arXiv:1306.2471v1 [astro-ph.CO] 11 Jun 2013 Keywords: h hsc fteeryUies n atra xrm condi extreme at matter and Universe early experimentall the labo- probing of in matter, physics the of recreate form argu- to deconfined the opportunity the of the ratory was One presented 1970’s. we late ments th in spearheaded program who physics physicists heavy-ion particle and nuclear of group hadronization. called process a in we formed as is matter it how know restricted explore particles We free domain. as space-time roam deconfined can confirm gluons We and QGP. quarks of he domain that relativistic space-time con- in small their laboratory a mat- collisions the into ion QGP in dissolved form In are we them, Thus matter. know stituents. of we structure as the particles in Universe ter, hot change the the in vacuum to the now leads we of properties [3]: in years explain change 35 To past a in think Universe. occurred early has shift the paradigm in a this existed they yet world, our formed. was di matter a before imagine Universe to the of possible ture not is it knowledge day temperature a persiste to QGP down expansion Universe the in that demonstrate e and These [2]. continu q simulations lattice of chromo-dynamics and tum years [1] the (RHI) thirty ion of over heavy view relativistic of dedicated This ous product (QGP). the is plasma Universe quark-gluon early of quarks, deconfined state with the filled in was Universe our big-bang the Universe quark-hadron Exploring 1. primord a from emerged antimatter di and and similarities matter how i describe plasma We quark-gluon of evolution and properties discuss We Abstract h ur-nvrecnet eensetaogthe among nascent were concepts quark-Universe The in found be never will gluons or quarks propagating Freely after that predicts physics particle of model standard The oncigQPHayInPyist h al Universe Early the to Physics Ion QGP-Heavy Connecting ur nvre ur-arntasto,Hdo freeze-o Hadron transition, Quark-Hadron Universe, Quark ff rne ewe h al nvreadtelbrtr exper laboratory the and Universe early the between erences T ≃ 5 e.Cnieigtepresent the Considering MeV. 150 eateto hsc,TeUiest fAioa usn 8 Tucson, Arizona, of University The Physics, of Department ula hsc rceig upeet0 21)1–8 (2018) 00 Supplement Proceedings B Physics Nuclear ff rscombine orts ff rn struc- erent oanRafelski Johann uan- avy to h al nvreadcmaet aoaoyhayinexpe ion heavy laboratory to compare and Universe early the n y d e - - 1 a opo ursadgun.W ou u icsinon discussion our focus We gluons. and quarks of soup ial u te eetrltdsre [9]. survey related recent other our di those on which emphasis features with micro-bang and si big-bang the several between are there laboratory exact; the di not However, nificant is big-bang Universe. the of early recreation the in big-ban the stage and laboratory QGP the similar- in greater micro-bang even the an between is ity There big- hadronization. the QGP in evolve in and bang emerge hadrons how clarifies periment ear the in formed Universe. was matter how experime clarifies several also conditions in tal observed [11] propert universal process of hadronization presence exper-of The LHC large [10]. of presented a study is detailed into iments a turns particles; phase hadronic QGP of the number how study micro- laboratory we In experiments 9]. 8, t [7, qualitative understanding from quantitative today progresses formed surroundin been matter have must how us of understanding our collisions, RHI occur. remnant not e ‘quark’ quark an word Universe, heavy hadronic about the the is whenever in discussion re- [6], the cosmological text, as in major such appears the period In the of took accepted. views and be physics nuclear to and years particle several of [ midst Universe the early in the born matter. of was structure quark quark-gluon of of testi- understanding theory are evolving This [5] rapidly 1981 the Moriond to de Biele mony Rencontres period, and this [4], of 1980 proceedings feld conference two The tions. htw er bu arndnmc ntelbrtr ex- laboratory the in dynamics hadron about learn we What the of study experimental and theoretical of years 30 After ut ff iments. rne.I hsrpr erve h relationship the review we report this In erences. ff r nti eadti eotcomplements report this regard this In er. 71USA 5721 ff c hc sntdaoe can- above, noted as which ect hsc B Physics Proceed- Nuclear Supple- ment ings riments. bang ies n- g- 3] ly g g o s - Johann Rafelski / Nuclear Physics B Proceedings Supplement 00 (2018) 1–8 2

