Abstract
We investigate the thermalization of high-energy particles injected from the perturbative decay of inflaton during the pre-thermal phase of reheating in detail. In general, thermalization takes a relatively long time in a low-temperature plasma; therefore, the instantaneous thermalization approximation is not justified, even for the reheating of the Standard Model (SM) sector. We consider a pure Yang-Mills (YM) theory as an approximation of the SM sector or a possible dark sector, considering the Landau-Pomeranchuk-Migdal effect, a quantum interference effect in a finite temperature plasma. We perform the first numerical calculation to solve the time evolution of the system, including the redshift due to the expansion of the Universe, and show the details of the temperature evolution near the maximum and the behavior of the quasi-attractors at later times. The maximal temperature Tmax and time scale tmax are determined quantitatively, such as Tmax ≃ 0.05 × \( {\left({\Gamma}_I{M}_{\textrm{PI}}^2/{m}_I^3\right)}^{2/5}{m}_I \) and tmax ≃ 2 × 103 × \( {\left({\Gamma}_I{M}_{\textrm{PI}}^2/{m}_I^3\right)}^{-3/5}{m}_I^{-1} \) in the SM-like system, where mI and ΓI are the mass and decay rate of inflaton. We also provide a similar formula for pure SU(N) and SO(N) YM theories for general values of N and coupling constant α, including Tmax ∝ α4/5 and tmax ∝ N−2α−16/5 behaviors and their numerical coefficients. The thermalization occurs in a finite time scale, resulting in a lower maximal temperature of the Universe after inflation than that under the instantaneous thermalization approximation.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D.N. Schramm and M.S. Turner, Big bang nucleosynthesis enters the precision era, Rev. Mod. Phys. 70 (1998) 303 [astro-ph/9706069] [INSPIRE].
G. Steigman, Primordial nucleosynthesis in the precision cosmology era, Ann. Rev. Nucl. Part. Sci. 57 (2007) 463 [arXiv:0712.1100] [INSPIRE].
A.A. Penzias and R.W. Wilson, A measurement of excess antenna temperature at 4080 Mc/s, Astrophys. J. 142 (1965) 419 [INSPIRE].
J.C. Mather et al., Measurement of the cosmic microwave background spectrum by the COBE FIRAS instrument, Astrophys. J. 420 (1994) 439 [INSPIRE].
A. Kosowsky, M.S. Turner and R. Watkins, Gravitational waves from first order cosmological phase transitions, Phys. Rev. Lett. 69 (1992) 2026 [INSPIRE].
A. Kosowsky, M.S. Turner and R. Watkins, Gravitational radiation from colliding vacuum bubbles, Phys. Rev. D 45 (1992) 4514 [INSPIRE].
A. Kosowsky and M.S. Turner, Gravitational radiation from colliding vacuum bubbles: envelope approximation to many bubble collisions, Phys. Rev. D 47 (1993) 4372 [astro-ph/9211004] [INSPIRE].
M. Kamionkowski, A. Kosowsky and M.S. Turner, Gravitational radiation from first order phase transitions, Phys. Rev. D 49 (1994) 2837 [astro-ph/9310044] [INSPIRE].
A. Vilenkin, Cosmic strings and domain walls, Phys. Rept. 121 (1985) 263 [INSPIRE].
A. Vilenkin, Gravitational radiation from cosmic strings, Phys. Lett. B 107 (1981) 47 [INSPIRE].
F.S. Accetta and L.M. Krauss, The stochastic gravitational wave spectrum resulting from cosmic string evolution, Nucl. Phys. B 319 (1989) 747 [INSPIRE].
R.R. Caldwell and B. Allen, Cosmological constraints on cosmic string gravitational radiation, Phys. Rev. D 45 (1992) 3447 [INSPIRE].
Y. Gouttenoire, G. Servant and P. Simakachorn, Beyond the standard models with cosmic strings, JCAP 07 (2020) 032 [arXiv:1912.02569] [INSPIRE].
