Abstract
We consider the Higgs inflation in the extension of the Standard Model with two Higgs doublets coupled to gravity non-minimally. In the presence of an approximate global U(1) symmetry in the Higgs sector, both radial and angular modes of neutral Higgs bosons drive inflation where large non-Gaussianity is possible from appropriate initial conditions on the angular mode. We also discuss the case with single-field inflation for which the U(1) symmetry is broken to a Z 2 subgroup. We show that inflationary constraints, perturbativity and stability conditions restrict the parameter space of the Higgs quartic couplings at low energy in both multi- and single-field cases. Focusing on the inert doublet models where Z 2 symmetry remains unbroken at low energy, we show that the extra neutral Higgs boson can be a dark matter candidate consistent with the inflationary constraints. The doublet dark matter is always heavy in multi-field inflation while it can be light due to the suppression of the co-annihilation in single-field inflation. The implication of the extra quartic couplings on the vacuum stability bound is also discussed in the light of the recent LHC limits on the Higgs mass.
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References
A.H. Guth, The inflationary universe: a possible solution to the horizon and flatness problems, Phys. Rev. D 23 (1981) 347 [INSPIRE].
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].
A. Albrecht and P.J. Steinhardt, Cosmology for grand unified theories with radiatively induced symmetry breaking, Phys. Rev. Lett. 48 (1982) 1220 [INSPIRE].
A.R. Liddle and D.H. Lyth, Cosmological inflation and large-scale structure, Cambridge University Press, Cambridge U.K. (2000), pg. 400.
V. Mukhanov, Physical foundations of cosmology, Cambridge University Press, Cambridge U.K. (2005), pg. 421.
S. Weinberg, Cosmology, Cambridge University Press, Cambridge U.K. (2008), pg. 593.
WMAP collaboration, E. Komatsu et al., Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation, Astrophys. J. Suppl. 192 (2011) 18 [arXiv:1001.4538] [INSPIRE].
F. Bezrukov and M. Shaposhnikov, The Standard Model Higgs boson as the inflaton, Phys. Lett. B 659 (2008) 703 [arXiv:0710.3755] [INSPIRE].
F. Bezrukov, A. Magnin, M. Shaposhnikov and S. Sibiryakov, Higgs inflation: consistency and generalisations, JHEP 01 (2011) 016 [arXiv:1008.5157] [INSPIRE].
B. Spokoiny, Inflation and generation of perturbations in broken symmetric theory of gravity, Phys. Lett. B 147 (1984) 39 [INSPIRE].
F.S. Accetta, D.J. Zoller and M.S. Turner, Induced gravity inflation, Phys. Rev. D 31 (1985) 3046 [INSPIRE].
D. Salopek, J. Bond and J.M. Bardeen, Designing density fluctuation spectra in inflation, Phys. Rev. D 40 (1989) 1753 [INSPIRE].
C. 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] [INSPIRE].
C. Burgess, H.M. Lee and M. Trott, Comment on Higgs inflation and naturalness, JHEP 07 (2010) 007 [arXiv:1002.2730] [INSPIRE].
J. Barbon and J. Espinosa, On the naturalness of Higgs inflation, Phys. Rev. D 79 (2009) 081302 [arXiv:0903.0355] [INSPIRE].
M.P. Hertzberg, On inflation with non-minimal coupling, JHEP 11 (2010) 023 [arXiv:1002.2995] [INSPIRE].
G.F. Giudice and H.M. Lee, Unitarizing Higgs inflation, Phys. Lett. B 694 (2011) 294 [arXiv:1010.1417] [INSPIRE].
ATLAS collaboration, G. Aad et al., Combined search for the Standard Model Higgs boson using up to 4.9 fb −1 of pp collision data at \( \sqrt {s} { } = 7 \) TeV with the ATLAS detector at the LHC, Phys. Lett. B 710 (2012) 49 [arXiv:1202.1408] [INSPIRE].
CMS collaboration, S. Chatrchyan et al., Combined results of searches for the standard model Higgs boson in pp collisions at \( \sqrt {s} { } = 7 \) TeV, arXiv:1202.1488 [INSPIRE].
