# A Short Survey of Matter-Antimatter Evolution in the Primordial Universe

^{*}

## Abstract

**:**

## 1. Timeline of Particles and Plasmas in the Universe

#### 1.1. Guide to 130 GeV > 20 > keV

#### 1.2. The Five Plasma Epochs

- A
- Case of baryonic number (charge) conservation: In order to separate space domains in which either matter or antimatter is albeit very slightly dominant we need a ’force’ capable of dynamically creating this matter-antimatter separation. This requires that two of the three Sakharov [14,15] conditions be fulfilled:
- Violation of CP-invariance allowing to distinguish matter from antimatter
- Non-stationary conditions in absence of local thermodynamic equilibrium

- B
- There is no known cause for baryon charge conservation. Therefore it is possible to consider the full Sakharov model with
- 3.
- Absence of baryonic charge conservation

Allowing the dynamical formation of the uniform matter-antimatter asymmetry typically occurring prior to the epoch governed by physics confirmed by current experiment to which environs we restrict this short survey. A well studied example is the Affleck-Dine mechanism [20].

**Primordial quark-gluon plasma**: At early times when the temperature was between $130\phantom{\rule{4.pt}{0ex}}\mathrm{GeV}>T>150\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}$ we have the building blocks of the Universe as we know them today, including the leptons, vector bosons, and all three families of deconfined quarks and gluons which propagated freely. As all hadrons are dissolved into their constituents during this time, strongly interacting particles $u,d,s,t,b,c,g$ controlled the fate of the Universe. Here we will only look at the late-stage evolution at around $150\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}$.**Hadronic epoch**: Around the hadronization temperature ${T}_{h}\approx 150\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}$, a phase transformation occurred forcing the strongly interacting particles such as quarks and gluons to condense into confined states [22]. It is here where matter as we know it today forms and the Universe becomes hadronic-matter dominated. In the temperature range $150\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}>T>20\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}$ the Universe is rich in physics phenomena involving strange mesons and (anti)baryons including (anti)hyperon abundances [23,24].**Lepton-photon epoch**: For temperature $10\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}>T>2\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}$, the Universe contained relativistic electrons, positrons, photons, and three species of (anti)neutrinos. Muons vanish partway through this temperature scale. In this range, neutrinos were still coupled to the charged leptons via the weak interaction [25,26]. During this time the expansion of the Universe is controlled by leptons and photons almost on equal footing.**Final antimatter epoch**: After neutrinos decoupled and become free-streaming, referred to as neutrino freeze-out, from the cosmic plasma at $T=2\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}$, the cosmic plasma was dominated by electrons, positrons, and photons. We have shown in [27] that this plasma existed until $T\approx 0.02\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}$ such that BBN occurred within a rich electron-positron plasma. This is the last time the Universe will contain a significant fraction of its content in antimatter.**Moving towards a matter dominated Universe**: The final major plasma stage in the Universe began after the annihilation of the majority of ${e}^{\pm}$ pairs leaving behind a residual amount of electrons determined by the baryon asymmetry in the Universe and charge conservation. The Universe was still opaque to photons at this point and remained so until the recombination period at $T\approx 0.25\phantom{\rule{4.pt}{0ex}}\mathrm{eV}$ starting the era of observational cosmology with the CMB. This final epoch of the primordial Universe will not be described in detail here, but is well covered in [28].

**Figure 2.**Normalized Universe constituent matter and radiation components ${\Omega}_{i}$ are evolved over cosmological timescales (top scale, bottom scale is temperature T) from contemporary observational cosmology to the QGP epoch of the Universe. Vertical lines denote transitions between distinct epochs. Solid neutrino (green) line shows contribution of massless neutrinos, while the dashed line shows 1 massless and $2\times 0.1$ eV neutrinos (Neutrino mass choice is just for illustration. Other values are possible).

#### 1.3. The Lambda-CDM Universe

## 2. QGP Epoch

#### 2.1. Conservation Laws in QGP

- Electric charge neutrality $Q=0$, given by$$\begin{array}{c}\hfill \frac{Q}{V}={n}_{Q}\equiv \sum _{f}\phantom{\rule{0.166667em}{0ex}}{Q}_{f}\phantom{\rule{0.166667em}{0ex}}{n}_{f}({\mu}_{f},T)=0\end{array}$$
- Baryon number and lepton number neutrality $B-L=0$, given by$$\begin{array}{c}\hfill \frac{B-L}{V}={n}_{B}-{n}_{L}\equiv \sum _{f}({B}_{f}-{L}_{f}){n}_{f}({\mu}_{f},T)=0\end{array}$$
- The entropy-per-baryon density ratio $s/{n}_{B}$ is a constant and can be written as$$\begin{array}{c}\hfill \frac{S}{B}=\frac{s}{{n}_{B}}=\frac{{\sum}_{f}{s}_{f}({\mu}_{f},T)}{{\sum}_{f}{B}_{f}{n}_{f}({\mu}_{f},T)}=\mathrm{const}\end{array}$$

#### 2.2. Heavy Flavor: Bottom and Charm in QGP

## 3. Hadronic Epoch

#### 3.1. The Formation of Matter

#### 3.2. Strangeness Abundance

- Strangeness in the mesons
- Strangeness in the (anti)hyperons

#### 3.3. Pion Abundance

## 4. Leptonic Epoch

#### 4.1. Thermal Degrees of Freedom

#### 4.2. Muon Abundance

#### 4.3. Neutrino Masses and Oscillation

#### 4.4. Neutrino Freeze-Out

#### 4.5. Effective Number of Neutrinos

## 5. Electron-Positron Epoch

#### 5.1. The Last Bastion of Antimatter

#### 5.2. Cosmic Magnetism

#### 5.3. Landau Eigen-Energies in Cosmology

#### 5.4. Electron-Positron Statistical Physics

#### 5.5. Charge Neutrality and Chemical Potential

#### 5.6. Magnetization of the Electron-Positron Plasma

- The aligned polarized gas is described by ${\tilde{m}}_{+}={m}_{e}$ and $x={\tilde{m}}_{+}/T$. The magnetization of this contribution is therefore$$\begin{array}{cc}\hfill {M}_{+}& =\frac{e{T}^{2}}{{\pi}^{2}}\sqrt{1+{sinh}^{2}({\eta}_{e}/T)}\left(\frac{1}{2}{x}_{+}{K}_{1}\left({x}_{+}\right)+\frac{{b}_{0}}{6}{K}_{0}\left({x}_{+}\right)\right)\hfill \end{array}$$
- The spin anti-aligned gas has effective masses ${\tilde{m}}_{-}=\sqrt{{m}_{e}^{2}+2eB}$, and ${x}_{-}={\tilde{m}}_{-}/T$. This yields a magnetization contribution of$$\begin{array}{cc}\hfill {M}_{-}& =-\frac{e{T}^{2}}{{\pi}^{2}}\sqrt{1+{sinh}^{2}({\eta}_{e}/T)}\left[\left(\frac{1}{2}+\frac{{b}_{0}^{2}}{12{x}_{-}^{2}}\right){x}_{-}{K}_{1}\left({x}_{-}\right)+\frac{{b}_{0}}{3}{K}_{0}\left({x}_{-}\right)\right]\hfill \end{array}$$

## 6. Looking in the Cosmic Rear-View Mirror

**perseistnce of:**

- Strangeness abundance, present beyond the loss of the antibaryons at $T=38.2\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}$.
- Pions, which are equilibrated via photon production long after the other hadrons disappear; these lightest hadrons are also dominating the Universe baryon abundance down to $T=5.6\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}$.
- Muons, disappearing at around $T=4.2\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}$, the condition when their decay rate outpaces their production rate.