A. Vilenkin, Gravitational field of vacuum domain walls and strings, Phys. Rev. D 23 (1981) 852 [INSPIRE].
J. Preskill, S.P. Trivedi, F. Wilczek and M.B. Wise, Cosmology and broken discrete symmetry, Nucl. Phys. B 363 (1991) 207 [INSPIRE].
K. Saikawa, A review of gravitational waves from cosmic domain walls, Universe 3 (2017) 40 [arXiv:1703.02576] [INSPIRE].
A. Vilenkin, Cosmological evolution of monopoles connected by strings, Nucl. Phys. B 196 (1982) 240 [INSPIRE].
L. Leblond, B. Shlaer and X. Siemens, Gravitational waves from broken cosmic strings: the bursts and the beads, Phys. Rev. D 79 (2009) 123519 [arXiv:0903.4686] [INSPIRE].
W. Buchmuller, V. Domcke, H. Murayama and K. Schmitz, Probing the scale of grand unification with gravitational waves, Phys. Lett. B 809 (2020) 135764 [arXiv:1912.03695] [INSPIRE].
S. Chang, C. Hagmann and P. Sikivie, Studies of the motion and decay of axion walls bounded by strings, Phys. Rev. D 59 (1999) 023505 [hep-ph/9807374] [INSPIRE].
D.I. Dunsky et al., GUTs, hybrid topological defects, and gravitational waves, Phys. Rev. D 106 (2022) 075030 [arXiv:2111.08750] [INSPIRE].
A.H. Guth, The inflationary universe: a possible solution to the horizon and flatness problems, Phys. Rev. D 23 (1981) 347 [INSPIRE].
A.A. Starobinsky, A new type of isotropic cosmological models without singularity, Phys. Lett. B 91 (1980) 99 [INSPIRE].
K. Sato, First order phase transition of a vacuum and expansion of the universe, Mon. Not. Roy. Astron. Soc. 195 (1981) 467 [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, Dissipative effects on reheating after inflation, JCAP 03 (2013) 002 [arXiv:1212.4985] [INSPIRE].
K. Mukaida and K. Nakayama, Dynamics of oscillating scalar field in thermal environment, JCAP 01 (2013) 017 [arXiv:1208.3399] [INSPIRE].
M. Drewes and J.U. Kang, The kinematics of cosmic reheating, Nucl. Phys. B 875 (2013) 315 [Erratum ibid. 888 (2014) 284] [arXiv:1305.0267] [INSPIRE].
R. Baier, A.H. Mueller, D. Schiff and D.T. Son, ‘Bottom up’ thermalization in heavy ion collisions, Phys. Lett. B 502 (2001) 51 [hep-ph/0009237] [INSPIRE].
A. Kurkela and G.D. Moore, Thermalization in weakly coupled non-Abelian plasmas, JHEP 12 (2011) 044 [arXiv:1107.5050] [INSPIRE].
A. Kurkela and E. Lu, Approach to equilibrium in weakly coupled non-Abelian plasmas, Phys. Rev. Lett. 113 (2014) 182301 [arXiv:1405.6318] [INSPIRE].
Y. Fu, J. Ghiglieri, S. Iqbal and A. Kurkela, Thermalization of non-Abelian gauge theories at next-to-leading order, Phys. Rev. D 105 (2022) 054031 [arXiv:2110.01540] [INSPIRE].
K. Harigaya and K. Mukaida, Thermalization after/during reheating, JHEP 05 (2014) 006 [arXiv:1312.3097] [INSPIRE].
K. Mukaida and M. Yamada, Thermalization process after inflation and effective potential of scalar field, JCAP 02 (2016) 003 [arXiv:1506.07661] [INSPIRE].
S. Passaglia, W. Hu, A.J. Long and D. Zegeye, Achieving the highest temperature during reheating with the Higgs condensate, Phys. Rev. D 104 (2021) 083540 [arXiv:2108.00962] [INSPIRE].
M. Drees and B. Najjari, Energy spectrum of thermalizing high energy decay products in the early universe, JCAP 10 (2021) 009 [arXiv:2105.01935] [INSPIRE].
