Unitarity and predictiveness in new Higgs inflation

  • Jacopo FumagalliEmail author
  • Sander Mooij
  • Marieke Postma
Open Access
Regular Article - Theoretical Physics


In new Higgs inflation the Higgs kinetic terms are non-minimally coupled to the Einstein tensor, allowing the Higgs field to play the role of the inflaton. The new interaction is non-renormalizable, and the model only describes physics below some cutoff scale. Even if the unknown UV physics does not affect the tree level inflaton potential significantly, it may still enter at loop level and modify the running of the Standard Model (SM) parameters. This is analogous to what happens in the original model for Higgs inflation. A key difference, though, is that in new Higgs inflation the inflationary predictions are sensitive to this running. Thus the boundary conditions at the EW scale as well as the unknown UV completion may leave a signature on the inflationary parameters. However, this dependence can be evaded if the kinetic terms of the SM fermions and gauge fields are non-minimally coupled to gravity as well. Our approach to determine the model’s UV dependence and the connection between low and high scale physics can be used in any particle physics model of inflation.


Cosmology of Theories beyond the SM Higgs Physics Renormalization Group Effective Field Theories 


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]
    M. Bastero-Gil, A. Berera and B.M. Jackson, Power suppression from disparate mass scales in effective scalar field theories of inflation and quintessence, JCAP 07 (2011) 010 [arXiv:1003.5636] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    A.D. Linde, Chaotic inflation, Phys. Lett. B 129 (1983) 177 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    R. Fakir and W.G. Unruh, Improvement on cosmological chaotic inflation through nonminimal coupling, Phys. Rev. D 41 (1990) 1783 [INSPIRE].ADSGoogle Scholar
  4. [4]
    D.S. Salopek, J.R. Bond and J.M. Bardeen, Designing density fluctuation spectra in inflation, Phys. Rev. D 40 (1989) 1753 [INSPIRE].ADSGoogle Scholar
  5. [5]
    F.L. Bezrukov and M. Shaposhnikov, The Standard Model Higgs boson as the inflaton, Phys. Lett. B 659 (2008) 703 [arXiv:0710.3755] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    C. Germani and A. Kehagias, New model of inflation with non-minimal derivative coupling of Standard Model Higgs boson to gravity, Phys. Rev. Lett. 105 (2010) 011302 [arXiv:1003.2635] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    T. Kobayashi, M. Yamaguchi and J. Yokoyama, G-inflation: inflation driven by the galileon field, Phys. Rev. Lett. 105 (2010) 231302 [arXiv:1008.0603] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    K. Kamada, T. Kobayashi, M. Yamaguchi and J. Yokoyama, Higgs G-inflation, Phys. Rev. D 83 (2011) 083515 [arXiv:1012.4238] [INSPIRE].ADSGoogle Scholar
  9. [9]
    K. Nakayama and F. Takahashi, Higgs chaotic inflation in Standard Model and NMSSM, JCAP 02 (2011) 010 [arXiv:1008.4457] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    K. Nakayama and F. Takahashi, Higgs chaotic inflation and the primordial B-mode polarization discovered by BICEP2, Phys. Lett. B 734 (2014) 96 [arXiv:1403.4132] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    G.W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space, Int. J. Theor. Phys. 10 (1974) 363 [INSPIRE].MathSciNetCrossRefGoogle Scholar
  12. [12]
    K. Kamada, T. Kobayashi, T. Takahashi, M. Yamaguchi and J. Yokoyama, Generalized Higgs inflation, Phys. Rev. D 86 (2012) 023504 [arXiv:1203.4059] [INSPIRE].ADSGoogle Scholar
  13. [13]
    U. Aydemir, M.M. Anber and J.F. Donoghue, Self-healing of unitarity in effective field theories and the onset of new physics, Phys. Rev. D 86 (2012) 014025 [arXiv:1203.5153] [INSPIRE].ADSGoogle Scholar
  14. [14]
    C.P. Burgess, S.P. Patil and M. Trott, On the predictiveness of single-field inflationary models, JHEP 06 (2014) 010 [arXiv:1402.1476] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    J. Fumagalli and M. Postma, UV (in)sensitivity of Higgs inflation, JHEP 05 (2016) 049 [arXiv:1602.07234] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    J. Fumagalli, Renormalization group independence of cosmological attractors, Phys. Lett. B 769 (2017) 451 [arXiv:1611.04997] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    F. Bezrukov, A. Magnin, M. Shaposhnikov and S. Sibiryakov, Higgs inflation: consistency and generalisations, JHEP 01 (2011) 016 [arXiv:1008.5157] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  18. [18]
