diff --git a/plasma-partition.bbl b/plasma-partition.bbl index 82eda20..bcd3691 100644 --- a/plasma-partition.bbl +++ b/plasma-partition.bbl @@ -1,4 +1,4 @@ -\begin{thebibliography}{48} +\begin{thebibliography}{52} \providecommand{\natexlab}[1]{#1} \providecommand{\url}[1]{\texttt{#1}} \expandafter\ifx\csname urlstyle\endcsname\relax @@ -79,6 +79,24 @@ C.~Grayson, C.~T. Yang, M.~Formanek, and J.~Rafelski. \newblock \doi{10.48550/arXiv.2307.11264}. \newblock [in press in Annals of Physics]. +\bibitem[{Pomakov} et~al.(2022){Pomakov}, {O'Sullivan}, {Br{\"u}ggen}, {Vazza}, + {Carretti}, {Heald}, {Horellou}, {Shimwell}, {Shulevski}, and + {Vernstrom}]{Pomakov:2022cem} +V.~P. {Pomakov}, S.~P. {O'Sullivan}, M.~{Br{\"u}ggen}, F.~{Vazza}, + E.~{Carretti}, G.~H. {Heald}, C.~{Horellou}, T.~{Shimwell}, A.~{Shulevski}, + and T.~{Vernstrom}. +\newblock {The redshift evolution of extragalactic magnetic fields}. +\newblock \emph{Monthly Notices of the Royal Astronomical Society}, + 515\penalty0 (1):\penalty0 256--270, 2022. +\newblock \doi{10.1093/mnras/stac1805}. + +\bibitem[Jedamzik and Pogosian(2020)]{Jedamzik:2020krr} +K.~Jedamzik and L.~Pogosian. +\newblock Relieving the hubble tension with primordial magnetic fields. +\newblock \emph{Physical Review Letters}, 125\penalty0 (18):\penalty0 181302, + 2020. +\newblock \doi{10.1103/PhysRevLett.125.181302}. + \bibitem[Rafelski et~al.(2018)Rafelski, Formanek, and Steinmetz]{Rafelski:2017hce} J.~Rafelski, M.~Formanek, and A.~Steinmetz. @@ -115,24 +133,6 @@ R.~Durrer and A.~Neronov. 2013. \newblock \doi{10.1007/s00159-013-0062-7}. -\bibitem[{Pomakov} et~al.(2022){Pomakov}, {O'Sullivan}, {Br{\"u}ggen}, {Vazza}, - {Carretti}, {Heald}, {Horellou}, {Shimwell}, {Shulevski}, and - {Vernstrom}]{Pomakov:2022cem} -V.~P. {Pomakov}, S.~P. {O'Sullivan}, M.~{Br{\"u}ggen}, F.~{Vazza}, - E.~{Carretti}, G.~H. {Heald}, C.~{Horellou}, T.~{Shimwell}, A.~{Shulevski}, - and T.~{Vernstrom}. -\newblock {The redshift evolution of extragalactic magnetic fields}. -\newblock \emph{Monthly Notices of the Royal Astronomical Society}, - 515\penalty0 (1):\penalty0 256--270, 2022. -\newblock \doi{10.1093/mnras/stac1805}. - -\bibitem[Jedamzik and Pogosian(2020)]{Jedamzik:2020krr} -K.~Jedamzik and L.~Pogosian. -\newblock Relieving the hubble tension with primordial magnetic fields. -\newblock \emph{Physical Review Letters}, 125\penalty0 (18):\penalty0 181302, - 2020. -\newblock \doi{10.1103/PhysRevLett.125.181302}. - \bibitem[Birrell et~al.(2014)Birrell, Yang, and Rafelski]{Birrell:2014uka} J.~Birrell, C.~T. Yang, and J.~Rafelski. \newblock {Relic Neutrino Freeze-out: Dependence on Natural Constants}. @@ -221,7 +221,7 @@ A.~Steinmetz, M.~Formanek, and J.~Rafelski. \bibitem[Tiesinga et~al.(2021)Tiesinga, Mohr, Newell, and Taylor]{Tiesinga:2021myr} -Eite Tiesinga, Peter~J. Mohr, David~B. Newell, and Barry~N. Taylor. +E.~Tiesinga, P.~J. Mohr, D.~B. Newell, and B.~N. Taylor. \newblock {CODATA recommended values of the fundamental physical constants: 2018}. \newblock \emph{Rev. Mod. Phys.}, 93\penalty0 (2):\penalty0 025010, 2021. @@ -262,6 +262,13 @@ T.~Vachaspati. \newblock \emph{Rept. Prog. Phys.