M. Drees and B. Najjari, Multi-species thermalization cascade of energetic particles in the early universe, JCAP 08 (2023) 037 [arXiv:2205.07741] [INSPIRE].
K. Mukaida and M. Yamada, Cascades of high-energy SM particles in the primordial thermal plasma, JHEP 10 (2022) 116 [arXiv:2208.11708] [INSPIRE].
K. Harigaya, M. Kawasaki, K. Mukaida and M. Yamada, Dark matter production in late time reheating, Phys. Rev. D 89 (2014) 083532 [arXiv:1402.2846] [INSPIRE].
K. Harigaya, K. Mukaida and M. Yamada, Dark matter production during the thermalization era, JHEP 07 (2019) 059 [arXiv:1901.11027] [INSPIRE].
M.A.G. Garcia and M.A. Amin, Prethermalization production of dark matter, Phys. Rev. D 98 (2018) 103504 [arXiv:1806.01865] [INSPIRE].
D. Chowdhury and A. Hait, Thermalization in the presence of a time-dependent dissipation and its impact on dark matter production, JHEP 09 (2023) 085 [arXiv:2302.06654] [INSPIRE].
L.D. Landau and I. Pomeranchuk, Limits of applicability of the theory of Bremsstrahlung electrons and pair production at high-energies, Dokl. Akad. Nauk Ser. Fiz. 92 (1953) 535 [INSPIRE].
A.B. Migdal, Bremsstrahlung and pair production in condensed media at high-energies, Phys. Rev. 103 (1956) 1811 [INSPIRE].
M. Gyulassy and X.-N. Wang, Multiple collisions and induced gluon Bremsstrahlung in QCD, Nucl. Phys. B 420 (1994) 583 [nucl-th/9306003] [INSPIRE].
P.B. Arnold, G.D. Moore and L.G. Yaffe, Photon emission from ultrarelativistic plasmas, JHEP 11 (2001) 057 [hep-ph/0109064] [INSPIRE].
P.B. Arnold, G.D. Moore and L.G. Yaffe, Photon emission from quark gluon plasma: complete leading order results, JHEP 12 (2001) 009 [hep-ph/0111107] [INSPIRE].
P.B. Arnold, G.D. Moore and L.G. Yaffe, Photon and gluon emission in relativistic plasmas, JHEP 06 (2002) 030 [hep-ph/0204343] [INSPIRE].
A. Kurkela and U.A. Wiedemann, Picturing perturbative parton cascades in QCD matter, Phys. Lett. B 740 (2015) 172 [arXiv:1407.0293] [INSPIRE].
P.B. Arnold, G.D. Moore and L.G. Yaffe, Effective kinetic theory for high temperature gauge theories, JHEP 01 (2003) 030 [hep-ph/0209353] [INSPIRE].
P.B. Arnold and C. Dogan, QCD splitting/joining functions at finite temperature in the deep LPM regime, Phys. Rev. D 78 (2008) 065008 [arXiv:0804.3359] [INSPIRE].
A.E. Faraggi and M. Pospelov, Selfinteracting dark matter from the hidden heterotic string sector, Astropart. Phys. 16 (2002) 451 [hep-ph/0008223] [INSPIRE].
J.L. Feng and Y. Shadmi, WIMPless dark matter from non-Abelian hidden sectors with anomaly-mediated supersymmetry breaking, Phys. Rev. D 83 (2011) 095011 [arXiv:1102.0282] [INSPIRE].
K.K. Boddy, J.L. Feng, M. Kaplinghat and T.M.P. Tait, Self-interacting dark matter from a non-Abelian hidden sector, Phys. Rev. D 89 (2014) 115017 [arXiv:1402.3629] [INSPIRE].
K.K. Boddy et al., Strongly interacting dark matter: self-interactions and keV lines, Phys. Rev. D 90 (2014) 095016 [arXiv:1408.6532] [INSPIRE].