- The study of matter baryogenesis in the context of bottom quarks chemical non-equilibrium persistence near to QGP hadronization;
- The impact of relatively dense ${e}^{\pm}$ plasma on BBN processes;
- Exploration of spatial inhomogeneities in dense ${e}^{\pm}$ plasma and eventual large scale structure formation and related spontaneous self magnetization process.
- Appearance of a significant positron abundance at $T>25$ keV creates interest in understanding astrophysical object with core temperatures at, and beyond, this super-hot value; the high positron content enables in case of instability a rapid gamma ray formation akin to GRB events.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

**Figure 23.**ICRANet group at work, Remo Ruffini on right. Photo by Johann Rafelski.

**Figure 24.**Lizhi Fang (on right), his wife Shuxian Li (center) and Shufang Su (Today: Physics Department Head at the University of Arizona) in April 2004. Photo taken by Johann Rafelski at his home in Tucson.

**Figure 25.**Remo Ruffini (on left) and Johann Rafelski beneath a sunset in Tucson, AZ on October 7th, 2012. The photo was taken by She Sheng Xue at a celebratory gathering honoring the life of Lizhi Fang.

## Conflicts of Interest

## References

- Fang, L.; Ruffini, R. (Eds.) Cosmology of the Early Universe. In Advanced Series in Astrophysics and Cosmology; World Scientific: Singapore, 1984; Volume 1. [Google Scholar]
- Fang, L.; Ruffini, R. (Eds.) Galaxies, Quasars, and Cosmology. In Advanced Series in Astrophysics and Cosmology; World Scientific: Singapore, 1985; Volume 2. [Google Scholar]
- Fang, L.; Ruffini, R. (Eds.) Quantum cosmology. In Advanced Series in Astrophysics and Cosmology; World Scientific: Singapore, 1987; Volume 3. [Google Scholar]
- Ruffini, R.; Bianco, C.L.; Chardonnet, P.; Fraschetti, F.; Xue, S.S. On the interpretation of the burst structure of grbs. Astrophys. J. Lett.
**2001**, 555, L113–L116. [astro-ph/0106532]. [CrossRef] - Aksenov, A.G.; Bianco, C.L.; Ruffini, R.; Vereshchagin, G.V. GRBs and the thermalization process of electron-positron plasmas. AIP Conf. Proc.
**2008**, 1000, 309–312. [arXiv:astro-ph/0804.2807]. [CrossRef] - Aksenov, A.G.; Ruffini, R.; Vereshchagin, G.V. Pair plasma relaxation time scales. Phys. Rev. E
**2010**, 81, 046401. [arXiv:astroph.HE/1003.5616]. [CrossRef] [PubMed] - Ruffini, R.; Vereshchagin, G. Electron-positron plasma in GRBs and in cosmology. Nuovo Cim. C
**2013**, 036, 255–266. [arXiv:astroph.CO/1205.3512]. [CrossRef] - Ruffini, R.; Vitagliano, L.; Xue, S.S. Electron-positron-photon plasma around a collapsing star. In Proceedings of the 10th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (MG X MMIII), Rio de Janeiro, Brazil, 20–26 July 2003; pp. 295–302. [astro-ph/0304306]. [CrossRef]
- Ruffini, R.; Vereshchagin, G.; Xue, S.S. Electron-positron pairs in physics and astrophysics: From heavy nuclei to black holes. Phys. Rept.
**2010**, 487, 1–140. [arXiv:astro-ph.HE/0910.0974]. [CrossRef] - Ruffini, R.; Salmonson, J.D.; Wilson, J.R.; Xue, S.S. On the pair-electromagnetic pulse from an electromagnetic black hole surrounded by a baryonic remnant. Astron. Astrophys.
**2000**, 359, 855. [astro-ph/0004257]. - Han, W.B.; Ruffini, R.; Xue, S.S. Electron and positron pair production of compact stars. Phys. Rev. D
**2012**, 86, 84004. [arXiv:astro-ph.HE/1110.0700]. [CrossRef] - Belvedere, R.; Pugliese, D.; Rueda, J.A.; Ruffini, R.; Xue, S.S. Neutron star equilibrium configurations within a fully relativistic theory with strong, weak, electromagnetic, and gravitational interactions. Nucl. Phys. A
**2012**, 883, 1–24. [arXiv:astroph.SR/1202.6500]. [CrossRef] - Rafelski, J. Melting Hadrons, Boiling Quarks. Eur. Phys. J. A
**2015**, 51, 114. [arXiv:nucl-th/1508.03260]. [CrossRef] - Sakharov, A.D. Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe. Pisma Zh. Eksp. Teor. Fiz.
**1967**, 5, 32–35. [Google Scholar] [CrossRef] - Sakharov, A.D. Baryon asymmetry of the universe. Sov. Phys. Uspekhi
**1991**, 34, 417–421. [Google Scholar] [CrossRef] - Cohen, A.G.; De Rujula, A.; Glashow, S.L. A Matter-antimatter universe? Astrophys. J.
**1998**, 495, 539–549. [astro-ph/9707087]. [CrossRef] - Khlopov, M.Y.; Rubin, S.G.; Sakharov, A.S. Possible origin of antimatter regions in the baryon dominated universe. Phys. Rev. D
**2000**, 62, 083505. [hep-ph/0003285]. [CrossRef] - Blinnikov, S.I.; Dolgov, A.D.; Postnov, K.A. Antimatter and antistars in the universe and in the Galaxy. Phys. Rev. D
**2015**, 92, 023516. [arXiv:astro-ph.HE/1409.5736]. [CrossRef] - Khlopov, M.Y.; Lecian, O.M. The Formalism of Milky-Way Antimatter-Domains Evolution. Galaxies
**2023**, 11, 50. [Google Scholar] [CrossRef] - Affleck, I.; Dine, M. A New Mechanism for Baryogenesis. Nucl. Phys. B
**1985**, 249, 361–380. [Google Scholar] [CrossRef] - Rubakov, V.A.; Shaposhnikov, M.E. Electroweak baryon number nonconservation in the early universe and in high-energy collisions. Usp. Fiz. Nauk
**1996**, 166, 493–537. [hep-ph/9603208]. [CrossRef] - Letessier, J.; Rafelski, J. Hadron production and phase changes in relativistic heavy ion collisions. Eur. Phys. J. A
**2008**, 35, 221–242. [nucl-th/0504028]. [CrossRef] - Fromerth, M.J.; Kuznetsova, I.; Labun, L.; Letessier, J.; Rafelski, J. From Quark-Gluon Universe to Neutrino Decoupling: 200 < T < 2MeV. Acta Phys. Polon. B
**2012**, 43, 2261–2284. [arXiv:nucl-th/1211.4297]. [CrossRef] - Yang, C.T.; Rafelski, J. Cosmological strangeness abundance. Phys. Lett. B
**2022**, 827, 136944. [arXiv:hep-ph/2108.01752]. [CrossRef] - Birrell, J.; Yang, C.T.; Chen, P.; Rafelski, J. Relic neutrinos: Physically consistent treatment of effective number of neutrinos and neutrino mass. Phys. Rev. D
**2014**, 89, 23008. [arXiv:astro-ph.CO/1212.6943]. [CrossRef] - Birrell, J. Non-Equilibrium Aspects of Relic Neutrinos: From Freeze-out to the Present Day. Ph.D. Thesis, University of Arizona, Tucson, AZ, USA, 2014. [arXiv:nucl-th/1409.4500].
- Grayson, C.; Yang, C.T.; Rafelski, J. Electron-Positron Plasma in the BBN epoch. 2023; in preparation. [Google Scholar]
- Aghanim, N.; Akrami, Y.; Ashdown,, M.; Aumont, J.; Baccigalupi, C.; Ballardini, M.; Banday, A.J.; Barreiro, R.B.; Bartolo, N.; Basak, S.; et al. Planck 2018 results. VI. Cosmological parameters. Astron. Astrophys.
