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.
Similar content being viewed by others
References
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].
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].
A.S. Goncharov, A.D. Linde and M.I. Vysotsky, Cosmological problems for spontaneously broken supergravity, Phys. Lett. B 147 (1984) 279 [INSPIRE].
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].
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].
A. Berera, Warm inflation, Phys. Rev. Lett. 75 (1995) 3218 [astro-ph/9509049] [INSPIRE].
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].
M. Bastero-Gil and A. Berera, Warm inflation model building, Int. J. Mod. Phys. A 24 (2009) 2207 [arXiv:0902.0521] [INSPIRE].
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].
J. Yokoyama, Can oscillating scalar fields decay into particles with a large thermal mass?, Phys. Lett. B 635 (2006) 66 [hep-ph/0510091] [INSPIRE].
M. Drewes, On the role of quasiparticles and thermal masses in nonequilibrium processes in a plasma, arXiv:1012.5380 [INSPIRE].
M. Drewes and J.U. Kang, The kinematics of cosmic reheating, Nucl. Phys. B 875 (2013) 315 [arXiv:1305.0267] [INSPIRE].
L. Kofman, A.D. Linde and A.A. Starobinsky, Reheating after inflation, Phys. Rev. Lett. 73 (1994) 3195 [hep-th/9405187] [INSPIRE].
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].
K. Mukaida and K. Nakayama, Dynamics of oscillating scalar field in thermal environment, JCAP 01 (2013) 017 [arXiv:1208.3399] [INSPIRE].
K. Mukaida and K. Nakayama, Dissipative effects on reheating after inflation, JCAP 03 (2013) 002 [arXiv:1212.4985] [INSPIRE].
V. Silveira and A. Zee, Scalar phantoms, Phys. Lett. B 161 (1985) 136 [INSPIRE].
J. McDonald, Gauge singlet scalars as cold dark matter, Phys. Rev. D 50 (1994) 3637 [hep-ph/0702143] [INSPIRE].
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].
N. Okada and Q. Shafi, WIMP dark matter inflation with observable gravity waves, Phys. Rev. D 84 (2011) 043533 [arXiv:1007.1672] [INSPIRE].
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].
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].
T. Moroi, K. Mukaida, K. Nakayama and M. Takimoto, Scalar trapping and saxion cosmology, JHEP 06 (2013) 040 [arXiv:1304.6597] [INSPIRE].
L. Dolan and R. Jackiw, Symmetry behavior at finite temperature, Phys. Rev. D 9 (1974) 3320 [INSPIRE].
A. Anisimov and M. Dine, Some issues in flat direction baryogenesis, Nucl. Phys. B 619 (2001) 729 [hep-ph/0008058] [INSPIRE].
G.N. Felder, L. Kofman and A.D. Linde, Instant preheating, Phys. Rev. D 59 (1999) 123523 [hep-ph/9812289] [INSPIRE].
A. Kurkela and G.D. Moore, Thermalization in weakly coupled non-Abelian plasmas, JHEP 12 (2011) 044 [arXiv:1107.5050] [INSPIRE].
D. Bödeker, Moduli decay in the hot early universe, JCAP 06 (2006) 027 [hep-ph/0605030] [INSPIRE].
M. Laine, On bulk viscosity and moduli decay, Prog. Theor. Phys. Suppl. 186 (2010) 404 [arXiv:1007.2590] [INSPIRE].
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].
L.P. Kadanoff and G. Baym, Quantum statistical mechanics, Benjamin, New York U.S.A. (1962).
G. Baym and L.P. Kadanoff, Conservation laws and correlation functions, Phys. Rev. 124 (1961) 287 [INSPIRE].
J.M. Cornwall, R. Jackiw and E. Tomboulis, Effective action for composite operators, Phys. Rev. D 10 (1974) 2428 [INSPIRE].
K.-C. Chou, Z.-B. Su, B.-L. Hao and L. Yu, Equilibrium and nonequilibrium formalisms made unified, Phys. Rept. 118 (1985) 1 [INSPIRE].
