Skip to main content
Log in

Fate of Z 2 symmetric scalar field

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

The evolution of a coherently oscillating scalar field with Z 2 symmetry is studied in detail. We calculate the dissipation rate of the scalar field based on the closed time path formalism. Consequently, it is shown that the energy density of the coherent oscillation can be efficiently dissipated if the coupling constant is larger than the critical value, even though the scalar particle is stable due to the Z 2 symmetry.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. G. Coughlan, W. Fischler, E.W. Kolb, S. Raby and G.G. Ross, Cosmological problems for the Polonyi potential, Phys. Lett. B 131 (1983) 59 [INSPIRE].

    Article  ADS  Google Scholar 

  2. J.R. Ellis, D.V. Nanopoulos and M. Quirós, On the axion, dilaton, Polonyi, gravitino and shadow matter problems in supergravity and superstring models, Phys. Lett. B 174 (1986) 176 [INSPIRE].

    Article  ADS  Google Scholar 

  3. A.S. Goncharov, A.D. Linde and M.I. Vysotsky, Cosmological problems for spontaneously broken supergravity, Phys. Lett. B 147 (1984) 279 [INSPIRE].

    Article  ADS  Google Scholar 

  4. B. de Carlos, J. Casas, F. Quevedo and E. Roulet, Model independent properties and cosmological implications of the dilaton and moduli sectors of 4D strings, Phys. Lett. B 318 (1993) 447 [hep-ph/9308325] [INSPIRE].

    Article  ADS  Google Scholar 

  5. T. Banks, D.B. Kaplan and A.E. Nelson, Cosmological implications of dynamical supersymmetry breaking, Phys. Rev. D 49 (1994) 779 [hep-ph/9308292] [INSPIRE].

    ADS  Google Scholar 

  6. A. Berera, Warm inflation, Phys. Rev. Lett. 75 (1995) 3218 [astro-ph/9509049] [INSPIRE].

    Article  ADS  Google Scholar 

  7. A. Berera, I.G. Moss and R.O. Ramos, Warm inflation and its microphysical basis, Rept. Prog. Phys. 72 (2009) 026901 [arXiv:0808.1855] [INSPIRE].

    Article  ADS  Google Scholar 

  8. M. Bastero-Gil and A. Berera, Warm inflation model building, Int. J. Mod. Phys. A 24 (2009) 2207 [arXiv:0902.0521] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  9. J. Yokoyama, Fate of oscillating scalar fields in the thermal bath and their cosmological implications, Phys. Rev. D 70 (2004) 103511 [hep-ph/0406072] [INSPIRE].

    ADS  Google Scholar 

  10. J. Yokoyama, Can oscillating scalar fields decay into particles with a large thermal mass?, Phys. Lett. B 635 (2006) 66 [hep-ph/0510091] [INSPIRE].

    Article  ADS  Google Scholar 

  11. M. Drewes, On the role of quasiparticles and thermal masses in nonequilibrium processes in a plasma, arXiv:1012.5380 [INSPIRE].

  12. M. Drewes and J.U. Kang, The kinematics of cosmic reheating, Nucl. Phys. B 875 (2013) 315 [arXiv:1305.0267] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. L. Kofman, A.D. Linde and A.A. Starobinsky, Reheating after inflation, Phys. Rev. Lett. 73 (1994) 3195 [hep-th/9405187] [INSPIRE].

    Article  ADS  Google Scholar 

  14. 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].

    ADS  Google Scholar 

  15. K. Mukaida and K. Nakayama, Dynamics of oscillating scalar field in thermal environment, JCAP 01 (2013) 017 [arXiv:1208.3399] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  16. K. Mukaida and K. Nakayama, Dissipative effects on reheating after inflation, JCAP 03 (2013) 002 [arXiv:1212.4985] [INSPIRE].

    Article  ADS  Google Scholar 

  17. V. Silveira and A. Zee, Scalar phantoms, Phys. Lett. B 161 (1985) 136 [INSPIRE].

    Article  ADS  Google Scholar 

  18. J. McDonald, Gauge singlet scalars as cold dark matter, Phys. Rev. D 50 (1994) 3637 [hep-ph/0702143] [INSPIRE].

    ADS  Google Scholar 

  19. J.M. Cline, K. Kainulainen, P. Scott and C. Weniger, Update on scalar singlet dark matter, Phys. Rev. D 88 (2013) 055025 [arXiv:1306.4710] [INSPIRE].

    ADS  Google Scholar 

  20. N. Okada and Q. Shafi, WIMP dark matter inflation with observable gravity waves, Phys. Rev. D 84 (2011) 043533 [arXiv:1007.1672] [INSPIRE].