**2021**, 641, A6. [arXiv:astro-ph.CO/1807.06209]. [CrossRef] - Rafelski, J.; Birrell, J. Traveling Through the Universe: Back in Time to the Quark-Gluon Plasma Era. J. Phys. Conf. Ser.
**2014**, 509, 012014. [arXiv:nucl-th/1311.0075]. [CrossRef] - Wantz, O.; Shellard, E.P.S. Axion Cosmology Revisited. Phys. Rev. D
**2010**, 82, 123508. [arXiv:astro-ph.CO/0910.1066]. [CrossRef] - Kronfeld, A.S. Lattice Gauge Theory and the Origin of Mass. In 100 Years of Subatomic Physics; World Scientific: Singapore, 2013; pp. 493–518. [arXiv:physics.hist-ph/1209.3468]. [CrossRef]
- D’Elia, M.; Mariti, M.; Negro, F. Susceptibility of the QCD vacuum to CP-odd electromagnetic background fields. Phys. Rev. Lett.
**2013**, 110, 082002. [arXiv:hep-lat/1209.0722]. [CrossRef] [PubMed] - Bonati, C.; Cossu, G.; D’Elia, M.; Mariti, M.; Negro, F. Effective θ term by CP-odd electromagnetic background fields. PoS
**2014**, LATTICE2013, 360. [arXiv:hep-lat/1312.2805]. [CrossRef] - Borsanyi, S. Thermodynamics of the QCD transition from lattice. Nucl. Phys. A
**2013**, 904–905, 270c–277c. [arXiv:heplat/1210.6901]. [CrossRef] - Borsanyi, S.; Fodor, Z.; Hoelbling, C.; Katz, S.D.; Krieg, S.; Szabo, K.K. Full result for the QCD equation of state with 2 + 1 flavors. Phys. Lett. B
**2014**, 730, 99–104. [arXiv:hep-lat/1309.5258]. [CrossRef] - Bernstein, J. Kinetic Theory in the Expanding Universe; Cambridge Monographs on Mathematical Physics, Cambridge University Press: Cambridge, UK, 1988. [Google Scholar] [CrossRef]
- Philipsen, O. The QCD equation of state from the lattice. Prog. Part. Nucl. Phys.
**2013**, 70, 55–107. [arXiv:hep-lat/1207.5999]. [CrossRef] - Mangano, G.; Miele, G.; Pastor, S.; Pinto, T.; Pisanti, O.; Serpico, P.D. Relic neutrino decoupling including flavor oscillations. Nucl. Phys. B
**2005**, 729, 221–234. [hep-ph/0506164]. [CrossRef] - Fornengo, N.; Kim, C.W.; Song, J. Finite temperature effects on the neutrino decoupling in the early universe. Phys. Rev. D
**1997**, 56, 5123–5134. [hep-ph/9702324]. [CrossRef] - Mangano, G.; Miele, G.; Pastor, S.; Peloso, M. A Precision calculation of the effective number of cosmological neutrinos. Phys. Lett. B
**2002**, 534, 8–16. [astro-ph/0111408]. [CrossRef] - Planck Collaboration. Planck 2013 results. XVI. Cosmological parameters. Astron. Astrophys.
**2014**, 571, A16. [arXiv:astroph.CO/1303.5076]. [CrossRef] - Planck Collaboration. Planck 2015 results. XIII. Cosmological parameters. Astron. Astrophys.
**2016**, 594, A13. [arXiv:astroph.CO/1502.01589]. [CrossRef] - Caldwell, R.R.; Kamionkowski, M.; Weinberg, N.N. Phantom energy and cosmic doomsday. Phys. Rev. Lett.
**2003**, 91, 071301. [astro-ph/0302506]. [CrossRef] - Bilic, N.; Tupper, G.B.; Viollier, R.D. Unification of dark matter and dark energy: The Inhomogeneous Chaplygin gas. Phys. Lett. B
**2002**, 535, 17–21. [astro-ph/0111325]. [CrossRef] - Benevento, G.; Hu, W.; Raveri, M. Can Late Dark Energy Transitions Raise the Hubble constant? Phys. Rev. D
**2020**, 101, 103517. [arXiv:astro-ph.CO/2002.11707]. [CrossRef] - Perivolaropoulos, L.; Skara, F. Challenges for ΛCDM: An update. New Astron. Rev.
**2022**, 95, 101659. [arXiv:astroph.CO/2105.05208]. [CrossRef] - Di Valentino, E.; Mena, O.; Pan, S.; Visinelli, L.; Yang, W.; Melchiorri, A.; Mota, D.F.; Riess, A.G.; Silk, J. In the realm of the Hubble tension—A review of solutions. Class. Quant. Grav.
**2021**, 38, 153001. [arXiv:astro-ph.CO/2103.01183]. [CrossRef] - Aluri, P.K.; Cea, P.; Chingangbam, P.; Chu, M.C.; Clowes, R.G.; Hutsemekers, D.; Kochappan, J.P.; Lopez, A.M.; Liu, L.; Liu, L.; et al. Is the observable Universe consistent with the cosmological principle? Class. Quant. Grav.
**2023**, 40, 094001. [arXiv:astro-ph.CO/2207.05765]. [CrossRef] - Yan, H.; Ma, Z.; Ling, C.; Cheng, C.; Huang, J.S. First Batch of z ≈ 11–20 Candidate Objects Revealed by the James Webb Space Telescope Early Release Observations on SMACS 0723-73. Astrophys. J. Lett.
**2023**, 942, L9. [arXiv:astro-ph.GA/2207.11558]. [CrossRef] - Weinberg, S. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity; John Wiley and Sons: New York, NY, USA, 1972. [Google Scholar]
- Castellani, V.; Degl’Innocenti, S.; Fiorentini, G.; Lissia, M.; Ricci, B. Solar neutrinos: Beyond standard solar models. Phys. Rept.
**1997**, 281, 309–398. [astro-ph/9606180]. [CrossRef] - Rafelski, J.; Letessier, J.; Torrieri, G. Strange hadrons and their resonances: A Diagnostic tool of QGP freezeout dynamics. Phys. Rev. C
**2002**, 64, 054907. [Google Scholar] [CrossRef] - Ollitrault, J.Y. Anisotropy as a signature of transverse collective flow. Phys. Rev. D
**1992**, 46, 229–245. [Google Scholar] [CrossRef] [PubMed] - Petrán, M.; Letessier, J.; Petráček, V.; Rafelski, J. Hadron production and quark-gluon plasma hadronization in Pb-Pb collisions at s
_{NN}=2.76 TeV. Phys. Rev. C**2013**, 88, 034907. [arXiv:hep-ph/1303.2098]. [CrossRef] - Ryu, S.; Paquet, J.F.; Shen, C.; Denicol, G.S.; Schenke, B.; Jeon, S.; Gale, C. Importance of the Bulk Viscosity of QCD in Ultrarelativistic Heavy-Ion Collisions. Phys. Rev. Lett.
**2015**, 115, 132301. [arXiv:nucl-th/1502.01675]. [CrossRef] - Rafelski, J. Formation and Observables of the Quark-Gluon Plasma. Phys. Rept.
**1982**, 88, 331. [Google Scholar] - Rafelski, J.; Schnabel, A. Quark-Gluon Plasma in Nuclear Collisions at 200-GeV/A. Phys. Lett. B
**1988**, 207, 6–10. [Google Scholar] [CrossRef] - Letessier, J.; Rafelski, J. Hadrons and Quark–Gluon Plasma; Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology; Cambridge University Press: Cambridge, UK, 2023. [Google Scholar] [CrossRef]
- Bazavov, A.; Bhattacharya, T.; DeTar, C.; Ding, H.-T.; Gottlieb, S.; Gupta, R.; Hegde, P.; Heller, U.; Karsch, F.; Laermann, E.; et al. Equation of state in (2 + 1)-flavor QCD. Phys. Rev. D
**2014**, 90, 094503. [arXiv:hep-lat/1407.6387]. [CrossRef] - Jacak, B.V.; Muller, B. The exploration of hot nuclear matter. Science
**2012**, 337, 310–314. [Google Scholar] [CrossRef] - Fromerth, M.J.; Rafelski, J. Hadronization of the Quark Universe; University of Arizona: Tucson, AZ, USA, 2005; [astro-ph/0211346].
- Rafelski, J. Discovery of Quark-Gluon-Plasma: Strangeness Diaries. Eur. Phys. J. ST
