Real scalar dark matter: relativistic treatment

  • Giorgio ArcadiEmail author
  • Oleg Lebedev
  • Stefan Pokorski
  • Takashi Toma
Open Access
Regular Article - Theoretical Physics


A stable real scalar provides one of the simplest possibilities to account for dark matter. We consider the regime where its coupling to the Standard Model fields is negligibly small. Due to self-coupling, the scalar field can reach thermal or at least kinetic equilibrium, in which case the system is characterized by its temperature and effective chemical potential. We perform a fully relativistic analysis of dark matter evolution, thermalization conditions and different freeze-out regimes, including the chemical potential effects. To this end, we derive a relativistic Bose-Einstein analog of the Gelmini-Gondolo formula for a thermal averaged cross section. Finally, we perform a comprehensive parameter space analysis to determine regions consistent with observational constraints. Dark matter can be both warm and cold in this model.


Beyond Standard Model Cosmology of Theories beyond the SM 


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]
    XENON collaboration, Dark matter search results from a one ton-year exposure of XENON1T, Phys. Rev. Lett.121 (2018) 111302 [arXiv:1805.12562] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    V. Silveira and A. Zee, Scalar phantoms, Phys. Lett.B 161 (1985) 136 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    L.J. Hall, K. Jedamzik, J. March-Russell and S.M. West, Freeze-in production of FIMP dark matter, JHEP03 (2010) 080 [arXiv:0911.1120] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    E.D. Carlson, M.E. Machacek and L.J. Hall, Self-interacting dark matter, Astrophys. J.398 (1992) 43 [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    P. Gondolo and G. Gelmini, Cosmic abundances of stable particles: improved analysis, Nucl. Phys.B 360 (1991) 145 [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    J. McDonald, Gauge singlet scalars as cold dark matter, Phys. Rev.D 50 (1994) 3637 [hep-ph/0702143] [INSPIRE].
  7. [7]
    C.P. Burgess, M. Pospelov and T. ter Veldhuis, The minimal model of nonbaryonic dark matter: a singlet scalar, Nucl. Phys.B 619 (2001) 709 [hep-ph/0011335] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    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].ADSCrossRefGoogle Scholar
  9. [9]
    J.M. Cline, K. Kainulainen, P. Scott and C. Weniger, Update on scalar singlet dark matter, Phys. Rev.D 88 (2013) 055025 [Erratum ibid. D 92 (2015) 039906] [arXiv:1306.4710] [INSPIRE].ADSGoogle Scholar
  10. [10]
    GAMBIT collaboration, Global fits of scalar singlet dark matter with GAMBIT, arXiv:1611.05065 [INSPIRE].
  11. [11]
    T. Binder, T. Bringmann, M. Gustafsson and A. Hryczuk, Early kinetic decoupling of dark matter: when the standard way of calculating the thermal relic density fails, Phys. Rev.D 96 (2017) 115010 [arXiv:1706.07433] [INSPIRE].ADSGoogle Scholar
  12. [12]
    N. Bernal, C. Garcia-Cely and R. Rosenfeld, WIMP and SIMP dark matter from the spontaneous breaking of a global group, JCAP04 (2015) 012 [arXiv:1501.01973] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    N. Bernal and X. Chu, Z 2SIMP dark matter, JCAP01 (2016) 006 [arXiv:1510.08527] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    M. Heikinheimo, T. Tenkanen, K. Tuominen and V. Vaskonen, Observational constraints on decoupled hidden sectors, Phys. Rev.D 94 (2016) 063506 [Erratum ibid. D 96 (2017) 109902] [arXiv:1604.02401] [INSPIRE].ADSGoogle Scholar
  15. [15]
    N. Bernal, M. Heikinheimo, T. Tenkanen, K. Tuominen and V. Vaskonen, The dawn of FIMP dark matter: a review of models and constraints, Int. J. Mod. Phys.A 32 (2017) 1730023 [arXiv:1706.07442] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    M. Fairbairn, K. Kainulainen, T. Markkanen and S. Nurmi, Despicable dark relics: generated by gravity with unconstrained masses, JCAP04 (2019) 005 [arXiv:1808.08236] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    A.D. Dolgov and K. Kainulainen, Fermi-Dirac corrections to the relic abundances, Nucl. Phys.B 402 (1993) 349 [hep-ph/9211231] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    P. Adshead, Y. Cui and J. Shelton, Chilly dark sectors and asymmetric reheating, JHEP06 (2016) 016 [arXiv:1604.02458] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    M. Olechowski and P.L. Szczerbiak, Effects of quantum statistics on relic density of dark radiation, Eur. Phys. J.C 78 (2018) 704 [arXiv:1807.00490] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    J. Bernstein, L.S. Brown and G. Feinberg, The cosmological heavy neutrino problem revisited, Phys. Rev.D 32 (1985) 3261 [INSPIRE].ADSGoogle Scholar
  21. [21]
    J. Bernstein, Kinetic theory in the expanding universe, Cambridge University Press, Cambridge, U.K. (1988) [INSPIRE].CrossRefGoogle Scholar
  22. [22]
    E.W. Kolb and M.S. Turner, The early universe, Front. Phys.69 (1990) 1 [INSPIRE].ADSMathSciNetGoogle Scholar
  23. [23]
    K. Enqvist, M. Karciauskas, O. Lebedev, S. Rusak and M. Zatta, Postinflationary vacuum instability and Higgs-inflaton couplings, JCAP11 (2016) 025 [arXiv:1608.08848] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    A.K. Das, Finite temperature field theory, World Scientific, Singapore (1997) [INSPIRE].
  25. [25]
    A. Belyaev, N.D. Christensen and A. Pukhov, CalcHEP 3.4 for collider physics within and beyond the Standard Model, Comput. Phys. Commun. 184 (2013) 1729 [arXiv:1207.6082] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    M.E. Peskin and D.V. Schroeder, An introduction to quantum field theory, Addison-Wesley, Reading, MA, U.S.A. (1997) [INSPIRE].Google Scholar
  27. [27]
    C.-Y. Chen, S. Dawson and I.M. Lewis, Exploring resonant di-Higgs boson production in the Higgs singlet model, Phys. Rev.D 91 (2015) 035015 [arXiv:1410.5488] [INSPIRE].ADSGoogle Scholar
  28. [28]
    H.E. Haber and H.A. Weldon, Thermodynamics of an ultrarelativistic Bose gas, Phys. Rev. Lett.46 (1981) 1497 [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    H.E. Haber and H.A. Weldon, Finite temperature symmetry breaking as Bose-Einstein condensation, Phys. Rev.D 25 (1982) 502 [INSPIRE].ADSGoogle Scholar
  30. [30]
    Particle Data Group collaboration, Review of particle physics, Phys. Rev.D 98 (2018) 030001 [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Giorgio Arcadi
    • 1
    • 2
    • 3
    Email author
  • Oleg Lebedev
    • 4
  • Stefan Pokorski
    • 5
  • Takashi Toma
    • 6
  1. 1.Max-Planck-Institut fur KernphysikHeidelbergGermany
  2. 2.Dipartimento di Matematica e FisicaUniversità di Roma 3RomeItaly
  3. 3.INFN Sezione Roma 3RomeItaly
  4. 4.Department of PhysicsUniversity of HelsinkiHelsinkiFinland
  5. 5.Institute of Theoretical Physics, Faculty of PhysicsUniversity of WarsawWarsawPoland
  6. 6.Department of PhysicsMcGill UniversityMontréalQCCanada

Personalised recommendations