Abstract
We analyse the self-consistency of inflation in the Standard Model, where the Higgs field has a large non-minimal coupling to gravity. We determine the domain of energies in which this model represents a valid effective field theory as a function of the background Higgs field. This domain is bounded above by the cutoff scale which is found to be higher than the relevant dynamical scales throughout the whole history of the Universe, including the inflationary epoch and reheating. We present a systematic scheme to take into account quantum loop corrections to the inflationary calculations within the framework of effective field theory. We discuss the additional assumptions that must be satisfied by the ultra-violet completion of the theory to allow connection between the parameters of the inflationary effective theory and those describing the low-energy physics relevant for the collider experiments. A class of generalisations of inflationary theories with similar properties is constructed.
Similar content being viewed by others
References
F.L. Bezrukov and M. Shaposhnikov, The Standard Model Higgs boson as the inflaton, Phys. Lett. B 659 (2008) 703 [arXiv:0710.3755] [SPIRES].
B.L. Spokoiny, Inflation and generation of perturbations in broken symmetric theory of gravity, Phys. Lett. B 147 (1984) 39 [SPIRES].
T. Futamase and K.-i. Maeda, Chaotic inflationary scenario in models having nonminimal coupling with curvature, Phys. Rev. D 39 (1989) 399 [SPIRES].
D.S. Salopek, J.R. Bond and J.M. Bardeen, Designing Density Fluctuation Spectra in Inflation, Phys. Rev. D 40 (1989) 1753 [SPIRES].
R. Fakir and W.G. Unruh, Improvement on cosmological chaotic inflation through nonminimal coupling, Phys. Rev. D 41 (1990) 1783 [SPIRES].
D.I. Kaiser, Primordial spectral indices from generalized Einstein theories, Phys. Rev. D 52 (1995) 4295 [astro-ph/9408044] [SPIRES].
E. Komatsu and T. Futamase, Complete constraints on a nonminimally coupled chaotic inflationary scenario from the cosmic microwave background, Phys. Rev. D 59 (1999) 064029 [astro-ph/9901127] [SPIRES].
S. Tsujikawa and B. Gumjudpai, Density perturbations in generalized Einstein scenarios and constraints on nonminimal couplings from the Cosmic Microwave Background, Phys. Rev. D 69 (2004) 123523 [astro-ph/0402185] [SPIRES].
A.D. Linde, Chaotic Inflation, Phys. Lett. B 129 (1983) 177 [SPIRES].
A.O. Barvinsky, A.Y. Kamenshchik and A.A. Starobinsky, Inflation scenario via the Standard Model Higgs boson and LHC, JCAP 11 (2008) 021 [arXiv:0809.2104] [SPIRES].
F. Bezrukov, D. Gorbunov and M. Shaposhnikov, On initial conditions for the Hot Big Bang, JCAP 06 (2009) 029 [arXiv:0812.3622] [SPIRES].
J. García-Bellido, D.G. Figueroa and J. Rubio, Preheating in the Standard Model with the Higgs-Inflaton coupled to gravity, Phys. Rev. D 79 (2009) 063531 [arXiv:0812.4624] [SPIRES].
A. De Simone, M.P. Hertzberg and F. Wilczek, Running Inflation in the Standard Model, Phys. Lett. B 678 (2009) 1 [arXiv:0812.4946] [SPIRES].
F.L. Bezrukov, A. Magnin and M. Shaposhnikov, Standard Model Higgs boson mass from inflation, Phys. Lett. B 675 (2009) 88 [arXiv:0812.4950] [SPIRES].
F. Bezrukov and M. Shaposhnikov, Standard Model Higgs boson mass from inflation: two loop analysis, JHEP 07 (2009) 089 [arXiv:0904.1537] [SPIRES].
A.O. Barvinsky, A.Y. Kamenshchik, C. Kiefer, A.A. Starobinsky and C. Steinwachs, Asymptotic freedom in inflationary cosmology with a non-minimally coupled Higgs field, JCAP 12 (2009) 003 [arXiv:0904.1698] [SPIRES].