J. Berges, Introduction to nonequilibrium quantum field theory, AIP Conf. Proc. 739 (2005) 3 [hep-ph/0409233] [INSPIRE].
E.A. Calzetta and B.L. Hu, Nonequilibrium quantum field theory, Cambridge University Press, Cambridge U.K. (2008).
J.S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. 2 (1961) 407 [INSPIRE].
P.M. Bakshi and K.T. Mahanthappa, Expectation value formalism in quantum field theory. 1, J. Math. Phys. 4 (1963) 1 [INSPIRE].
L. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz. 47 (1964) 1515 [Sov. Phys. JETP 20 (1965) 1018] [INSPIRE].
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].
P.C. Martin and J.S. Schwinger, Theory of many particle systems. 1, Phys. Rev. 115 (1959) 1342 [INSPIRE].
G. Aarts and A. Tranberg, Thermal effects on slow-roll dynamics, Phys. Rev. D 77 (2008) 123521 [arXiv:0712.1120] [INSPIRE].
A. Tranberg, Quantum field thermalization in expanding backgrounds, JHEP 11 (2008) 037 [arXiv:0806.3158] [INSPIRE].
J. Berges and J. Serreau, Parametric resonance in quantum field theory, Phys. Rev. Lett. 91 (2003) 111601 [hep-ph/0208070] [INSPIRE].
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].
J. Berges, D. Gelfand and J. Pruschke, Quantum theory of fermion production after inflation, Phys. Rev. Lett. 107 (2011) 061301 [arXiv:1012.4632] [INSPIRE].
J. Berges and D. Sexty, Bose condensation far from equilibrium, Phys. Rev. Lett. 108 (2012) 161601 [arXiv:1201.0687] [INSPIRE].
J. Berges, D. Gelfand and D. Sexty, Amplified fermion production from overpopulated Bose fields, arXiv:1308.2180 [INSPIRE].
B. Garbrecht, T. Prokopec and M.G. Schmidt, Particle number in kinetic theory, Eur. Phys. J. C 38 (2004) 135 [hep-th/0211219] [INSPIRE].
S. Jeon, Hydrodynamic transport coefficients in relativistic scalar field theory, Phys. Rev. D 52 (1995) 3591 [hep-ph/9409250] [INSPIRE].
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].
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].
S. Kasuya and M. Kawasaki, Restriction to parametric resonant decay after inflation, Phys. Lett. B 388 (1996) 686 [hep-ph/9603317] [INSPIRE].
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].
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].
Y. Ivanov, J. Knoll and D. Voskresensky, Resonance transport and kinetic entropy, Nucl. Phys. A 672 (2000) 313 [nucl-th/9905028] [INSPIRE].
T. Prokopec, M.G. Schmidt and S. Weinstock, Transport equations for chiral fermions to order ℏ and electroweak baryogenesis. Part 1, Annals Phys. 314 (2004) 208 [hep-ph/0312110] [INSPIRE].
T. Prokopec, M.G. Schmidt and S. Weinstock, Transport equations for chiral fermions to order ℏ and electroweak baryogenesis. Part 2, Annals Phys. 314 (2004) 267 [hep-ph/0406140] [INSPIRE].
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].
J. Berges and S. Borsányi, Range of validity of transport equations, Phys. Rev. D 74 (2006) 045022 [hep-ph/0512155] [INSPIRE].
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].
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].
B. Garbrecht and M. Garny, Finite width in out-of-equilibrium propagators and kinetic theory, Annals Phys. 327 (2012) 914 [arXiv:1108.3688] [INSPIRE].
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].
M. Drewes, S. Mendizabal and C. Weniger, The Boltzmann equation from quantum field theory, Phys. Lett. B 718 (2013) 1119 [arXiv:1202.1301] [INSPIRE].
Y. Shtanov, J.H. Traschen and R.H. Brandenberger, Universe reheating after inflation, Phys. Rev. D 51 (1995) 5438 [hep-ph/9407247] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1308.4394
Rights 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
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2013)053