    ADS  Google Scholar 

  21. K. Enqvist, D.G. Figueroa and R.N. Lerner, Curvaton decay by resonant production of the Standard Model Higgs, JCAP 01 (2013) 040 [arXiv:1211.5028] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  22. K. Enqvist, R.N. Lerner and S. Rusak, Reheating dynamics affects non-perturbative decay of spectator fields, JCAP 11 (2013) 034 [arXiv:1308.3321] [INSPIRE].

    ADS  Google Scholar 

  23. T. Moroi, K. Mukaida, K. Nakayama and M. Takimoto, Scalar trapping and saxion cosmology, JHEP 06 (2013) 040 [arXiv:1304.6597] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. L. Dolan and R. Jackiw, Symmetry behavior at finite temperature, Phys. Rev. D 9 (1974) 3320 [INSPIRE].

    ADS  Google Scholar 

  25. A. Anisimov and M. Dine, Some issues in flat direction baryogenesis, Nucl. Phys. B 619 (2001) 729 [hep-ph/0008058] [INSPIRE].

    Article  ADS  Google Scholar 

  26. G.N. Felder, L. Kofman and A.D. Linde, Instant preheating, Phys. Rev. D 59 (1999) 123523 [hep-ph/9812289] [INSPIRE].

    ADS  Google Scholar 

  27. A. Kurkela and G.D. Moore, Thermalization in weakly coupled non-Abelian plasmas, JHEP 12 (2011) 044 [arXiv:1107.5050] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  28. D. Bödeker, Moduli decay in the hot early universe, JCAP 06 (2006) 027 [hep-ph/0605030] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  29. M. Laine, On bulk viscosity and moduli decay, Prog. Theor. Phys. Suppl. 186 (2010) 404 [arXiv:1007.2590] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  30. T. Moroi and M. Takimoto, Thermal effects on saxion in supersymmetric model with Peccei-Quinn symmetry, Phys. Lett. B 718 (2012) 105 [arXiv:1207.4858] [INSPIRE].

    Article  ADS  Google Scholar 

  31. L.P. Kadanoff and G. Baym, Quantum statistical mechanics, Benjamin, New York U.S.A. (1962).

    MATH  Google Scholar 

  32. G. Baym and L.P. Kadanoff, Conservation laws and correlation functions, Phys. Rev. 124 (1961) 287 [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. J.M. Cornwall, R. Jackiw and E. Tomboulis, Effective action for composite operators, Phys. Rev. D 10 (1974) 2428 [INSPIRE].

    ADS  MATH  Google Scholar 

  34. K.-C. Chou, Z.-B. Su, B.-L. Hao and L. Yu, Equilibrium and nonequilibrium formalisms made unified, Phys. Rept. 118 (1985) 1 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  35. J. Berges, Introduction to nonequilibrium quantum field theory, AIP Conf. Proc. 739 (2005) 3 [hep-ph/0409233] [INSPIRE].

    Article  ADS  Google Scholar 

  36. E.A. Calzetta and B.L. Hu, Nonequilibrium quantum field theory, Cambridge University Press, Cambridge U.K. (2008).

    Book  MATH  Google Scholar 

  37. J.S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. 2 (1961) 407 [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  38. P.M. Bakshi and K.T. Mahanthappa, Expectation value formalism in quantum field theory. 1, J. Math. Phys. 4 (1963) 1 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  39. L. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz. 47 (1964) 1515 [Sov. Phys. JETP 20 (1965) 1018] [INSPIRE].

  40. R. Kubo, Statistical mechanical theory of irreversible processes. 1. General theory and simple applications in magnetic and conduction problems, J. Phys. Soc. Jap. 12 (1957) 570 [INSPIRE].

    Article  ADS  Google Scholar 

  41. P.C. Martin and J.S. Schwinger, Theory of many particle systems. 1, Phys. Rev. 115 (1959) 1342 [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  42. G. Aarts and A. Tranberg, Thermal effects on slow-roll dynamics, Phys. Rev. D 77 (2008) 123521 [arXiv:0712.1120] [INSPIRE].

    ADS  Google Scholar 

  43. A. Tranberg, Quantum field thermalization in expanding backgrounds, JHEP 11 (2008) 037 [arXiv:0806.3158] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  44. J. Berges and J. Serreau, Parametric resonance in quantum field theory, Phys. Rev. Lett. 91 (2003) 111601 [hep-ph/0208070] [INSPIRE].

    Article  ADS  Google Scholar 

  45. J. Berges, A. Rothkopf and J. Schmidt, Non-thermal fixed points: effective weak-coupling for strongly correlated systems far from equilibrium, Phys. Rev. Lett. 101 (2008) 041603 [arXiv:0803.0131] [INSPIRE].

    Article  ADS  Google Scholar 

  46. J. Berges, D. Gelfand and J. Pruschke, Quantum theory of fermion production after inflation, Phys. Rev. Lett. 107 (2011) 061301 [arXiv:1012.4632] [INSPIRE].