2. Quark-gluon expansion much more complex, and the entropy preserving expan- sion is described in terms of relativistic hydrodynamic When modeling the expansion of QGP for laboratory flow [12]. experiments, once the particle system is thermally equi- This works as follows: upon introduction of initial librated, it is hard to identify entropy-generating mech- conditions which result from primary interactions of anisms. This is so since particle production, e.g. flavor colliding partons, relativistic hydrodynamics allows to changing reactions, involve primarily conversion of two integrate the equations towards hadronization condition. particles into each other at a scale where the mass does One can learn much from this exercise, for example that not matter, and where mass matters, few reactions are it is for most part a quark-gluon fluid that flows. Even possible. Thus QGP expansion is an entropy-preserving so, this has little to do with particle interactions: it is the process. This remark applies even more to the case of relativistic kinematics which connects the initial state expanding Universe considering that this process is in to the designated final free-flow or hadronization condi- comparison considerably slower. tion. This is so, since the main effect of interactions be- The dilution of energy in expansion must thus be con- tween quarks and gluons is to reduce the effective count strained by the conservation of entropy S of degrees of freedom by a factor that is rather slowly dependent on temperature [13], a phenomenon related dE + PdV = TdS = 0, dE = d(εV). (1) to properties of quantum chromo-dynamics. The rela- tivistic QGP fluid is a (nearly) ‘perfect liquid’. As usual we will use for energy the symbol E, energy Unlike heavy ion collisions, in the case of the early density ε, temperature T, pressure P, volume V. Lower Universe there is at the time of QGP very likely a true case letters denote densities, e.g. entropy density s, par- homogeneity of the Universe. On the other hand, the ticle density n. From Eq.(1) we obtain force of gravity controls the dynamics of expansion. dε dV dR This circumstance is accounted for considering in the − = = D . (2) ε + P V R FRWL cosmology the Hubble equation arising from Einstein equations: Here R is the dominant size scale, and thus D = 3, counting the number of expanding dimensions. R˙2 8πG = ε ≡ H2(t). (5) In absence of particle mass scales the particle compo- R2 3 nent (subscript ‘p’) in energy density and pressure satis- fies the relativistic equation of state and both depend on Combining Eq.(2) with Eq.(5) we obtain for the evolu- only a power of T tion of the Universe energy density 2 2 1 ε˙ = 24πG ε(ε + P) (6) P (ε) = ε , ε ∝ T 4 (3) p 3 p p For purely radiative Universe we obtain the well-known Combining Eq.(2) with Eq.(3) produces the well- radiative Universe power law dependence on time known result ε 3 1 TR = Const. (4) = → ε = . P 2 (7) 3 32πG (t0 + t) Considering cosmic micro-wave background radiation (CMB) in current epoch Eq.(4) conveys the remarkable Integration constant t0 defines the initial energy density constraint that while the local photon density diminishes for t = 0. with diminishing temperature, photons fill a larger vol- Turning now to look at expansion of a bag-model ume and thus their number, and thus also entropy con- like Universe [7], we recall that we complement particle tent, remains exactly preserved. only properties by a positive volume energy B contribut- One of tacit assumptions we made in the above dis- ing a corresponding negative pressure cussion which lead to Eq.(4) is that the physical sys- h h → h −B h B tem is homogeneous. However, for a small drop of εp = 3Pp ε = 3(P + ) (8) QGP produced in heavy ion collisions this cannot be the case: aside from the fact that there are edges defin- and thus 3(Ph + ε)h = 4(εh −B), where the superscript ing the size of the QGP drop, there is energy density ‘h’ refers to hadronic component. Note that B is just and local velocity field spatial dependence arising from like the vacuum energy described by the Einstein term the initial state formation process. Thus the situation is B ↔ Λ/8πG. 2 Johann Rafelski / Nuclear Physics B Proceedings Supplement 00 (2018) 1–8 3