N. Cabibbo, L. Maiani, G. Parisi and R. Petronzio, Bounds on the fermions and Higgs boson masses in grand unified theories, Nucl. Phys. B 158 (1979) 295 [INSPIRE].
M. Sher, Electroweak Higgs potentials and vacuum stability, Phys. Rept. 179 (1989) 273 [INSPIRE].
J. Elias-Miro et al., Higgs mass implications on the stability of the electroweak vacuum, Phys. Lett. B 709 (2012) 222 [arXiv:1112.3022] [INSPIRE].
G. Branco et al., Theory and phenomenology of two-Higgs-doublet models, arXiv:1106.0034 [INSPIRE].
J.F. Gunion, H.E. Haber, G.L. Kane and S. Dawson, Frontiers in Physics. Vol. 80: The Higgs Hunter’s Guide, Perseus Books, New York U.S.A. (2000).
J.D. Wells, Lectures on Higgs Boson Physics in the Standard Model and Beyond, arXiv:0909.4541 [INSPIRE].
J.-O. Gong and H.M. Lee, Large non-Gaussianity in non-minimal inflation, JCAP 11 (2011) 040 [arXiv:1105.0073] [INSPIRE].
O. Lebedev and H.M. Lee, Higgs portal inflation, Eur. Phys. J. C 71 (2011) 1821 [arXiv:1105.2284] [INSPIRE].
R.N. Lerner and J. McDonald, Gauge singlet scalar as inflaton and thermal relic dark matter, Phys. Rev. D 80 (2009) 123507 [arXiv:0909.0520] [INSPIRE].
R.N. Lerner and J. McDonald, Distinguishing Higgs inflation and its variants, Phys. Rev. D 83 (2011) 123522 [arXiv:1104.2468] [INSPIRE].
J. Elias-Miro, J.R. Espinosa, G.F. Giudice, H.M. Lee and A. Strumia, Stabilization of the electroweak vacuum by a scalar threshold effect, arXiv:1203.0237 [INSPIRE].
N.G. Deshpande and E. Ma, Pattern of symmetry breaking with two Higgs doublets, Phys. Rev. D 18 (1978) 2574 [INSPIRE].
R. Barbieri, L.J. Hall and V.S. Rychkov, Improved naturalness with a heavy Higgs: an alternative road to LHC physics, Phys. Rev. D 74 (2006) 015007 [hep-ph/0603188] [INSPIRE].
L. Lopez Honorez, E. Nezri, J.F. Oliver and M.H. Tytgat, The inert doublet model: an archetype for dark matter, JCAP 02 (2007) 028 [hep-ph/0612275] [INSPIRE].
M. Gustafsson, E. Lundstrom, L. Bergstrom and J. Edsjo, Significant gamma lines from inert Higgs dark matter, Phys. Rev. Lett. 99 (2007) 041301 [astro-ph/0703512] [INSPIRE].
E.M. Dolle and S. Su, The inert dark matter, Phys. Rev. D 80 (2009) 055012 [arXiv:0906.1609] [INSPIRE].
L. Lopez Honorez and C.E. Yaguna, A new viable region of the inert doublet model, JCAP 01 (2011) 002 [arXiv:1011.1411] [INSPIRE].
A. Melfo, M. Nemevšek, F. Nesti, G. Senjanović and Y. Zhang, Inert doublet dark matter and mirror/extra families after Xenon100, Phys. Rev. D 84 (2011) 034009 [arXiv:1105.4611] [INSPIRE].
M. Gustafsson, The inert doublet model and its phenomenology, PoS(Charged 2010)030 [arXiv:1106.1719] [INSPIRE].
S.L. Glashow and S. Weinberg, Natural conservation laws for neutral currents, Phys. Rev. D 15 (1977) 1958 [INSPIRE].
J.F. Gunion and H.E. Haber, The CP conserving two Higgs doublet model: the approach to the decoupling limit, Phys. Rev. D 67 (2003) 075019 [hep-ph/0207010] [INSPIRE].