**2020**, 229, 1–140. [arXiv:hep-ph/1911.00831]. [CrossRef] - Yang, C.T.; Rafelski, J. Possibility of bottom-catalyzed matter genesis near to primordial QGP hadronization. arXiv
**2023**, arXiv:2004.06771. [arXiv:hep-ph/2004.06771]. - Roberts, C.D. On Mass and Matter. AAPPS Bull.
**2021**, 31, 6. [arXiv:hep-ph/2101.08340]. [CrossRef] - Roberts, C.D. Origin of the Proton Mass. EPJ Web Conf.
**2023**, 282, 01006. [arXiv:hep-ph/2211.09905]. [CrossRef] - Hagedorn, R. How We Got to QCD Matter from the Hadron Side: 1984. Lect. Notes Phys.
**1985**, 221, 53–76. [Google Scholar] [CrossRef] - Fromerth, M.J.; Rafelski, J. Limit on CPT violating quark anti-quark mass difference from the neutral kaon system. Acta Phys. Polon. B
**2003**, 34, 4151–4156. [hep-ph/0211362]. - Tanabashi, M. et al. (Particle Data Group) Review of Particle Physics. Phys. Rev. D
**2018**, 98, 030001. [Google Scholar] [CrossRef] - Kolb, E.W.; Turner, M.S. The Early Universe; CRC Press: Boca Raton, FL, USA, 1990. [Google Scholar]
- Kuznetsova, I.; Habs, D.; Rafelski, J. Pion and muon production in e−, e+, gamma plasma. Phys. Rev. D
**2008**, 78, 014027. [arXiv:hep-ph/0803.1588]. [CrossRef] - Kuznetsova, I.; Rafelski, J. Unstable Hadrons in Hot Hadron Gas in Laboratory and in the Early Universe. Phys. Rev. C
**2010**, 82, 035203. [arXiv:hep-th/1002.0375]. [CrossRef] - Rafelski, J.; Yang, C.T. The muon abundance in the primordial Universe. Acta Phys. Polon. B
**2021**, 52, 277. [arXiv:hepph/2103.07812]. [CrossRef] - Kuznetsova, I. Particle Production in Matter at Extreme Conditions. Master’s Thesis, The University of Arizona, Tucson, AZ, USA, 2009. [arXiv:hep-th/0909.0524].
- Kopp, J.; Maltoni, M.; Schwetz, T. Are There Sterile Neutrinos at the eV Scale? Phys. Rev. Lett.
**2011**, 107, 091801. [arXiv:hepph/1103.4570]. [CrossRef] - Hamann, J.; Hannestad, S.; Raffelt, G.G.; Wong, Y.Y.Y. Sterile neutrinos with eV masses in cosmology: How disfavoured exactly? J. Cosmol. Astropart. Phys.
**2011**, 9, 34. [arXiv:astro-ph.CO/1108.4136]. [CrossRef] - Kopp, J.; Machado, P.A.N.; Maltoni, M.; Schwetz, T. Sterile Neutrino Oscillations: The Global Picture. J. High Energy Phys.
**2013**, 5, 50. [arXiv:hep-ph/1303.3011]. [CrossRef] - Lello, L.; Boyanovsky, D. Cosmological Implications of Light Sterile Neutrinos produced after the QCD Phase Transition. Phys. Rev. D
**2015**, 91, 063502. [arXiv:astro-ph.CO/1411.2690]. [CrossRef] - Birrell, J.; Rafelski, J. Proposal for Resonant Detection of Relic Massive Neutrinos. Eur. Phys. J. C
**2015**, 75, 91. [arXiv:hepph/1402.3409]. [CrossRef] - Weinberg, S. Goldstone Bosons as Fractional Cosmic Neutrinos. Phys. Rev. Lett.
**2013**, 110, 241301. [arXiv:astro-ph.CO/1305.1971]. [CrossRef] [PubMed] - Giusarma, E.; Di Valentino, E.; Lattanzi, M.; Melchiorri, A.; Mena, O. Relic Neutrinos, thermal axions and cosmology in early 2014. Phys. Rev. D
**2014**, 90, 043507. [arXiv:astro-ph.CO/1403.4852]. [CrossRef] - Fukuda, Y.; Hayakawa, T.; Ichihara, E.; Inoue, K.; Ishihara, K.; Ishino, H.; Itow, Y.; Kajita, T.; Kameda, J.; Kasuga, S.; et al. Evidence for oscillation of atmospheric neutrinos. Phys. Rev. Lett.
**1998**, 81, 1562–1567. [hep-ex/9807003]. [CrossRef] - Eguchi, K.; Enomoto, S.; Furuno, K.; Goldman, J.; Hanada, H.; Ikeda, H.; Ikeda, K.; Inoue, K.; Ishihara, K.; Itoh, W.; et al. First results from KamLAND: Evidence for reactor antineutrino disappearance. Phys. Rev. Lett.
**2003**, 90, 21802. [hep-ex/0212021]. [CrossRef] [PubMed] - Fogli, G.L.; Lisi, E.; Marrone, A.; Palazzo, A. Global analysis of three-flavor neutrino masses and mixings. Prog. Part. Nucl. Phys.
**2006**, 57, 742–795. [hep-ph/0506083]. [CrossRef] - Giunti, C.; Studenikin, A. Neutrino electromagnetic interactions: A window to new physics. Rev. Mod. Phys.
**2015**, 87, 531. [arXiv:hep-ph/1403.6344]. [CrossRef] - Fritzsch, H.; Xing, Z.Z. Mass and flavor mixing schemes of quarks and leptons. Prog. Part. Nucl. Phys.
**2000**, 45, 1–81. [hep-ph/9912358]. [CrossRef] - Giunti, C.; Kim, C.W. Fundamentals of Neutrino Physics and Astrophysics; Oxford University Press: Oxford, UK, 2007. [Google Scholar]
- Fritzsch, H. Neutrino Masses and Flavor Mixing. Mod. Phys. Lett. A
**2015**, 30, 1530012. [arXiv:hep-ph/1503.01857]. [CrossRef] - Dolinski, M.J.; Poon, A.W.P.; Rodejohann, W. Neutrinoless Double-Beta Decay: Status and Prospects. Ann. Rev. Nucl. Part. Sci.
**2019**, 69, 219–251. [arXiv:nucl-ex/1902.04097]. [CrossRef] - Arkani-Hamed, N.; Dimopoulos, S.; Dvali, G.R.; March-Russell, J. Neutrino masses from large extra dimensions. Phys. Rev. D
**2001**, 65, 024032. [hep-ph/9811448]. [CrossRef] - Ellis, J.R.; Lola, S. Can neutrinos be degenerate in mass? Phys. Lett. B
**1999**, 458, 310–321. [hep-ph/9904279]. [CrossRef] - Casas, J.A.; Ibarra, A. Oscillating neutrinos and μ→e,γ. Nucl. Phys. B
**2001**, 618, 171–204. [hep-ph/0103065]. [CrossRef] - King, S.F.; Luhn, C. Neutrino Mass and Mixing with Discrete Symmetry. Rept. Prog. Phys.
**2013**, 76, 56201. [arXiv:hepph/1301.1340]. [CrossRef] - Fernandez-Martinez, E.; Hernandez-Garcia, J.; Lopez-Pavon, J. Global constraints on heavy neutrino mixing. J. High Energy Phys.
**2016**, 8, 33. [arXiv:hep-ph/1605.08774]. [CrossRef] - Pascoli, S.; Petcov, S.T.; Riotto, A. Leptogenesis and Low Energy CP Violation in Neutrino Physics. Nucl. Phys. B
**2007**, 774, 1–52. [hep-ph/0611338]. [CrossRef] - Schwartz, M.D. Quantum Field Theory and the Standard Model; Cambridge University Press: Cambridge, UK, 2014. [Google Scholar]
- Particle Data Group. Review of Particle Physics. Prog. Theor. Exp. Phys.