q Combining hadronic with non-hadronic components The meaning of this time scale τu Eq.(11) is un- ε = εh + εEW we obtain the dynamical equation derstood recalling that e.g. at a temperature scale a 1000 times larger than the hadronic transition, TEW ≃ 128πG ε˙2 = ε(ε −B)2. (9) 150GeV the electroweak phase was symmetric - and all 3 quarks were massless. In order to describe a reduction To solve this equation we choose dimensionless vari- of temperature by a factor 1000 and thus energy density ables by 12 orders of magnitude, the initial time would need to be according to the scaling we discussed 3c2 ε = z2B, t = xτq, τq ≡ . (10) τq u u r32πGB τEW = u , (15) u 106 The time constant is thus the electro-weak transition time scale is measured B in terms of 10’s of picoseconds. Seen this we realize that τq = µ 0 u 36 s B (11) as we go from pico to micro seconds we pass through r q the entire QGP era of the Universe. τu is thus the effec- B1/4 tive lifespan of the quark Universe. where the benchmark is for 0 = 195MeV or equiva- 3 lently B0 = 0.19 GeV/fm Using Eq.(10) we find for Eq.(9) 3. Baryon asymmetry

dz 2 ±1 We are interested in comparing the Universe entropy = ±(z − 1), z = coth (x + x0) (12) dx content per baryon s/nB = S/NB with what is achieved in laboratory experiments. Assuming that the baryon with x0 being the integration constant. A solution with decreasing energy density in time requires ‘+’sign number is conserved and recalling that the expansion of the Universe is adiabatic, the ratio s/nB, a dimensionless 2 q number, is preserved in the Universe evolution. ε(t) = B coth (x0 + t/τu). (13) Considering particle components in the Universe where the initial energy density at time t = 0 is ε(0) = when the entropy is dominated by photons, e, µ, τ- 2 ε0 = B coth (x0). It is common to consider x0 → 0, a neutrinos, and electron-positron pairs, which is the case point-size Universe of infinite energy density. However e.g in the temperature range 50 > T > 2 MeV, we have this is a special case which will not work as we show B → s 1 nγ sγ nν sν ne se below. Note that in the limit 0, solution Eq.(13) = si = , + + (16) n n n n n n n n ! reduces to radiative Universe solution Eq.(7). B B i=Xγ,ν,e B γ γ ν γ e We recover the usual scaling of the energy density of the Universe as follows: using in Eq.(2) the equation of For photons (s/n)boson = 3.60 and for neutrinos as state Eq.(8) and adding to it non-hadronic components, well in the above temperature domain where electrons we find that are effectively massless, (s/n)fermion = 4.20. For rela- 4 ε0 −B R tive quantum distribution massless particle densities we = (14) recall the Riemann function relation n /n = ε −B R0 ! fermion boson η(3)/ζ(3) = 3/4. Canceling the spin factor 2 between which reaffirms that the energy density in particles photons and fermions, we are left with the count of scales with inverse 4th power of R, and thus we also the number of fermions, anti-fermions, but only single- recover the scaling Eq.(4). handed neutrinos of the three flavor. We find In time period when the energy density is well above B s n 3 3 , the form of the solution Eq.(13) is the same as the B = 3.60 + 3 4.20 + 2 4.20 = 19.35. (17) purely radiative Universe Eq.(7). When the energy den- nB nγ 4 4 sity decreases to the scale of B, that is on scale of tu time t is not small, the energy density of the Universe The value of nB/nγ can be obtained considering BBN is nearly constant and dominated by the vacuum energy nucleo-synthesis yields in the BBN era, and later, we B. At that condition with a proper choice for B the tran- can also obtain it at the recombination period. We adopt sition to hadron Universe must occur. The time con- the value stant for this expansion towards transition is as stated in B η ≡ = 6.27 ± 0.34 × 10−10, (18) Eq.(11). nγ 3 Johann Rafelski / Nuclear Physics B Proceedings Supplement 00 (2018) 1–8 4