N. Arkani-Hamed and S. Dimopoulos, Supersymmetric unification without low energy supersymmetry and signatures for fine-tuning at the LHC, JHEP 06 (2005) 073 [hep-th/0405159] [INSPIRE].
G. Giudice and A. Romanino, Split supersymmetry, Nucl. Phys. B 699 (2004) 65 [Erratum ibid. B 706 (2005) 65-89] [hep-ph/0406088] [INSPIRE].
G.F. Giudice and A. Strumia, Probing high-scale and split supersymmetry with Higgs mass measurements, Nucl. Phys. B 858 (2012) 63 [arXiv:1108.6077] [INSPIRE].
M.B. Einhorn and D.T. Jones, Inflation with non-minimal gravitational couplings in supergravity, JHEP 03 (2010) 026 [arXiv:0912.2718] [INSPIRE].
S. Ferrara, R. Kallosh, A. Linde, A. Marrani and A. Van Proeyen, Jordan frame supergravity and inflation in NMSSM, Phys. Rev. D 82 (2010) 045003 [arXiv:1004.0712] [INSPIRE].
H.M. Lee, Chaotic inflation in Jordan frame supergravity, JCAP 08 (2010) 003 [arXiv:1005.2735] [INSPIRE].
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].
A.A. Starobinsky, Multicomponent de Sitter (Inflationary) Stages and the Generation of Perturbations, JETP Lett. 42 (1985) 152 [Pisma Zh. Eksp. Teor. Fiz. 42 (1985) 124] [INSPIRE].
M. Sasaki and E.D. Stewart, A general analytic formula for the spectral index of the density perturbations produced during inflation, Prog. Theor. Phys. 95 (1996) 71 [astro-ph/9507001] [INSPIRE].
M. Sasaki and T. Tanaka, Superhorizon scale dynamics of multiscalar inflation, Prog. Theor. Phys. 99 (1998) 763 [gr-qc/9801017] [INSPIRE].
J.-O. Gong and E.D. Stewart, The power spectrum for a multicomponent inflaton to second order corrections in the slow roll expansion, Phys. Lett. B 538 (2002) 213 [astro-ph/0202098] [INSPIRE].
D.H. Lyth and Y. Rodriguez, The inflationary prediction for primordial non-Gaussianity, Phys. Rev. Lett. 95 (2005) 121302 [astro-ph/0504045] [INSPIRE].
J.-O. Gong, J.-c. Hwang, W.-I. Park, M. Sasaki and Y.-S. Song, Conformal invariance of curvature perturbation, JCAP 09 (2011) 023 [arXiv:1107.1840] [INSPIRE].
A. Barvinsky, A.Y. Kamenshchik and A. Starobinsky, Inflation scenario via the Standard Model Higgs boson and LHC, JCAP 11 (2008) 021 [arXiv:0809.2104] [INSPIRE].
A. De Simone, M.P. Hertzberg and F. Wilczek, Running inflation in the Standard Model, Phys. Lett. B 678 (2009) 1 [arXiv:0812.4946] [INSPIRE].
F.L. Bezrukov, A. Magnin and M. Shaposhnikov, Standard Model Higgs boson mass from inflation, Phys. Lett. B 675 (2009) 88 [arXiv:0812.4950] [INSPIRE].
A. Barvinsky, A.Y. Kamenshchik, C. Kiefer, A. Starobinsky and C. Steinwachs, Asymptotic freedom in inflationary cosmology with a non-minimally coupled Higgs field, JCAP 12 (2009) 003 [arXiv:0904.1698] [INSPIRE].
G. Bélanger, F. Boudjema, A. Pukhov and A. Semenov, MicrOMEGAs 2.0.7: A program to calculate the relic density of dark matter in a generic model, Comput. Phys. Commun. 177 (2007) 894 [INSPIRE].
G. Bélanger, F. Boudjema, A. Pukhov and A. Semenov, Dark matter direct detection rate in a generic model with MicrOMEGAs 2.2, Comput. Phys. Commun. 180 (2009) 747 [arXiv:0803.2360] [INSPIRE].
