×

Phase transitions in an expanding universe: stochastic gravitational waves in standard and non-standard histories. (English) Zbl 1486.83163

The article studies a cosmological first order phase transition and the ensuing production of stochastic gravitational waves in radiation and matter dominated universes as a result of bubble collisions. It is noted that a rescaling relates the velocity proficle of a single bubble with that of Minkowski space-time in the bag model. The resulting spectrum of gravitational waves includes an additional suppresion factor depending on the lifetime of the source.

MSC:

83F05 Relativistic cosmology
83E05 Geometrodynamics and the holographic principle
82B26 Phase transitions (general) in equilibrium statistical mechanics
83C35 Gravitational waves
53C05 Connections (general theory)
PDF BibTeX XML Cite
Full Text: DOI arXiv

References:

[1] C. Caprini et al., 2016 Science with the space-based interferometer eLISA. II: Gravitational waves from cosmological phase transitions J. Cosmol. Astropart. Phys.2016 04 001 [1512.06239]
[2] D.J. Weir, 2018 Gravitational waves from a first order electroweak phase transition: a brief review, https://doi.org/10.1098/rsta.2017.0126 Phil. Trans. Roy. Soc. Lond. A376 20170126 [1705.01783] · Zbl 1402.81014
[3] A. Mazumdar and G. White, 2019 Review of cosmic phase transitions: their significance and experimental signatures, https://doi.org/10.1088/1361-6633/ab1f55 Rept. Prog. Phys.82 076901 [1811.01948]
[4] G. Bertone et al., Gravitational wave probes of dark matter: challenges and opportunities, [1907.10610]
[5] C. Caprini et al., 2020 Detecting gravitational waves from cosmological phase transitions with LISA: an update J. Cosmol. Astropart. Phys.2020 03 024 [1910.13125]
[6] E. Barausse et al., 2020 Prospects for fundamental physics with LISA, https://doi.org/10.1007/s10714-020-02691-1 Gen. Rel. Grav.52 81 [2001.09793]
[7] LIGO Scientific and Virgo collaborations, 2017 Upper limits on the stochastic gravitational-wave background from Advanced LIGO’s first observing run, https://doi.org/10.1103/PhysRevLett.118.121101 Phys. Rev. Lett.118 121101 [Erratum ibid 119 (2017) 029901] [1612.02029]
[8] LIGO Scientific and Virgo collaborations, 2019 Search for the isotropic stochastic background using data from Advanced LIGO’s second observing run, https://doi.org/10.1103/PhysRevD.100.061101 Phys. Rev. D100 061101 [1903.02886]
[9] LISA collaboration, Laser interferometer space antenna, [1702.00786]
[10] K. Yagi and N. Seto, 2011 Detector configuration of DECIGO/BBO and identification of cosmological neutron-star binaries, https://doi.org/10.1103/PhysRevD.83.044011 Phys. Rev. D83 044011 [Erratum ibid 95 (2017) 109901] [1101.3940]
[11] X. Gong et al., 2015 Descope of the ALIA mission, https://doi.org/10.1088/1742-6596/610/1/012011 J. Phys. Conf. Ser.610 012011 [1410.7296]
[12] TianQin collaboration, 2016 TianQin: a space-borne gravitational wave detector, https://doi.org/10.1088/0264-9381/33/3/035010 Class. Quant. Grav.33 035010 [1512.02076]
[13] C. Grojean and G. Servant, 2007 Gravitational waves from phase transitions at the electroweak scale and beyond, https://doi.org/10.1103/PhysRevD.75.043507 Phys. Rev. D75 043507 [hep-ph/0607107]
[14] V. Vaskonen, 2017 Electroweak baryogenesis and gravitational waves from a real scalar singlet, https://doi.org/10.1103/PhysRevD.95.123515 Phys. Rev. D95 123515 [1611.02073]
[15] G.C. Dorsch, S.J. Huber, T. Konstandin and J.M. No, 2017 A second Higgs doublet in the early universe: baryogenesis and gravitational waves J. Cosmol. Astropart. Phys.2017 05 052 [1611.05874]