A. Soni and Y. Zhang, Hidden SU(N) glueball dark matter, Phys. Rev. D 93 (2016) 115025 [arXiv:1602.00714] [INSPIRE].
G.D. Kribs and E.T. Neil, Review of strongly-coupled composite dark matter models and lattice simulations, Int. J. Mod. Phys. A 31 (2016) 1643004 [arXiv:1604.04627] [INSPIRE].
L. Forestell, D.E. Morrissey and K. Sigurdson, Non-Abelian dark forces and the relic densities of dark glueballs, Phys. Rev. D 95 (2017) 015032 [arXiv:1605.08048] [INSPIRE].
A. Soni, H. Xiao and Y. Zhang, Cosmic selection rule for the glueball dark matter relic density, Phys. Rev. D 96 (2017) 083514 [arXiv:1704.02347] [INSPIRE].
L. Forestell, D.E. Morrissey and K. Sigurdson, Cosmological bounds on non-Abelian dark forces, Phys. Rev. D 97 (2018) 075029 [arXiv:1710.06447] [INSPIRE].
B. Jo, H. Kim, H.D. Kim and C.S. Shin, Exploring the universe with dark light scalars, Phys. Rev. D 103 (2021) 083528 [arXiv:2010.10880] [INSPIRE].
C. Gross, S. Karamitsos, G. Landini and A. Strumia, Gravitational vector dark matter, JHEP 03 (2021) 174 [arXiv:2012.12087] [INSPIRE].
P. Carenza, R. Pasechnik, G. Salinas and Z.-W. Wang, Glueball dark matter revisited, Phys. Rev. Lett. 129 (2022) 261302 [arXiv:2207.13716] [INSPIRE].
P. Carenza, T. Ferreira, R. Pasechnik and Z.-W. Wang, Glueball dark matter, Phys. Rev. D 108 (2023) 123027 [arXiv:2306.09510] [INSPIRE].
M. Yamada and K. Yonekura, Dark baryon from pure Yang-Mills theory and its GW signature from cosmic strings, JHEP 09 (2023) 197 [arXiv:2307.06586] [INSPIRE].
M. Reichert, F. Sannino, Z.-W. Wang and C. Zhang, Dark confinement and chiral phase transitions: gravitational waves vs matter representations, JHEP 01 (2022) 003 [arXiv:2109.11552] [INSPIRE].
E. Morgante, N. Ramberg and P. Schwaller, Gravitational waves from dark SU(3) Yang-Mills theory, Phys. Rev. D 107 (2023) 036010 [arXiv:2210.11821] [INSPIRE].
S. He, L. Li, Z. Li and S.-J. Wang, Gravitational waves and primordial black hole productions from gluodynamics by holography, Sci. China Phys. Mech. Astron. 67 (2024) 240411 [arXiv:2210.14094] [INSPIRE].
M. Reichert and Z.-W. Wang, Gravitational waves from dark composite dynamics, EPJ Web Conf. 274 (2022) 08003 [arXiv:2211.08877] [INSPIRE].
E. Witten, Cosmic superstrings, Phys. Lett. B 153 (1985) 243 [INSPIRE].
M. Yamada and K. Yonekura, Cosmic strings from pure Yang-Mills theory, Phys. Rev. D 106 (2022) 123515 [arXiv:2204.13123] [INSPIRE].
M. Yamada and K. Yonekura, Cosmic F- and D-strings from pure Yang-Mills theory, Phys. Lett. B 838 (2023) 137724 [arXiv:2204.13125] [INSPIRE].
Acknowledgments
K. M. was supported by MEXT Leading Initiative for Excellent Young Researchers Grant No. JPMXS0320200430, and JSPS KAKENHI Grant No. JP22K14044. M. Y. was supported by MEXT Leading Initiative for Excellent Young Researchers, and by JSPS KAKENHI Grant No. JP20H05851 and JP23K13092.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2402.14054
Rights and permissions
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.
About this article
Cite this article
Mukaida, K., Yamada, M. Perturbative reheating and thermalization of pure Yang-Mills plasma. J. High Energ. Phys. 2024, 174 (2024). https://doi.org/10.1007/JHEP05(2024)174
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2024)174