    S. Ferrara, R. Kallosh, A. Linde, A. Marrani and A. Van Proeyen, Superconformal symmetry, NMSSM and inflation, Phys. Rev. D 83 (2011) 025008 [arXiv:1008.2942] [INSPIRE].ADSGoogle Scholar
  19. [19]
    G.F. Giudice and H.M. Lee, Unitarizing Higgs inflation, Phys. Lett. B 694 (2011) 294 [arXiv:1010.1417] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    J.L.F. Barbon, J.A. Casas, J. Elias-Miro and J.R. Espinosa, Higgs inflation as a mirage, JHEP 09 (2015) 027 [arXiv:1501.02231] [INSPIRE].CrossRefGoogle Scholar
  21. [21]
    D.P. George, S. Mooij and M. Postma, Quantum corrections in Higgs inflation: the Standard Model case, JCAP 04 (2016) 006 [arXiv:1508.04660] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    F. Bezrukov, J. Rubio and M. Shaposhnikov, Living beyond the edge: Higgs inflation and vacuum metastability, Phys. Rev. D 92 (2015) 083512 [arXiv:1412.3811] [INSPIRE].ADSGoogle Scholar
  23. [23]
    F. Bezrukov and M. Shaposhnikov, Higgs inflation at the critical point, Phys. Lett. B 734 (2014) 249 [arXiv:1403.6078] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    V.-M. Enckell, K. Enqvist and S. Nurmi, Observational signatures of Higgs inflation, JCAP 07 (2016) 047 [arXiv:1603.07572] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    F. Bezrukov, M. Pauly and J. Rubio, On the robustness of the primordial power spectrum in renormalized Higgs inflation, JCAP 02 (2018) 040 [arXiv:1706.05007] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    A. Escrivà and C. Germani, Beyond dimensional analysis: Higgs and new Higgs inflations do not violate unitarity, Phys. Rev. D 95 (2017) 123526 [arXiv:1612.06253] [INSPIRE].ADSGoogle Scholar
  27. [27]
    C. Germani, Spontaneous localization on a brane via a gravitational mechanism, Phys. Rev. D 85 (2012) 055025 [arXiv:1109.3718] [INSPIRE].ADSGoogle Scholar
  28. [28]
    S. Di Vita and C. Germani, Electroweak vacuum stability and inflation via nonminimal derivative couplings to gravity, Phys. Rev. D 93 (2016) 045005 [arXiv:1508.04777] [INSPIRE].ADSGoogle Scholar
  29. [29]
    A.B. Balakin and J.P.S. Lemos, Non-minimal coupling for the gravitational and electromagnetic fields: a general system of equations, Class. Quant. Grav. 22 (2005) 1867 [gr-qc/0503076] [INSPIRE].
  30. [30]
    J. Beltran Jimenez, R. Durrer, L. Heisenberg and M. Thorsrud, Stability of Horndeski vector-tensor interactions, JCAP 10 (2013) 064 [arXiv:1308.1867] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  31. [31]
    Y. Ema, R. Jinno, K. Mukaida and K. Nakayama, Particle production after inflation with non-minimal derivative coupling to gravity, JCAP 10 (2015) 020 [arXiv:1504.07119] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  32. [32]
    C. Germani and A. Kehagias, Cosmological perturbations in the new Higgs inflation, JCAP 05 (2010) 019 [Erratum ibid. 06 (2010) E01] [arXiv:1003.4285] [INSPIRE].
  33. [33]
    Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XX. Constraints on inflation, Astron. Astrophys. 594 (2016) A20 [arXiv:1502.02114] [INSPIRE].
  34. [34]
    R. Contino, The Higgs as a composite Nambu-Goldstone boson, in Physics of the large and the small, TASI 09, proceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics, Boulder CO U.S.A., 1–26 June 2009, World Scientific, Singapore, (2011), pg. 235 [arXiv:1005.4269] [INSPIRE].
  35. [35]
    K. Allison, Higgs ξ-inflation for the 125126 GeV Higgs: a two-loop analysis, JHEP 02 (2014) 040 [arXiv:1306.6931] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    Y. Hamada, H. Kawai, K.-Y. Oda and S.C. Park, Higgs inflation is still alive after the results from BICEP2, Phys. Rev. Lett. 112 (2014) 241301 [arXiv:1403.5043] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    F. Bezrukov and M. Shaposhnikov, Higgs inflation at the critical point, Phys. Lett. B 734 (2014) 249 [arXiv:1403.6078] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    Y. Hamada, H. Kawai, K.-Y. Oda and S.C. Park, Higgs inflation from Standard Model criticality, Phys. Rev. D 91 (2015) 053008 [arXiv:1408.4864] [INSPIRE].ADSGoogle Scholar
  39. [39]
    S.R. Coleman and E.J. Weinberg, Radiative corrections as the origin of spontaneous symmetry breaking, Phys. Rev. D 7 (1973) 1888 [INSPIRE].ADSGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Jacopo Fumagalli
    • 1
    Email author
  • Sander Mooij
    • 2
  • Marieke Postma
    • 1
  1. 1.NikhefAmsterdamThe Netherlands
  2. 2.Institute of Physics, Laboratory of Particle Physics and CosmologyÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland

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