Lyth, The hybrid inflation waterfall and the primordial curvature perturbation, JCAP 05 (2012) 022 [arXiv:1201.4312] [INSPIRE].CrossRefADSGoogle Scholar
  68. [68]
    E. Bugaev and P. Klimai, Curvature perturbation spectra from waterfall transition, black hole constraints and non-Gaussianity, JCAP 11 (2011) 028 [arXiv:1107.3754] [INSPIRE].CrossRefADSGoogle Scholar
  69. [69]
    E. Bugaev and P. Klimai, Formation of primordial black holes from non-Gaussian perturbations produced in a waterfall transition, Phys. Rev. D 85 (2012) 103504 [arXiv:1112.5601] [INSPIRE].ADSGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Graham G. Ross
    • 1
  • Gabriel Germán
    • 1
  • J. Alberto Vázquez
    • 2
  1. 1.Rudolf Peierls Centre for Theoretical PhysicsUniversity of OxfordOxfordU.K.
  2. 2.Brookhaven National LaboratoryUptonU.S.A.

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