**2022**, 2022, 083C01. [Google Scholar] [CrossRef] - Avignone, F.T., III; Elliott, S.R.; Engel, J. Double Beta Decay, Majorana Neutrinos, and Neutrino Mass. Rev. Mod. Phys.
**2008**, 80, 481–516. [arXiv:nucl-ex/0708.1033]. [CrossRef] - Esteban, I.; Gonzalez-Garcia, M.C.; Maltoni, M.; Schwetz, T.; Zhou, A. The fate of hints: Updated global analysis of three-flavor neutrino oscillations. J. High Energy Phys.
**2020**, 9, 178. [arXiv:hep-ph/2007.14792]. [CrossRef] - Alvarez-Ruso, L.; Sajjad Athar, M.; Barbaro, M.B.; Cherdack, D.; Christy, M.E.; Coloma, P.; Donnelly, T.W.; Dytman, S.; de Gouvea, A.; Hill, R.J.; et al. NuSTEC White Paper: Status and challenges of neutrino–nucleus scattering. Prog. Part. Nucl. Phys.
**2018**, 100, 1–68. [arXiv:hep-ph/1706.03621]. [CrossRef] - Abi, B.; Acciarri, R.; Acero, M.A.; Adamov, G.; Adams, D.; Adinolfi, M.; Ahmad, Z.; Ahmed, J.; Alion, T.; Monsalve, S.A.; et al. Deep Underground Neutrino Experiment (DUNE), Far Detector Technical Design Report, Volume II: DUNE Physics. arXiv
**2002**, arXiv:2002.03005. [arXiv:hep-ex/2002.03005]. - Morgan, J.A. Cosmological upper limit to neutrino magnetic moments. Phys. Lett. B
**1981**, 102, 247–250. [Google Scholar] [CrossRef] - Fukugita, M.; Yazaki, S. Reexamination of Astrophysical and Cosmological Constraints on the Magnetic Moment of Neutrinos. Phys. Rev. D
**1987**, 36, 3817. [Google Scholar] [CrossRef] [PubMed] - Vogel, P.; Engel, J. Neutrino Electromagnetic Form-Factors. Phys. Rev. D
**1989**, 39, 3378. [Google Scholar] [CrossRef] - Elmfors, P.; Enqvist, K.; Raffelt, G.; Sigl, G. Neutrinos with magnetic moment: Depolarization rate in plasma. Nucl. Phys. B
**1997**, 503, 3–23. [hep-ph/9703214]. [CrossRef] - Giunti, C.; Studenikin, A. Neutrino electromagnetic properties. Phys. Atom. Nucl.
**2009**, 72, 2089–2125. [arXiv:hep-ph/0812.3646]. [CrossRef] - Canas, B.C.; Miranda, O.G.; Parada, A.; Tortola, M.; Valle, J.W.F. Updating neutrino magnetic moment constraints. Phys. Lett. B
**2016**, 753, 191–198. [arXiv:hep-ph/1510.01684]. [CrossRef] - Choquet-Bruhat, Y. General Relativity and the Einstein Equations; Oxford University Press: Oxford, UK, 2008. [Google Scholar]
- Birrell, J.; Wilkening, J.; Rafelski, J. Boltzmann Equation Solver Adapted to Emergent Chemical Non-equilibrium. J. Comput. Phys.
**2015**, 281, 896–916. [arXiv:math.NA/1403.2019]. [CrossRef] - Birrell, J.; Yang, C.T.; Rafelski, J. Relic Neutrino Freeze-out: Dependence on Natural Constants. Nucl. Phys. B
**2014**, 890, 481–517. [arXiv:nucl-th/1406.1759]. [CrossRef] - Dreiner, H.K.; Hanussek, M.; Kim, J.S.; Sarkar, S. Gravitino cosmology with a very light neutralino. Phys. Rev. D
**2012**, 85, 65027. [arXiv:hep-ph/1111.5715]. [CrossRef] - Boehm, C.; Dolan, M.J.; McCabe, C. Increasing Neff with particles in thermal equilibrium with neutrinos. J. Cosmol. Astropart. Phys.
**2012**, 12, 27. [arXiv:astro-ph.CO/1207.0497]. [CrossRef] - Blennow, M.; Fernandez-Martinez, E.; Mena, O.; Redondo, J.; Serra, P. Asymmetric Dark Matter and Dark Radiation. J. Cosmol. Astropart. Phys.
**2012**, 7, 22. [arXiv:hep-ph/1203.5803]. [CrossRef] - Dicus, D.A.; Kolb, E.W.; Gleeson, A.M.; Sudarshan, E.C.G.; Teplitz, V.L.; Turner, M.S. Primordial Nucleosynthesis Including Radiative, Coulomb, and Finite Temperature Corrections to Weak Rates. Phys. Rev. D
**1982**, 26, 2694. [Google Scholar] [CrossRef] - Heckler, A.F. Astrophysical applications of quantum corrections to the equation of state of a plasma. Phys. Rev. D
**1994**, 49, 611–617. [Google Scholar] [CrossRef] - Mangano, G.; Miele, G.; Pastor, S.; Pinto, T.; Pisanti, O.; Serpico, P.D. Effects of non-standard neutrino-electron interactions on relic neutrino decoupling. Nucl. Phys. B
**2006**, 756, 100–116. [hep-ph/0607267]. [CrossRef] - Anchordoqui, L.A.; Goldberg, H. Neutrino cosmology after WMAP 7-Year data and LHC first Z’ bounds. Phys. Rev. Lett.
**2012**, 108, 81805. [arXiv:hep-ph/1111.7264]. [CrossRef] [PubMed] - Abazajian, K.N.; Acero, M.A.; Agarwalla, S.K.; Aguilar-Arevalo, A.A.; Albright, C.H.; Antusch, S.; Arguelles, C.A.; Balantekin, A.B.; Barenboim, G.; Barger, V.; et al. Light Sterile Neutrinos: A White Paper. arXiv
**2012**, arXiv:1204.5379. [arXiv:hep-ph/1204.5379]. - Anchordoqui, L.A.; Goldberg, H.; Steigman, G. Right-Handed Neutrinos as the Dark Radiation: Status and Forecasts for the LHC. Phys. Lett. B
**2013**, 718, 1162–1165. [arXiv:hep-ph/1211.0186]. [CrossRef] - Steigman, G. Equivalent Neutrinos, Light WIMPs, and the Chimera of Dark Radiation. Phys. Rev. D
**2013**, 87, 103517. [arXiv:astro-ph.CO/1303.0049]. [CrossRef] - Birrell, J.; Rafelski, J. Quark–gluon plasma as the possible source of cosmological dark radiation. Phys. Lett. B
**2015**, 741, 77–81. [arXiv:nucl-th/1404.6005]. [CrossRef] - Barenboim, G.; Kinney, W.H.; Park, W.I. Resurrection of large lepton number asymmetries from neutrino flavor oscillations. Phys. Rev. D
**2017**, 95, 43506. [arXiv:hep-ph/1609.01584]. [CrossRef] - Barenboim, G.; Park, W.I. A full picture of large lepton number asymmetries of the Universe. J. Cosmol. Astropart. Phys.
**2017**, 4, 48. [arXiv:hepph/1703.08258]. [CrossRef] - Yang, C.T.; Birrell, J.; Rafelski, J. Lepton Number and Expansion of the Universe. arXiv
**2018**, arXiv:1812.05157. [arXiv:hep-ph/1812.05157]. - Pitrou, C.; Coc, A.; Uzan, J.P.; Vangioni, E. Precision big bang nucleosynthesis with improved Helium-4 predictions. Phys. Rept.
**2018**, 754, 1–66. [arXiv:astro-ph.CO/1801.08023]. [CrossRef] - Wang, B.; Bertulani, C.A.; Balantekin, A.B. Electron screening and its effects on Big-Bang nucleosynthesis. Phys. Rev. C
**2011**, 83, 18801. [arXiv:astro-ph.CO/1010.1565]. [CrossRef] - Hwang, E.; Jang, D.; Park, K.; Kusakabe, M.; Kajino, T.; Balantekin, A.B.; Maruyama, T.; Ryu, C.M.; Cheoun, M.K. Dynamical screening effects on big bang nucleosynthesis. J. Cosmol. Astropart. Phys.
**2021**, 11, 17. [arXiv:nucl-th/2102.09801]. [CrossRef] - Bahcall, J.N.; Pinsonneault, M.H.; Basu, S. Solar models: Current epoch and time dependences, neutrinos, and helioseismological properties. Astrophys. J.
**2001**, 555, 990–1012. [astro-ph/0010346]. [CrossRef] - Kronberg, P.P. Extragalactic magnetic fields. Rept. Prog. Phys.
**1994**, 57, 325–382. [Google Scholar] [CrossRef] - Anchordoqui, L.A.; Goldberg, H. A Lower bound on the local extragalactic magnetic field. Phys. Rev. D
**2002**, 65, 21302. [hep-ph/0106217]. [CrossRef] - Widrow, L.M. Origin of galactic and extragalactic magnetic fields. Rev. Mod. Phys.
**2002**, 74, 775–823. [astro-ph/0207240]. [CrossRef] - Neronov, A.; Vovk, I. Evidence for strong extragalactic magnetic fields from Fermi observations of TeV blazars. Science
**2010**, 328, 73–75. [arXiv:astro-ph.HE/1006.3504]. [CrossRef] [PubMed] - Widrow, L.M.; Ryu, D.; Schleicher, D.R.G.; Subramanian, K.; Tsagas, C.G.; Treumann, R.A. The First Magnetic Fields. Space Sci. Rev.
**2012**, 166, 37–70. [arXiv:astro-ph.CO/1109.4052]. [CrossRef] - Vazza, F.; Locatelli, N.; Rajpurohit, K.; Banfi, S.; Dominguez-Fernandez, P.; Wittor, D.; Angelinelli, M.; Inchingolo, G.; Brienza, M.; Hackstein, S.; et al. Magnetogenesis and the Cosmic Web: A Joint Challenge for Radio Observations and Numerical Simulations. Galaxies
**2021**, 9, 109. [arXiv:astro-ph.CO/2111.09129]. [CrossRef] - Berezhiani, V.; Tsintsadze, L.; Shukla, P. Influence of electron-positron pairs on the wakefields in plasmas. Phys. Scr.
**1992**, 46, 55. [Google Scholar] [CrossRef] - Berezhiani, V.; Mahajan, S. Large relativistic density pulses in electron-positron-ion plasmas. Phys. Rev. E
**1995**, 52, 1968. [Google Scholar] [CrossRef] - Schlickeiser, R.; Kolberg, U.; Yoon, P.H. Primordial Plasma Fuctuations. I. Magnetization of the Early Universe by Dark Aperiodic Fluctuations in the Past Myon and Prior Electron–Positron Annihilation Epoch. Astrophys. J.
**2018**, 857, 29. [Google Scholar] [CrossRef] - Melrose, D. Quantum Plasmadynamics: Magnetized Plasmas; Springer: Berlin/Heidelberg, Germany, 2013. [Google Scholar] [CrossRef]
- Rafelski, J.; Formanek, M.; Steinmetz, A. Relativistic Dynamics of Point Magnetic Moment. Eur. Phys. J. C