[16] A. Beniwal, M. Lewicki, M. White and A.G. Williams, 2019 Gravitational waves and electroweak baryogenesis in a global study of the extended scalar singlet model J. High Energy Phys. JHEP02(2019)183 [1810.02380]
[17] Z. Kang, P. Ko and T. Matsui, 2018 Strong first order EWPT & strong gravitational waves in \(Z_3\)-symmetric singlet scalar extension J. High Energy Phys. JHEP02(2018)115 [1706.09721]
[18] C. Delaunay, C. Grojean and J.D. Wells, 2008 Dynamics of non-renormalizable electroweak symmetry breaking J. High Energy Phys. JHEP04(2008)029 [0711.2511]
[19] M. Chala, C. Krause and G. Nardini, 2018 Signals of the electroweak phase transition at colliders and gravitational wave observatories J. High Energy Phys. JHEP07(2018)062 [1802.02168]
[20] S.A.R. Ellis, S. Ipek and G. White, 2019 Electroweak baryogenesis from temperature-varying couplings J. High Energy Phys. JHEP08(2019)002 [1905.11994]
[21] A. Alves, D. Gonçalves, T. Ghosh, H.-K. Guo and K. Sinha, 2020 Di-Higgs production in the 4b channel and gravitational wave complementarity J. High Energy Phys. JHEP03(2020)053 [1909.05268]
[22] A. Alves, T. Ghosh, H.-K. Guo, K. Sinha and D. Vagie, 2019 Collider and gravitational wave complementarity in exploring the singlet extension of the standard model J. High Energy Phys. JHEP04(2019)052 [1812.09333]
[23] J. Ellis, M. Lewicki, J.M. No and V. Vaskonen, 2019 Gravitational wave energy budget in strongly supercooled phase transitions J. Cosmol. Astropart. Phys.2019 06 024 [1903.09642]
[24] A.P. Morais and R. Pasechnik, 2020 Probing multi-step electroweak phase transition with multi-peaked primordial gravitational waves spectra J. Cosmol. Astropart. Phys.2020 04 036 [1910.00717]
[25] A. Addazi, A. Marcianò, and R. Pasechnik, 2019 Probing trans-electroweak first order phase transitions from gravitational waves, MDPI Physics1 92, [http://arxiv.org/abs/1811.09074]
[26] C. Wainwright, S. Profumo and M.J. Ramsey-Musolf, 2011 Gravity waves from a cosmological phase transition: gauge artifacts and daisy resummations, https://doi.org/10.1103/PhysRevD.84.023521 Phys. Rev. D84 023521 [1104.5487]
[27] R. Zhou, L. Bian and H.-K. Guo, 2020 Connecting the electroweak sphaleron with gravitational waves, https://doi.org/10.1103/PhysRevD.101.091903 Phys. Rev. D101 091903 [1910.00234]
[28] J. Bernon, L. Bian and Y. Jiang, 2018 A new insight into the phase transition in the early Universe with two Higgs doublets J. High Energy Phys. JHEP05(2018)151 [1712.08430]
[29] P. Schwaller, 2015 Gravitational waves from a dark phase transition, https://doi.org/10.1103/PhysRevLett.115.181101 Phys. Rev. Lett.115 181101 [1504.07263]
[30] J. Jaeckel, V.V. Khoze and M. Spannowsky, 2016 Hearing the signal of dark sectors with gravitational wave detectors, https://doi.org/10.1103/PhysRevD.94.103519 Phys. Rev. D94 103519 [1602.03901]
[31] M. Chala, G. Nardini and I. Sobolev, 2016 Unified explanation for dark matter and electroweak baryogenesis with direct detection and gravitational wave signatures, https://doi.org/10.1103/PhysRevD.94.055006 Phys. Rev. D94 055006 [1605.08663]
[32] A. Addazi, 2017 Limiting first order phase transitions in dark gauge sectors from gravitational waves experiments, https://doi.org/10.1142/S0217732317500493 Mod. Phys. Lett. A32 1750049 [1607.08057] · Zbl 1360.81316
[33] W. Chao, H.-K. Guo and J. Shu, 2017 Gravitational wave signals of electroweak phase transition triggered by dark matter J. Cosmol. Astropart. Phys.2017 09 009 [1702.02698]