}, 84\penalty0 (7):\penalty0 074901, 2021. \newblock \doi{10.1088/1361-6633/ac03a9}. +\bibitem[Stoneking et~al.(2020)]{Stoneking:2020egj} +M.~R. Stoneking et~al. +\newblock {A new frontier in laboratory physics: magnetized + electron\textendash{}positron plasmas}. +\newblock \emph{J. Plasma Phys.}, 86\penalty0 (6):\penalty0 155860601, 2020. +\newblock \doi{10.1017/S0022377820001385}. + \bibitem[Gopal and Sethi(2005)]{Gopal:2004ut} R.~Gopal and S.~Sethi. \newblock {Generation of magnetic field in the pre-recombination era}. @@ -275,6 +282,14 @@ L.~M. Perrone, G.~Gregori, B.~Reville, L.~O. Silva, and R.~Bingham. \newblock \emph{Phys. Rev. D}, 104\penalty0 (12):\penalty0 123013, 2021. \newblock \doi{10.1103/PhysRevD.104.123013}. +\bibitem[Boyarsky et~al.(2012)Boyarsky, Frohlich, and + Ruchayskiy]{Boyarsky:2011uy} +A.~Boyarsky, J.~Frohlich, and O.~Ruchayskiy. +\newblock {Self-consistent evolution of magnetic fields and chiral asymmetry in + the early Universe}. +\newblock \emph{Phys. Rev. Lett.}, 108:\penalty0 031301, 2012. +\newblock \doi{10.1103/PhysRevLett.108.031301}. + \bibitem[Evans and Rafelski(2022)]{Evans:2022fsu} S.~Evans and J.~Rafelski. \newblock {Emergence of periodic in magnetic moment effective QED action}. @@ -316,6 +331,20 @@ E.~J. Ferrer and A.~Hackebill. \newblock \emph{J. Phys. Conf. Ser.}, 2536\penalty0 (1):\penalty0 012007, 2023. \newblock \doi{10.1088/1742-6596/2536/1/012007}. +\bibitem[Jedamzik et~al.(2000)Jedamzik, Katalinic, and Olinto]{Jedamzik:1999bm} +K.~Jedamzik, V.~Katalinic, and A.~V. Olinto. +\newblock {A Limit on primordial small scale magnetic fields from CMB + distortions}. +\newblock \emph{Phys. Rev. Lett.}, 85:\penalty0 700--703, 2000. +\newblock \doi{10.1103/PhysRevLett.85.700}. + +\bibitem[Kahniashvili et~al.(2013)Kahniashvili, Tevzadze, Brandenburg, and + Neronov]{Kahniashvili:2012uj} +T.~Kahniashvili, A.~G. Tevzadze, A.~Brandenburg, and A.~Neronov. +\newblock {Evolution of Primordial Magnetic Fields from Phase Transitions}. +\newblock \emph{Phys. Rev. D}, 87\penalty0 (8):\penalty0 083007, 2013. +\newblock \doi{10.1103/PhysRevD.87.083007}. + \bibitem[Yan et~al.(2023)Yan, Ma, Ling, Cheng, and Huang]{Yan:2022sxd} H.~Yan, Z.~Ma, C.~Ling, C.~Cheng, and J.~Huang. \newblock {First Batch of z \ensuremath{\approx} 11\textendash{}20 Candidate diff --git a/plasma-partition.pdf b/plasma-partition.pdf new file mode 100644 index 0000000..907b678 Binary files /dev/null and b/plasma-partition.pdf differ diff --git a/plasma-partition.tex b/plasma-partition.tex index e935bac..0555be7 100644 --- a/plasma-partition.tex +++ b/plasma-partition.tex @@ -115,7 +115,7 @@ \section{Introduction} As we see in~\rf{fig:densityratio} at $T>m_ec^2=511\keV$ the $e^{+}e^{-}$-pair abundance was nearly 450 million pairs per baryon, dropping to about 100 million pairs per baryon at the pre-BBN temperature of $T=100\keV$. The number of $e^{+}e^{-}$-pairs is large compared to the residual `unpaired' electrons neutralizing the baryon charge locally down to $T_\mathrm{split}=20.3\keV$. Since electrons and positrons have opposite magnetic moments, the magnetized dense $e^{+}e^{-}$-plasma entails negligible net local spin density in statistical average. The residual very small polarization of unpaired electrons complements the magnetic field induced polarization of the proton component. -As shown in Fig.