**2018**, 78, 6. [arXiv:physics.class-ph/1712.01825]. [CrossRef] - Formanek, M.; Evans, S.; Rafelski, J.; Steinmetz, A.; Yang, C.T. Strong fields and neutral particle magnetic moment dynamics. Plasma Phys. Control. Fusion
**2018**, 60, 74006. [arXiv:hep-ph/1712.07698]. [CrossRef] - Formanek, M.; Steinmetz, A.; Rafelski, J. Radiation reaction friction: Resistive material medium. Phys. Rev. D
**2020**, 102, 56015. [arXiv:hep-ph/2004.09634]. [CrossRef] - Formanek, M.; Steinmetz, A.; Rafelski, J. Motion of classical charged particles with magnetic moment in external plane-wave electromagnetic fields. Phys. Rev. A
**2021**, 103, 52218. [arXiv:physics.class-ph/2103.02594]. [CrossRef] - Thaller, B. The Dirac Equation; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2013. [Google Scholar]
- Strickland, M.; Dexheimer, V.; Menezes, D.P. Bulk Properties of a Fermi Gas in a Magnetic Field. Phys. Rev. D
**2012**, 86, 125032. [arXiv:nucl-th/1209.3276]. [CrossRef] - Steinmetz, A.; Formanek, M.; Rafelski, J. Magnetic Dipole Moment in Relativistic Quantum Mechanics. Eur. Phys. J. A
**2019**, 55, 40. [arXiv:hep-ph/1811.06233]. [CrossRef] - Rafelski, J.; Evans, S.; Labun, L. Study of QED singular properties for variable gyromagnetic ratio g≃2. Phys. Rev. D
**2023**, 107, 76002. [arXiv:hep-th/2212.13165]. [CrossRef] - Elze, H.T.; Greiner, W.; Rafelski, J. The relativistic ideal Fermi gas revisited. J. Phys. G
**1980**, 6, L149–L153. [Google Scholar] [CrossRef] - Borsanyi, S.; Fodor, Z.; Guenther, J.; Kampert, K.-H.; Katz, S.D.; Kawanai, T.; Kovacs, T.G.; Mages, S.W.; Pasztor, A.; Pittler, F.; et al. Calculation of the axion mass based on high-temperature lattice quantum chromodynamics. Nature
**2016**, 539, 69–71. [arXiv:hep-lat/1606.07494]. [CrossRef] [PubMed] - Rafelski, J. Connecting QGP-Heavy Ion Physics to the Early Universe. Nucl. Phys. B Proc. Suppl.
**2013**, 243–244, 155–162. [arXiv:astro-ph.CO/1306.2471]. [CrossRef] - Aksenov, A.G.; Ruffini, R.; Vereshchagin, G.V. Thermalization of electron-positron-photon plasmas with an application to GRB. AIP Conf. Proc.
**2008**, 966, 191–196. [Google Scholar] [CrossRef] - Burns, E.; Svinkin, D.; Fenimore, E.; Kann, D.A.; Fernandez, J.F.A.; Frederiks, D.; Hamburg, R.; Lesage, S.; Temiraev, Y.; Tsvetkova, A.; et al. GRB 221009A: The BOAT. Astrophys. J. Lett.
**2023**, 946, L31. [arXiv:astro-ph.HE/2302.14037]. [CrossRef] - Levan, A.J.; Lamb, G.P.; Schneider, B.; Hjorth, J.; Zafar, T.; Postigo, A.D.; Sargent, B.; Mullally, S.E.; Izzo, L.; D’Avanzo, P.; et al. The First JWST Spectrum of a GRB Afterglow: No Bright Supernova in Observations of the Brightest GRB of all Time, GRB 221009A. Astrophys. J. Lett.
**2023**, 946, L28. [arXiv:astro-ph.HE/2302.07761]. [CrossRef] - Davis, M.; Efstathiou, G.; Frenk, C.S.; White, S.D.M. The Evolution of Large Scale Structure in a Universe Dominated by Cold Dark Matter. Astrophys. J.
**1985**, 292, 371–394. [Google Scholar] [CrossRef] - Navarro, J.F.; Frenk, C.S.; White, S.D.M. The Structure of cold dark matter halos. Astrophys. J.
**1996**, 462, 563–575. [astroph/9508025]. [CrossRef] - Moore, B.; Ghigna, S.; Governato, F.; Lake, G.; Quinn, T.R.; Stadel, J.; Tozzi, P. Dark matter substructure within galactic halos. Astrophys. J. Lett.
**1999**, 524, L19–L22. [astro-ph/9907411]. [CrossRef] - Springel, V.; White, S.D.M.; Jenkins, A.; Frenk, C.S.; Yoshida, N.; Gao, L.; Navarro, J.; Thacker, R.; Croton, D.; Helly, J.; et al. Simulating the joint evolution of quasars, galaxies and their large-scale distribution. Nature
**2005**, 435, 629–636. [astro-ph/0504097]. [CrossRef] [PubMed] - Arbey, A.; Mahmoudi, F. Dark matter and the early Universe: A review. Prog. Part. Nucl. Phys.
**2021**, 119, 103865. [arXiv:hepph/2104.11488]. [CrossRef] - Planck Collaboration. Planck 2018 results. I. Overview and the cosmological legacy of Planck. Astron. Astrophys.
**2020**, 641, A1. [arXiv:astro-ph.CO/1807.06205]. [CrossRef] - Steigman, G. Primordial Nucleosynthesis in the Precision Cosmology Era. Ann. Rev. Nucl. Part. Sci.
**2007**, 57, 463–491. [arXiv:astro-ph/0712.1100]. [CrossRef] - Cyburt, R.H.; Fields, B.D.; Olive, K.A.; Yeh, T.H. Big Bang Nucleosynthesis: 2015. Rev. Mod. Phys.
**2016**, 88, 015004. [arXiv:astroph.CO/1505.01076]. [CrossRef] - Kuzmin, V.A.; Rubakov, V.A.; Shaposhnikov, M.E. On the Anomalous Electroweak Baryon Number Nonconservation in the Early Universe. Phys. Lett. B
**1985**, 155, 36. [Google Scholar] [CrossRef] - Canetti, L.; Drewes, M.; Shaposhnikov, M. Matter and Antimatter in the Universe. New J. Phys.
**2012**, 14, 95012. [arXiv:hepph/1204.4186]. [CrossRef] - Bertone, G.; Hooper, D.; Silk, J. Particle dark matter: Evidence, candidates and constraints. Phys. Rept.
**2005**, 405, 279–390. [hep-ph/0404175]. [CrossRef] - Peccei, R.D. The Strong CP problem and axions. Lect. Notes Phys.
**2008**, 741, 3–17. [hep-ph/0607268]. [CrossRef] - Baumann, D. Inflation. In Proceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics: Physics of the Large and the Small, Boulder, CO, USA, 1–26 June 2009; pp. 523–686. [arXiv:hep-th/0907.5424]. [CrossRef]
- Allahverdi, R.; Amin, M.A.; Berlin, A.; Bernal, N.; Byrnes, C.T.; Delos, M.S.; Erickcek, A.L.; Escudero, M.; Figueroa, D.G.; Freese, K.; et al. The First Three Seconds: A Review of Possible Expansion Histories of the Early Universe. Open J. Astrophys.
**2021**, 4, 1. [arXiv:astro-ph.CO/2006.16182]. [CrossRef]