[34] I. Baldes, 2017 Gravitational waves from the asymmetric-dark-matter generating phase transition J. Cosmol. Astropart. Phys.2017 05 028 [1702.02117]
[35] A. Addazi and A. Marciano, 2018 Gravitational waves from dark first order phase transitions and dark photons, https://doi.org/10.1088/1674-1137/42/2/023107 Chin. Phys. C42 023107 [1703.03248]
[36] D. Croon, V. Sanz and G. White, 2018 Model discrimination in gravitational wave spectra from dark phase transitions J. High Energy Phys. JHEP08(2018)203 [1806.02332]
[37] I. Baldes and C. Garcia-Cely, 2019 Strong gravitational radiation from a simple dark matter model J. High Energy Phys. JHEP05(2019)190 [1809.01198]
[38] M. Fairbairn, E. Hardy and A. Wickens, 2019 Hearing without seeing: gravitational waves from hot and cold hidden sectors J. High Energy Phys. JHEP07(2019)044 [1901.11038] · Zbl 1418.83013
[39] D. Dunsky, L.J. Hall and K. Harigaya, 2020 Dark matter, dark radiation and gravitational waves from mirror Higgs parity J. High Energy Phys. JHEP02(2020)078 [1908.02756]
[40] P. Archer-Smith, D. Linthorne and D. Stolarski, 2020 Gravitational wave signals from multiple hidden sectors, https://doi.org/10.1103/PhysRevD.101.095016 Phys. Rev. D101 095016 [1910.02083]
[41] E. Hall, T. Konstandin, R. McGehee and H. Murayama, Asymmetric matters from a dark first-order phase transition, [1911.12342]
[42] L. Bian, W. Cheng, H.-K. Guo and Y. Zhang, Gravitational waves triggered by B-L charged hidden scalar and leptogenesis, [1907.13589]
[43] X. Wang, F.P. Huang and X. Zhang, 2020 Phase transition dynamics and gravitational wave spectra of strong first-order phase transition in supercooled universe J. Cosmol. Astropart. Phys.2020 05 045 [2003.08892]
[44] D. Croon, T.E. Gonzalo and G. White, 2019 Gravitational waves from a Pati-Salam phase transition J. High Energy Phys. JHEP02(2019)083 [1812.02747]
[45] A. Greljo, T. Opferkuch and B.A. Stefanek, 2020 Gravitational imprints of flavor hierarchies, https://doi.org/10.1103/PhysRevLett.124.171802 Phys. Rev. Lett.124 171802 [1910.02014]
[46] W.-C. Huang, F. Sannino and Z.-W. Wang, 2020 Gravitational waves from Pati-Salam dynamics, https://doi.org/10.1103/PhysRevD.102.095025 Phys. Rev. D102 095025 [2004.02332]
[47] V. Brdar, L. Graf, A.J. Helmboldt and X.-J. Xu, 2019 Gravitational waves as a probe of left-right symmetry breaking J. Cosmol. Astropart. Phys.2019 12 027 [1909.02018]
[48] M. Hindmarsh, S.J. Huber, K. Rummukainen and D.J. Weir, 2014 Gravitational waves from the sound of a first order phase transition, https://doi.org/10.1103/PhysRevLett.112.041301 Phys. Rev. Lett.112 041301 [1304.2433]
[49] M. Hindmarsh, S.J. Huber, K. Rummukainen and D.J. Weir, 2015 Numerical simulations of acoustically generated gravitational waves at a first order phase transition, https://doi.org/10.1103/PhysRevD.92.123009 Phys. Rev. D92 123009 [1504.03291]
[50] M. Hindmarsh, S.J. Huber, K. Rummukainen and D.J. Weir, 2017 Shape of the acoustic gravitational wave power spectrum from a first order phase transition, https://doi.org/10.1103/PhysRevD.96.103520 Phys. Rev. D96 103520 [Erratum ibid 101 (2020) 089902] [1704.05871]
[51] J.R. Espinosa, T. Konstandin, J.M. No and G. Servant, 2010 Energy budget of cosmological first-order phase transitions J. Cosmol. Astropart. Phys.2010 06 028 [1004.4187]
[52] M. Hindmarsh, 2018 Sound shell model for acoustic gravitational wave production at a first-order phase transition in the early Universe, https://doi.org/10.1103/PhysRevLett.120.071301 Phys. Rev. Lett.120 071301 [1608.04735]