q see e.g. figure 4 of Ref. [14], where in first approxi- cτu ≃ 10km Eq.(11). At hadronization, the energy mation we assume that all entropy in the annihilating density scale is provided by 4B. Multiplying with q 3 57 58 electron-positron pairs reheats photons. Using Eq.(18) 4π(Ru) /3 we obtain the mass equivalent of 10 –10 we obtain protons. Most of this stuff, down to a fraction 10−10, s S 19.35 annihilates and feeds Universe expansion and present ≡ = ≃ 3 × 1010 . (19) day CMB. The insight we gain is that even if all this n N η B B hadronization energy were to go to make matter we see Possible reheating of neutrinos in e+e−-annihilation out the window, we still would be far from being able prior to BBN introduces some uncertainty here, and is to describe all matter. We are missing more than 40 or- a topic which remains under current investigation [14, ders of magnitude. The Universe at the time of QGP 15]. hadronization must have been very much larger which Turning attention now to the heavy ion collisions we means that before the QGP era it was already quite large note that it is understood that as the energy of the col- and not a ‘point’. lision increases, the number of quarks retained in the The question — how big is the hadronizing Universe central rapidity i.e. CM frame of the collision domain which provides the visible matter surrounding us? — diminishes. One can think of this situation akin to a shot leads us back to consider the entropy content in the Uni- through a thin target: there is energy deposition; how- verse. We recall that we know the entropy per baryon ever, since the target is thin, when the collision occurs s/nB. Moreover, the PDG [16] suggests that today we −3 at a sufficiently high energy these parton-bullets cannot have nB ≃ 0.25m in the Universe. Thus the present be stopped, and thus the baryon number they carry was day entropy density is expected to leave the interaction region. One expects s s that heavy ion collisions are producing a QGP that is as = = . × 10 −3 ≡ h . s nB 0 75 10 m 3 (21) free of net baryon number as is the early Universe. The nB (zh + 1) observation of a significant stopping of baryon number In the last relation we connected by the redshift factor in collisions of 100+100 GeV per nucleon for heaviest z to entropy content at time of hadronization. Note that nuclei at RHIC remains in need of a convincing expla- h in adiabatic expansion of the Universe the scaling with nation. z of entropy density must be just like that of a conserved At LHC where experiments at 1380+1380 GeV per particle number density. That this is true one can easily nucleon were recently carried out, the baryon yield in see contemplating how the ratio s/n can remain un- the central collision region is so small that its measure- B changed during the evolution history of the Universe. ment has become an experimental challenge. A recent The entropy density at hadronization sh can be in-depth analysis produces as an estimate [10] q seen as composed of two components: 1) σh is the s strong interaction part originating in quarks and glu- ≃ 5000. (20) n ons. Due to the color degree of freedom it is the B lab dominant component, over the second component; 2) The QGP we make today at LHC is by 6 order of mag- σEW, which includes contribution of effectively non- nitude baryon richer. By considering experiments at a h interacting electro-weak degrees of freedom which are: lower energy we can achieve QGP with significantly photons, electrons, muons, and the three single-handed higher baryon content. For some physics challenges this neutrinos. The quark-gluon component is measured could be an advantage: in the big-bang the large volume both in lattice gauge theory studies [2] and in hadroniza- available allows the smallest asymmetry to be amplified. tion studies of QGP [10, 11], where In the lab the smallness of the available volume of QGP requires a much greater baryon asymmetry for an effect q 3.5 of interest to become visible. s ≃ . (22) h fm3