**Figure 1.**Contemporary and recent Universe composition: In this example we assumed present day composition to be $69\%$ dark energy, $26\%$ dark matter, $5\%$ baryons, <1% photons and neutrinos. The dashed line shows how introduction of $2\times 0.1\phantom{\rule{4.pt}{0ex}}\mathrm{eV}$ mass in two of the three neutrinos impacts the energy density evolution (Neutrino mass choice is just for illustration. Other values are possible). The recombination temperature ${T}_{r}\approx 0.25\phantom{\rule{4.pt}{0ex}}\mathrm{eV}$ delimits the era when the Universe was opaque shown as the shaded region.

**Figure 3.**The evolution of the photon reheating (black line) process in terms of fractional temperature change in the Universe. Figure adapted from [29]. The dashed portion is a qualitative description subject to the exact model of QGP hadronization.

**Figure 4.**

**Left**: The numerically solved later $t>{10}^{-1}\phantom{\rule{4pt}{0ex}}\mathrm{yr}$ evolution of photon and neutrino background temperatures ${T}_{\gamma},\phantom{\rule{4pt}{0ex}}{T}_{\nu}$ (black and black dashed lines) and the deceleration parameter q (thin blue line) over the lifespan of the Universe.

**Right**: The evolution of the Hubble parameter $1/H$ (black line) and redshift z (blue dashed line) which is related to the scale parameter $a\left(t\right)$. Figure adapted from [29].

**Figure 5.**The evolution of the cosmic baryon chemical potential ${\mu}_{B}$ after hadronization (blue line). Curves for QGP (thin black line) created in terrestrial accelerators for differing entropy-per-baryon $s/b$ values are included [57]. The boundary (red line) where QGP condenses into hadrons is illustrated at an energy density of $0.5\phantom{\rule{4.pt}{0ex}}\mathrm{GeV}/{\mathrm{fm}}^{3}$ as determined through lattice computation [59].

**Figure 7.**Plot of the down quark chemical potential ${\mu}_{d}$ as a function of temperature for differing values of entropy-per-baryon $S/B$ ratios (2003 unpublished, Fromerth & Rafelski [62]).

**Figure 8.**Comparison of Hubble time $1/H$, quark lifespan ${\tau}_{q}$, and characteristic time for production via quark-gluon pair fusion for (

**Top**figure) charm and (

**Bottom**figure) bottom quarks as a function of temperature. Both figures end at approximately the hadronization temperature of ${T}_{h}\approx 150\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}$. Three different masses ${m}_{b}=4.2\phantom{\rule{4.pt}{0ex}}\mathrm{GeV}$ (blue short dashes), $4.7\phantom{\rule{4.pt}{0ex}}\mathrm{GeV}$, (solid black), $5.2\phantom{\rule{4.pt}{0ex}}\mathrm{GeV}$ (red long dashes) for bottom quarks are plotted to account for its decay width.

**Figure 9.**The generalized fugacity ${\mathrm{{\rm Y}}}_{b}$ of free unconfined bottom quark as a function of temperature in QGP up to the hadronization temperature of ${T}_{h}\approx 150\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}$ for three different bottom masses ${m}_{b}=4.2\phantom{\rule{4.pt}{0ex}}\mathrm{GeV}$ (solid blue), $4.7\phantom{\rule{4.pt}{0ex}}\mathrm{GeV}$, (solid black), $5.2\phantom{\rule{4.pt}{0ex}}\mathrm{GeV}$ (solid red).

**Figure 10.**The fractional energy density of the luminous Universe (photons and leptons (white), mesons (blue), and hadrons (red)) as a function of the temperature of the Universe from hadronization to the contemporary era. This figure is a companion figure to Figure 2 (2003 unpublished, Fromerth & Rafelski [62]).

**Figure 11.**The baryon (blue solid line) and antibaryon (red solid line) number density as a function of temperature in the range $150\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}>T>5\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}$. The green dashed line is the extrapolated value for baryon density. The temperature $T=38.2\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}$ (black dashed vertical line) is denoted when the ratio ${n}_{\overline{B}}/({n}_{B}-{n}_{\overline{B}})=1$ which define the condition where antibaryons disappear from the Universe.