[53] M. Hindmarsh and M. Hijazi, 2019 Gravitational waves from first order cosmological phase transitions in the Sound Shell Model J. Cosmol. Astropart. Phys.2019 12 062 [1909.10040]
[54] J. Ellis, M. Lewicki and J.M. No, 2019 On the maximal strength of a first-order electroweak phase transition and its gravitational wave signal J. Cosmol. Astropart. Phys.2019 04 003 [1809.08242]
[55] J. Ellis, M. Lewicki and J.M. No, 2020 Gravitational waves from first-order cosmological phase transitions: lifetime of the sound wave source J. Cosmol. Astropart. Phys.2020 07 050 [2003.07360]
[56] G. Kane, K. Sinha and S. Watson, 2015 Cosmological moduli and the post-inflationary universe: a critical review, https://doi.org/10.1142/S0218271815300220 Int. J. Mod. Phys. D24 1530022 [1502.07746]
[57] R. Allahverdi et al., The first three seconds: a review of possible expansion histories of the early universe, [2006.16182]
[58] T. Banks, M. Berkooz, S.H. Shenker, G.W. Moore and P.J. Steinhardt, 1995 Modular cosmology, https://doi.org/10.1103/PhysRevD.52.3548 Phys. Rev. D52 3548 [hep-th/9503114]
[59] T. Banks, M. Berkooz and P.J. Steinhardt, 1995 The Cosmological moduli problem, supersymmetry breaking, and stability in postinflationary cosmology, https://doi.org/10.1103/PhysRevD.52.705 Phys. Rev. D52 705 [hep-th/9501053]
[60] G.D. Coughlan, W. Fischler, E.W. Kolb, S. Raby and G.G. Ross, 1983 Cosmological problems for the Polonyi potential, https://doi.org/10.1016/0370-2693(83)91091-2 Phys. Lett. B131 59
[61] T. Banks, D.B. Kaplan and A.E. Nelson, 1994 Cosmological implications of dynamical supersymmetry breaking, https://doi.org/10.1103/PhysRevD.49.779 Phys. Rev. D49 779 [hep-ph/9308292]
[62] B. Dutta, L. Leblond and K. Sinha, 2009 Mirage in the sky: non-thermal dark matter, gravitino problem, and cosmic ray anomalies, https://doi.org/10.1103/PhysRevD.80.035014 Phys. Rev. D80 035014 [0904.3773]
[63] R. Allahverdi, B. Dutta and K. Sinha, 2013 Successful supersymmetric dark matter with thermal over/under-abundance from late decay of a visible sector scalar, https://doi.org/10.1103/PhysRevD.87.075024 Phys. Rev. D87 075024 [1212.6948]
[64] B.S. Acharya, P. Kumar, K. Bobkov, G. Kane, J. Shao and S. Watson, 2008 Non-thermal dark matter and the moduli problem in string frameworks J. High Energy Phys. JHEP06(2008)064 [0804.0863]
[65] B.S. Acharya, G. Kane, S. Watson and P. Kumar, 2009 A non-thermal WIMP miracle, https://doi.org/10.1103/PhysRevD.80.083529 Phys. Rev. D80 083529 [0908.2430]
[66] A.L. Erickcek, K. Sinha and S. Watson, 2016 Bringing isolated dark matter out of isolation: late-time reheating and indirect detection, https://doi.org/10.1103/PhysRevD.94.063502 Phys. Rev. D94 063502 [1510.04291]
[67] M. Sten Delos, T. Linden and A.L. Erickcek, 2019 Breaking a dark degeneracy: the gamma-ray signature of early matter domination, https://doi.org/10.1103/PhysRevD.100.123546 Phys. Rev. D100 123546 [1910.08553]
[68] A.L. Erickcek, 2015 The dark matter annihilation boost from low-temperature reheating, https://doi.org/10.1103/PhysRevD.92.103505 Phys. Rev. D92 103505 [1504.03335]
[69] M. Drees and F. Hajkarim, 2018 Dark matter production in an early matter dominated era J. Cosmol. Astropart. Phys.2018 02 057 [1711.05007]
[70] C. Cosme, M.a. Dutra, T. Ma, Y. Wu and L. Yang, Neutrino portal to FIMP dark matter with an early matter era, [2003.01723]
[71] R. Allahverdi, B. Dutta and K. Sinha, 2010 Baryogenesis and late-decaying moduli, https://doi.org/10.1103/PhysRevD.82.035004 Phys. Rev. D82 035004 [1005.2804]
[72] C. Pallis, 2006 Kination-dominated reheating and cold dark matter abundance, https://doi.org/10.1016/j.nuclphysb.2006.06.003 Nucl. Phys. B751 129 [hep-ph/0510234]