C.P. Burgess, H.M. Lee and M. Trott, Power-counting and the Validity of the Classical Approximation During Inflation, JHEP 09 (2009) 103 [arXiv:0902.4465] [SPIRES].
J.L.F. Barbon and J.R. Espinosa, On the Naturalness of Higgs Inflation, Phys. Rev. D 79 (2009) 081302 [arXiv:0903.0355] [SPIRES].
C.P. Burgess, H.M. Lee and M. Trott, Comment on Higgs Inflation and Naturalness, JHEP 07 (2010) 007 [arXiv:1002.2730] [SPIRES].
M.P. Hertzberg, On Inflation with Non-minimal Coupling, JHEP 11 (2010) 023 [arXiv:1002.2995] [SPIRES].
R.N. Lerner and J. McDonald, Higgs Inflation and Naturalness, JCAP 04 (2010) 015 [arXiv:0912.5463] [SPIRES].
K. Freese, J.A. Frieman and A.V. Olinto, Natural inflation with pseudo-Nambu-Goldstone bosons, Phys. Rev. Lett. 65 (1990) 3233 [SPIRES].
C. Cheung, P. Creminelli, A.L. Fitzpatrick, J. Kaplan and L. Senatore, The Effective Field Theory of Inflation, JHEP 03 (2008) 014 [arXiv:0709.0293] [SPIRES].
S. Weinberg, Effective Field Theory for Inflation, Phys. Rev. D 77 (2008) 123541 [arXiv:0804.4291] [SPIRES].
S. Ferrara, R. Kallosh, A. Linde, A. Marrani and A. Van Proeyen, Superconformal Symmetry, NMSSM and Inflation, arXiv:1008.2942 [SPIRES].
D. Baumann and D. Green, Desensitizing Inflation from the Planck Scale, JHEP 09 (2010) 057 [arXiv:1004.3801] [SPIRES].
A.O. Barvinsky, A.Y. Kamenshchik, C. Kiefer, A.A. Starobinsky and C.F. Steinwachs, Higgs boson, renormalization group and naturalness in cosmology, arXiv:0910.1041 [SPIRES].
J.M. Cornwall, D.N. Levin and G. Tiktopoulos, Derivation of Gauge Invariance from High-Energy Unitarity Bounds on the s Matrix, Phys. Rev. D 10 (1974) 1145 [SPIRES].
M.B. Voloshin, On strong high-energy scattering in theories with weak coupling, Phys. Rev. D 43 (1991) 1726 [SPIRES].
R. Kallosh, A.D. Linde, D.A. Linde and L. Susskind, Gravity and global symmetries, Phys. Rev. D 52 (1995) 912 [hep-th/9502069] [SPIRES].
M. Shaposhnikov and D. Zenhausern, Scale invariance, unimodular gravity and dark energy, Phys. Lett. B 671 (2009) 187 [arXiv:0809.3395] [SPIRES].
M. Shaposhnikov and D. Zenhausern, Quantum scale invariance, cosmological constant and hierarchy problem, Phys. Lett. B 671 (2009) 162 [arXiv:0809.3406] [SPIRES].
D.H. Lyth and A. Riotto, Particle physics models of inflation and the cosmological density perturbation, Phys. Rept. 314 (1999) 1 [hep-ph/9807278] [SPIRES].
R.N. Lerner and J. McDonald, A Unitarity-Conserving Higgs Inflation Model, Phys. Rev. D 82 (2010) 103525 [arXiv:1005.2978] [SPIRES].
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] [SPIRES].
C. Germani and A. Kehagias, Cosmological Perturbations in the New Higgs Inflation, JCAP 05 (2010) 019 [arXiv:1003.4285] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1008.5157
Rights and permissions
About this article
Cite this article
Bezrukov, F., Magnin, A., Shaposhnikov, M. et al. Higgs inflation: consistency and generalisations. J. High Energ. Phys. 2011, 16 (2011). https://doi.org/10.1007/JHEP01(2011)016
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2011)016