**Figure 12.**Ratios of hadronic particle number densities as a function of temperature $150\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}>T>5\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}$ in the early Universe with baryon B yields: Pions $\pi \left(q\overline{q}\right)$ (brown line), kaons $K\left(q\overline{s}\right)$ (blue line), antibaryon $\overline{B}$ (black line), hyperon Y (red line) and antihyperons $\overline{Y}$ (dashed red line). Also shown is the $\overline{K}/Y$ ratio (purple line) and the $\overline{B}$ to asymmetry $B-\overline{B}$ ratio (green line). Temperature crossings are included (as vertical dashed black lines) at $T=40\phantom{\rule{4.pt}{0ex}}\mathrm{MeV},\phantom{\rule{4pt}{0ex}}20\phantom{\rule{4.pt}{0ex}}\mathrm{MeV},\phantom{\rule{4pt}{0ex}}13\phantom{\rule{4.pt}{0ex}}\mathrm{MeV},\phantom{\rule{4pt}{0ex}}5.6\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}$ as different abundances become sub-dominate compared to other species. The dashed brown line represents the drop in overall pion $\pi $ abundance when the vanishing of the charged pions ${\pi}^{\pm}$ from the particle inventory is taken into account.

**Figure 13.**The strangeness abundance changing reactions in the primordial Universe. Red circles show strangeness carrying hadronic particles and thick red lines denote effectively instantaneous reactions. Thick black lines show relatively strong hadronic reactions.

**Figure 14.**The hadronic reaction relaxation times ${\tau}_{i}$ in the meson sector as a function of temperature compared to Hubble time $1/H$ (black solid line). The following processes are presented: The leptonic (solid blue line) and strong (dashed blue line) kaon K processes, the electronic (solid dark red line) and muonic (dashed dark red line) phi meson $\varphi $ processes, the forward and backward (thick black lines) electromagnetic pion $\pi $ processes, and the strong (red lines) rho meson $\rho $ processes.

**Figure 15.**Thermal reaction rate R per volume and time for important hadronic strangeness production, exchange and decay processes as a function of temperature $150\phantom{\rule{0.166667em}{0ex}}\mathrm{MeV}>T>10\phantom{\rule{0.166667em}{0ex}}\mathrm{MeV}$. The following processes are presented: $\Lambda \leftrightarrow N\pi $ (solid black line), $K\leftrightarrow \pi \pi $ (solid green line), $\pi N\leftrightarrow \Lambda K$ (solid blue line), $\overline{K}N\leftrightarrow \Lambda \pi $ (solid red line). Two temperature crossings are denoted at $T=40\phantom{\rule{4.pt}{0ex}}\mathrm{MeV},\phantom{\rule{4pt}{0ex}}12.9\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}$.

**Figure 16.**The thermal reaction rate per volume for muon related reactions as a function of temperature adapted from [72]. The dominant reaction rates for ${\mu}^{\pm}$ production are: The $\gamma \gamma $ channel (blue dashed line), ${e}^{\pm}$ (red dashed line), these two combined as the total electromagnetic rate (pink solid line), and the charged pion decay feed channel (black solid line). The muon decay rate is also shown (green solid line). The crossing point between the electromagnetic production processes and the muonic decay rate is seen as the dashed vertical black line at ${T}_{\mathrm{dis}}=4.2\phantom{\rule{4.pt}{0ex}}\mathrm{MeV}$.

**Figure 17.**The density ratio between ${\mu}^{\pm}$ and baryons ${n}_{{\mu}^{\pm}}/{n}_{B}$ (blue solid line) is plotted as a function of temperature. The red dashed line indicates a density ratio value of ${n}_{{\mu}^{\pm}}/{n}_{B}=1$. The density ratio at the muon disappearance temperature (vertical black dashed line) is about ${n}_{{\mu}^{\pm}}/{n}_{\mathrm{B}}\left({T}_{\mathrm{dis}}\right)\approx 0.911$.

**Figure 18.**Freeze-out temperatures for electron neutrinos (

**left**) and $\mu $, $\tau $ neutrinos (

**right**) for the three types of freeze-out processes adapted from paper [109]. Top panels print temperature curves as a function of ${sin}^{2}{\theta}_{W}$ for $\eta ={\eta}_{0}$, the vertical dashed line is ${sin}^{2}{\theta}_{W}=0.23$; bottom panels are printed as a function of relative change in interaction strength $\eta /{\eta}_{0}$ obtained for ${sin}^{2}{\theta}_{W}=0.23$.

**Figure 19.**The ${e}^{\pm}$ number densities as a function of temperature in the range $2\phantom{\rule{0.166667em}{0ex}}\mathrm{MeV}>T>10\phantom{\rule{0.166667em}{0ex}}\mathrm{keV}$. The blue solid line is the electron density ${n}_{{e}^{-}}$, the red solid line is the positron density ${n}_{{e}^{+}}$, and the brown solid line is the baryon density ${n}_{B}$. For comparison, we also show the green dotted line as the solar electron density within the solar core [127].

**Figure 20.**The energy density ratio $\chi $ (solid blue line) between ${e}^{\pm}$ and baryons as a function of temperature from $10\phantom{\rule{0.166667em}{0ex}}\mathrm{keV}<T<200\phantom{\rule{0.166667em}{0ex}}\mathrm{keV}$. The dashed red line crossing point represents where the baryon density exceeds that of the electron-positron pairs.

**Figure 21.**Qualitative value of the primordial magnetic field over the evolutionary lifespan of the Universe. The upper and lower black lines represent extrapolation of the EGMF bounds into the past. The major phases of the Universe are indicated with shaded regions. The values of the Schwinger critical field (purple line) and the upper bound of surface magnetar field strength (blue line) are included for scale.

**Figure 22.**Estimate for the spin magnetization as a function of temperature in the range ${10}^{3}\phantom{\rule{4.pt}{0ex}}\mathrm{keV}>T>10\phantom{\rule{4.pt}{0ex}}\mathrm{keV}$, see text for detail.

**Table 1.**The characteristic strangeness reaction, their freeze-out temperature, and temperature width in the hadronic epoch.

Reactions | Freeze-Out Temperature (MeV) | $\mathbf{\Delta}{\mathit{T}}_{\mathit{f}}$ (MeV) |
---|---|---|

${\mu}^{\pm}\nu \to {K}^{\pm}$ | ${T}_{f}=33.8$ MeV | $3.5$ MeV |

${e}^{+}{e}^{-}\to \varphi $ | ${T}_{f}=24.9$ MeV | $0.6$ MeV |

${\mu}^{+}{\mu}^{-}\to \varphi $ | ${T}_{f}=23.5$ MeV | $0.6$ MeV |

$\pi \pi \to K$ | ${T}_{f}=19.8$ MeV | $1.2$ MeV |

$\pi \pi \to \rho $ | ${T}_{f}=12.3$ MeV | $0.2$ MeV |

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## Share and Cite

**MDPI and ACS Style**

Rafelski, J.; Birrell, J.; Steinmetz, A.; Yang, C.T.
A Short Survey of Matter-Antimatter Evolution in the Primordial Universe. *Universe* **2023**, *9*, 309.
https://doi.org/10.3390/universe9070309

**AMA Style**

Rafelski J, Birrell J, Steinmetz A, Yang CT.
A Short Survey of Matter-Antimatter Evolution in the Primordial Universe. *Universe*. 2023; 9(7):309.
https://doi.org/10.3390/universe9070309

**Chicago/Turabian Style**

Rafelski, Johann, Jeremiah Birrell, Andrew Steinmetz, and Cheng Tao Yang.
2023. "A Short Survey of Matter-Antimatter Evolution in the Primordial Universe" *Universe* 9, no. 7: 309.
https://doi.org/10.3390/universe9070309