[73] J. Lankinen, O. Kerppo and I. Vilja, 2020 Reheating via gravitational particle production in the kination epoch, https://doi.org/10.1103/PhysRevD.101.063529 Phys. Rev. D101 063529 [1910.07520]
[74] K. Nakayama and F. Takahashi, 2010 Running kinetic inflation J. Cosmol. Astropart. Phys.2010 11 009 [1008.2956]
[75] C. Pallis, 2005 Quintessential kination and cold dark matter abundance J. Cosmol. Astropart. Phys.2005 10 015 [hep-ph/0503080]
[76] D. Grin, T.L. Smith and M. Kamionkowski, 2008 Axion constraints in non-standard thermal histories, https://doi.org/10.1103/PhysRevD.77.085020 Phys. Rev. D77 085020 [0711.1352]
[77] K. Dimopoulos and T. Markkanen, 2018 Non-minimal gravitational reheating during kination J. Cosmol. Astropart. Phys.2018 06 021 [1803.07399]
[78] K. Redmond and A.L. Erickcek, 2017 New constraints on dark matter production during kination, https://doi.org/10.1103/PhysRevD.96.043511 Phys. Rev. D96 043511 [1704.01056]
[79] D. Bettoni, G. Domènech and J. Rubio, 2019 Gravitational waves from global cosmic strings in quintessential inflation J. Cosmol. Astropart. Phys.2019 02 034 [1810.11117]
[80] D. Bettoni and J. Rubio, 2020 Hubble-induced phase transitions: walls are not forever J. Cosmol. Astropart. Phys.2020 01 002 [1911.03484]
[81] S. Bhattacharya, S. Mohanty and P. Parashari, 2020 Primordial black holes and gravitational waves in nonstandard cosmologies, https://doi.org/10.1103/PhysRevD.102.043522 Phys. Rev. D102 043522 [1912.01653]
[82] G. Barenboim and W.-I. Park, 2016 Gravitational waves from first order phase transitions as a probe of an early matter domination era and its inverse problem, https://doi.org/10.1016/j.physletb.2016.06.009 Phys. Lett. B759 430 [1605.03781] · Zbl 1367.83101
[83] N. Bernal and F. Hajkarim, 2019 Primordial gravitational waves in nonstandard cosmologies, https://doi.org/10.1103/PhysRevD.100.063502 Phys. Rev. D100 063502 [1905.10410]
[84] C. Caprini and D.G. Figueroa, 2018 Cosmological backgrounds of gravitational waves, https://doi.org/10.1088/1361-6382/aac608 Class. Quant. Grav.35 163001 [1801.04268] · Zbl 1409.83039
[85] F. D’Eramo and K. Schmitz, 2019 Imprint of a scalar era on the primordial spectrum of gravitational waves, https://doi.org/10.1103/PhysRevResearch.1.013010 Phys. Rev. Research.1 013010 [1904.07870]
[86] M. Geller, A. Hook, R. Sundrum and Y. Tsai, 2018 Primordial anisotropies in the gravitational wave background from cosmological phase transitions, https://doi.org/10.1103/PhysRevLett.121.201303 Phys. Rev. Lett.121 201303 [1803.10780]
[87] Y. Cui, M. Lewicki, D.E. Morrissey and J.D. Wells, 2018 Cosmic archaeology with gravitational waves from cosmic strings, https://doi.org/10.1103/PhysRevD.97.123505 Phys. Rev. D97 123505 [1711.03104]
[88] S. Weinberg, 2008 Cosmology, Oxford University Press · Zbl 1147.83002
[89] A.D. Linde, 1981 Fate of the false vacuum at finite temperature: theory and applications, https://doi.org/10.1016/0370-2693(81)90281-1 Phys. Lett. B100 37
[90] A.D. Linde, 1983 Decay of the false vacuum at finite temperature, https://doi.org/10.1016/0550-3213(83)90072-X Nucl. Phys. B216 421 [Erratum ibid 223 (1983) 544]
[91] G.V. Dunne and H. Min, 2005 Beyond the thin-wall approximation: Precise numerical computation of prefactors in false vacuum decay, https://doi.org/10.1103/PhysRevD.72.125004 Phys. Rev. D72 125004 [hep-th/0511156]
[92] A. Andreassen, D. Farhi, W. Frost and M.D. Schwartz, 2017 Precision decay rate calculations in quantum field theory, https://doi.org/10.1103/PhysRevD.95.085011 Phys. Rev. D95 085011 [1604.06090]