G. Bélanger et al., Indirect search for dark matter with MicrOMEGAs2.4, Comput. Phys. Commun. 182 (2011) 842 [arXiv:1004.1092] [INSPIRE].
G. Bélanger, F. Boudjema, A. Pukhov and A. Semenov, MicrOMEGAs: a tool for dark matter studies, arXiv:1005.4133 [INSPIRE].
A. Pierce and J. Thaler, Natural dark matter from an unnatural Higgs boson and new colored particles at the TeV scale, JHEP 08 (2007) 026 [hep-ph/0703056] [INSPIRE].
E. Lundstrom, M. Gustafsson and J. Edsjo, The inert doublet model and LEP II limits, Phys. Rev. D 79 (2009) 035013 [arXiv:0810.3924] [INSPIRE].
R. Young and A. Thomas, Octet baryon masses and sigma terms from an SU(3) chiral extrapolation, Phys. Rev. D 81 (2010) 014503 [arXiv:0901.3310] [INSPIRE].
MILC collaboration, D. Toussaint and W. Freeman, The Strange quark condensate in the nucleon in 2+1 flavor QCD, Phys. Rev. Lett. 103 (2009) 122002 [arXiv:0905.2432] [INSPIRE].
XENON100 collaboration, E. Aprile et al., Dark Matter Results from 100 Live Days of XENON100 Data, Phys. Rev. Lett. 107 (2011) 131302 [arXiv:1104.2549] [INSPIRE].
H. Sung Cheon, S.K. Kang and C. Kim, Low Scale Leptogenesis and Dark Matter Candidates in an Extended Seesaw Model, JCAP 05 (2008) 004 [Erratum ibid. 1103 (2011) E01] [arXiv:0710.2416] [INSPIRE].
O. Lebedev, H.M. Lee and Y. Mambrini, Vector Higgs-portal dark matter and the invisible Higgs, Phys. Lett. B 707 (2012) 570 [arXiv:1111.4482] [INSPIRE].
A. Djouadi, O. Lebedev, Y. Mambrini and J. Quevillon, Implications of LHC searches for Higgs-portal dark matter, Phys. Lett. B 709 (2012) 65 [arXiv:1112.3299] [INSPIRE].
A. Achucarro, J.-O. Gong, S. Hardeman, G.A. Palma and S.P. Patil, Mass hierarchies and non-decoupling in multi-scalar field dynamics, Phys. Rev. D 84 (2011) 043502 [arXiv:1005.3848] [INSPIRE].
A. Achucarro, J.-O. Gong, S. Hardeman, G.A. Palma and S.P. Patil, Features of heavy physics in the CMB power spectrum, JCAP 01 (2011) 030 [arXiv:1010.3693] [INSPIRE].
S. Cespedes, V. Atal and G.A. Palma, On the importance of heavy fields during inflation, arXiv:1201.4848 [INSPIRE].
A. Achucarro, J.-O. Gong, S. Hardeman, G.A. Palma and S.P. Patil, Effective theories of single field inflation when heavy fields matter, arXiv:1201.6342 [INSPIRE].
H.E. Haber, The Higgs sector in the minimal supersymmetric model: Radiative corrections and their implications, in Hiroshima 1991: Proceedings of Workshop on Electroweak symmetry breaking, Hiroshima Japan (1991).
H.E. Haber and R. Hempfling, The renormalization group improved Higgs sector of the minimal supersymmetric model, Phys. Rev. D 48 (1993) 4280 [hep-ph/9307201] [INSPIRE].
I.L. Buchbinder, S.D. Odintsov and I.L. Shapiro, Effective action in quantum gravity, IOP Publishing, Bristol U.K. (1992).
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Gong, JO., Lee, H.M. & Kang, S.K. Inflation and dark matter in two Higgs doublet models. J. High Energ. Phys. 2012, 128 (2012). https://doi.org/10.1007/JHEP04(2012)128
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DOI: https://doi.org/10.1007/JHEP04(2012)128