\,2 in Ref.~\cite{Rafelski:2023emw}, following hadronization of the quark-gluon plasma (QGP) and below about $T\!=\!100\,000\keV$, in terms of energy densitythe early universe's first hour consists of photons, neutrinos and the $e^{+}e^{-}$-pair plasma. Massive dark matter and dark energy are negligible during this era. While we study the magnetic moment polarization of $e^{+}e^{-}$-plasma we do not address here its origin. However, we recall that the pair plasma decouples from the neutrino background near to $T=2000\keV$~\cite{Birrell:2014uka}. Therefore we consider the magnetic properties of the $e^{+}e^{-}$-pair plasma in the temperature range $2000\keV>T>20\keV$ and focus on the range $200\keV>T>20\keV$ where the most rapid antimatter abundance changes occurs and where the Boltzmann approximation is valid. This is notably the final epoch where antimatter exists in large quantities in the cosmos~\cite{Rafelski:2023emw}. +As shown in Fig.\,2 in Ref.~\cite{Rafelski:2023emw}, following hadronization of the quark-gluon plasma (QGP) and below about $T\!=\!100\,000\keV$, in terms of energy density the early universe's first hour consists of photons, neutrinos and the $e^{+}e^{-}$-pair plasma. Massive dark matter and dark energy are negligible during this era. While we study the magnetic moment polarization of $e^{+}e^{-}$-plasma we do not address here its origin. However, we recall that the pair plasma decouples from the neutrino background near to $T=2000\keV$~\cite{Birrell:2014uka}. Therefore we consider the magnetic properties of the $e^{+}e^{-}$-pair plasma in the temperature range $2000\keV>T>20\keV$ and focus on the range $200\keV>T>20\keV$ where the most rapid antimatter abundance changes occurs and where the Boltzmann approximation is valid. This is notably the final epoch where antimatter exists in large quantities in the cosmos~\cite{Rafelski:2023emw}. The abundance of antimatter shown in~\rf{fig:densityratio} is obtained and discussed in more detail in~\rsec{sec:abundance}. Our analysis in~\rsec{sec:thermal} the four relativistic fermion gases (particle and antiparticle and both polarizations) where the spin and spin-orbit contributions are evaluated in~\rsec{sec:paradia}. The influence of magnetization on the charge chemical potential is determined in~\rsec{sec:chem}. We show in~\rsec{sec:magnetization}, accounting for the matter-antimatter asymmetry present in the universe, that magnetization is nonzero. Our description of relativistic paramagnetism is covered in~\rsec{sec:paramagnetism}. The balance between paramagnetic and diamagnetic response is evaluated as a function of particle gyromagnetic ratio in~\rsec{sec:gfac}. The per-lepton magnetization is examined in~\rsec{sec:perlepton} distinguishing between cosmic and laboratory cases, in the latter case the number of magnetic dipoles is fixed, while in the universe the (comoving) number can vary with $T$.