[93] S. Weinberg, 2013 The quantum theory of fields. Vol. 2: modern applications, Cambridge University Press
[94] R.J. Scherrer and M.S. Turner, 1985 Decaying particles do not heat up the universe, https://doi.org/10.1103/PhysRevD.31.681 Phys. Rev. D31 681
[95] A.H. Guth and E.J. Weinberg, 1981 Cosmological consequences of a first order phase transition in the SU(5) grand unified model, https://doi.org/10.1103/PhysRevD.23.876 Phys. Rev. D23 876
[96] G.D. Moore and T. Prokopec, 1995 How fast can the wall move? A study of the electroweak phase transition dynamics, https://doi.org/10.1103/PhysRevD.52.7182 Phys. Rev. D52 7182 [hep-ph/9506475]
[97] R. Apreda, M. Maggiore, A. Nicolis and A. Riotto, 2002 Gravitational waves from electroweak phase transitions, https://doi.org/10.1016/S0550-3213(02)00264-X Nucl. Phys. B631 342 [gr-qc/0107033]
[98] R.-G. Cai and S.-J. Wang, 2018 Energy budget of cosmological first-order phase transition in FLRW background, https://doi.org/10.1007/s11433-018-9216-7 Sci. China Phys. Mech. Astron.61 080411 [1803.03002]
[99] J. Ignatius, K. Kajantie, H. Kurki-Suonio and M. Laine, 1994 The growth of bubbles in cosmological phase transitions, https://doi.org/10.1103/PhysRevD.49.3854 Phys. Rev. D49 3854 [astro-ph/9309059]
[100] H. Kurki-Suonio and M. Laine, 1996 On bubble growth and droplet decay in cosmological phase transitions, https://doi.org/10.1103/PhysRevD.54.7163 Phys. Rev. D54 7163 [hep-ph/9512202]
[101] B.-H. Liu, L.D. McLerran and N. Turok, 1992 Bubble nucleation and growth at a baryon number producing electroweak phase transition, https://doi.org/10.1103/PhysRevD.46.2668 Phys. Rev. D46 2668
[102] D. Cutting, M. Hindmarsh and D.J. Weir, 2020 Vorticity, kinetic energy, and suppressed gravitational wave production in strong first order phase transitions, https://doi.org/10.1103/PhysRevLett.125.021302 Phys. Rev. Lett.125 021302 [1906.00480]
[103] T. Konstandin, G. Nardini and I. Rues, 2014 From Boltzmann equations to steady wall velocities J. Cosmol. Astropart. Phys.2014 09 028 [1407.3132]
[104] A. Brandenburg, K. Enqvist and P. Olesen, 1996 Large scale magnetic fields from hydromagnetic turbulence in the very early universe, https://doi.org/10.1103/PhysRevD.54.1291 Phys. Rev. D54 1291 [astro-ph/9602031]
[105] R.M. Gailis, N.E. Frankel and C.P. Dettmann, 1995 Magnetohydrodynamics in the expanding Universe, https://doi.org/10.1103/PhysRevD.52.6901 Phys. Rev. D52 6901
[106] H. Kurki-Suonio and M. Laine, 1995 Supersonic deflagrations in cosmological phase transitions, https://doi.org/10.1103/PhysRevD.51.5431 Phys. Rev. D51 5431 [hep-ph/9501216]
[107] U.-L. Pen and N. Turok, 2016 Shocks in the early universe, https://doi.org/10.1103/PhysRevLett.117.131301 Phys. Rev. Lett.117 131301 [1510.02985]
[108] M. Dine, R.G. Leigh, P.Y. Huet, A.D. Linde and D.A. Linde, 1992 Towards the theory of the electroweak phase transition, https://doi.org/10.1103/PhysRevD.46.550 Phys. Rev. D46 550 [hep-ph/9203203]
[109] C.L. Wainwright, 2012 CosmoTransitions: computing cosmological phase transition temperatures and bubble profiles with multiple fields, https://doi.org/10.1016/j.cpc.2012.04.004 Comput. Phys. Commun.183 2006 [1109.4189]
[110] P. Athron, C. Balázs, M. Bardsley, A. Fowlie, D. Harries and G. White, 2019 BubbleProfiler: finding the field profile and action for cosmological phase transitions, https://doi.org/10.1016/j.cpc.2019.05.017 Comput. Phys. Commun.244 448 [1901.03714]
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.