    Article  ADS  Google Scholar 

  47. J. Berges and D. Sexty, Bose condensation far from equilibrium, Phys. Rev. Lett. 108 (2012) 161601 [arXiv:1201.0687] [INSPIRE].

    Article  ADS  Google Scholar 

  48. J. Berges, D. Gelfand and D. Sexty, Amplified fermion production from overpopulated Bose fields, arXiv:1308.2180 [INSPIRE].

  49. B. Garbrecht, T. Prokopec and M.G. Schmidt, Particle number in kinetic theory, Eur. Phys. J. C 38 (2004) 135 [hep-th/0211219] [INSPIRE].

    Article  ADS  Google Scholar 

  50. S. Jeon, Hydrodynamic transport coefficients in relativistic scalar field theory, Phys. Rev. D 52 (1995) 3591 [hep-ph/9409250] [INSPIRE].

    ADS  Google Scholar 

  51. S. Jeon and L.G. Yaffe, From quantum field theory to hydrodynamics: transport coefficients and effective kinetic theory, Phys. Rev. D 53 (1996) 5799 [hep-ph/9512263] [INSPIRE].

    ADS  Google Scholar 

  52. M. Bastero-Gil, A. Berera and R.O. Ramos, Dissipation coefficients from scalar and fermion quantum field interactions, JCAP 09 (2011) 033 [arXiv:1008.1929] [INSPIRE].

    Article  ADS  Google Scholar 

  53. S. Kasuya and M. Kawasaki, Restriction to parametric resonant decay after inflation, Phys. Lett. B 388 (1996) 686 [hep-ph/9603317] [INSPIRE].

    Article  ADS  Google Scholar 

  54. M. Hotta, I. Joichi, S. Matsumoto and M. Yoshimura, Quantum system under periodic perturbation: effect of environment, Phys. Rev. D 55 (1997) 4614 [hep-ph/9608374] [INSPIRE].

    ADS  Google Scholar 

  55. E. Calzetta and B. Hu, Nonequilibrium quantum fields: closed time path effective action, Wigner function and Boltzmann equation, Phys. Rev. D 37 (1988) 2878 [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  56. Y. Ivanov, J. Knoll and D. Voskresensky, Resonance transport and kinetic entropy, Nucl. Phys. A 672 (2000) 313 [nucl-th/9905028] [INSPIRE].

    Article  ADS  Google Scholar 

  57. T. Prokopec, M.G. Schmidt and S. Weinstock, Transport equations for chiral fermions to orderand electroweak baryogenesis. Part 1, Annals Phys. 314 (2004) 208 [hep-ph/0312110] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  58. T. Prokopec, M.G. Schmidt and S. Weinstock, Transport equations for chiral fermions to orderand electroweak baryogenesis. Part 2, Annals Phys. 314 (2004) 267 [hep-ph/0406140] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  59. D. Boyanovsky, K. Davey and C. Ho, Particle abundance in a thermal plasma: quantum kinetics vs. Boltzmann equation, Phys. Rev. D 71 (2005) 023523 [hep-ph/0411042] [INSPIRE].

    ADS  Google Scholar 

  60. J. Berges and S. Borsányi, Range of validity of transport equations, Phys. Rev. D 74 (2006) 045022 [hep-ph/0512155] [INSPIRE].

    ADS  Google Scholar 

  61. A. Hohenegger, A. Kartavtsev and M. Lindner, Deriving Boltzmann equations from Kadanoff-Baym equations in curved space-time, Phys. Rev. D 78 (2008) 085027 [arXiv:0807.4551] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  62. A. Anisimov, W. Buchmüller, M. Drewes and S. Mendizabal, Nonequilibrium dynamics of scalar fields in a thermal bath, Annals Phys. 324 (2009) 1234 [arXiv:0812.1934] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  63. B. Garbrecht and M. Garny, Finite width in out-of-equilibrium propagators and kinetic theory, Annals Phys. 327 (2012) 914 [arXiv:1108.3688] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  64. K. Hamaguchi, T. Moroi and K. Mukaida, Boltzmann equation for non-equilibrium particles and its application to non-thermal dark matter production, JHEP 01 (2012) 083 [arXiv:1111.4594] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  65. M. Drewes, S. Mendizabal and C. Weniger, The Boltzmann equation from quantum field theory, Phys. Lett. B 718 (2013) 1119 [arXiv:1202.1301] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  66. Y. Shtanov, J.H. Traschen and R.H. Brandenberger, Universe reheating after inflation, Phys. Rev. D 51 (1995) 5438 [hep-ph/9407247] [INSPIRE].

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kyohei Mukaida.

Additional information

ArXiv ePrint: 1308.4394

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mukaida, K., Nakayama, K. & Takimoto, M. Fate of Z 2 symmetric scalar field. J. High Energ. Phys. 2013, 53 (2013). https://doi.org/10.1007/JHEP12(2013)053

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP12(2013)053

Keywords

Navigation