4. Size of hadronizing QGP Counting the free particle degrees of freedom one finds EW q ≃ that EW components contribute σh /sh 0.3. How- But how big was the Universe at the time of ever, actual contribution is at about 40% – 50%, where hadronization? To answer this we consider how the uncertainty comes from the exact magnitude of the much energy and mass is in the quark Universe that strong interaction part of entropy density which is not hadronizes. Consider first a Universe which was point- fully described counting degrees of freedom and which q like and expanded radiatively to the size given by Ru = changes rapidly at hadronization condition. We will 4 Johann Rafelski / Nuclear Physics B Proceedings Supplement 00 (2018) 1–8 5 here use Universe expands and the ambient temperature drops, q EW ≃ 5 for quite some time there is annihilation between matter sh = sh + sh . (23) fm3 and antimatter. A more detailed study of this era is pre- Using Eq.(23) in Eq.(21) we obtain sented in Ref.[9], we will develop two important physics points below, the evolution of hadron abundances and z = 0.9 × 1012 (24) h the potential for abundance distillation. This value checks out with a simple qualitative esti- The situation is very different in the micro-bang. mate: the radiative expansion dominated portion, ≃ 109 Given the relatively small volume of laboratory QGP, connects the recombination era Tr = 0.25eV with the one of the interesting outcomes is that after hadroniza- hadronization temperature Th = 150MeV, and there is tion particles begin to free-stream very early which pre- remaining factor zr ≃ 1000 connecting the present to vents antimatter annihilation and we produce antimatter recombination. Among the near future tasks in study of abundantly. For further details we refer the reader to the QGP Universe is a more precise determination of zh. recent analysis of the LHC hadron production results in Given the entropy density at hadronization Eq.(23) Refs.[10, 11]. However, this also means that big-bang and entropy per baryon Eq.(19) (or simply the scaling physics phenomena which depend on a slow distilla- with zh of baryon density) we also know that at the time tion process will not be easily visible in the micro-bang of hadronization the net baryon density of the Universe model. was relatively small The particle composition in QGP, both, in the hadronic Universe as well as in the micro-bang must 2 1 nh ≃ (z + 1)3n ≃ 1036 m−3 = 1.67 × 10−10fm−3. satisfy three global constraints B h B 3 4 (25) 1) Charge neutrality (Q = 0) Inorderto geta sufficiently large number of baryons we n ≡ Q n (µ , T) = 0, (28) must multiply Eq.(25) by a rather gigantic volume! For Q f f f f 80 X example if we wish to have a baryon content NB = 10 the Universe volume at time of hadronization was where Qi is the charge of species f , and the sum is over all particle species present in the considered par- 3 V = × 1090fm3, (26) ticle phase. u 5 2) Net lepton number equals net baryon number (L = which provides us with a radius Ru and time scale τu, B) is phenomenologically motivated in the context of 30 6 baryo-genesis. This leads to the constraint Ru ≃ 0.5 × 10 fm, τu = Ru/c = 1.5 × 10 s. (27) − ≡ − We are not taking sides here in any ongoing discussion nL nB (L f B f ) n f (µ f , T) = 0, (29) regarding the baryon inventory in the Universe. Irre- Xf spective of the precise baryon inventory value, the size where L f and B f are the lepton and baryon numbers of of the quark Universe at the time of hadronization is species f . This condition is of course not proved by large: the light takes a month to cross the diameter of experiment and future studies must consider drastically the hadronizing QGP domain. different variants. In comparisonto the QGP Universe which as we have 3) A given value of entropy-per-baryon (S/B). The now shown must be very large, the laboratory micro- value of s/nB is obtained from nγ/nB as already dis- bang is truly small. The laboratory micro-bang scale is cussed in section 3. governed by nuclear size and a more precise evaluation Considering how many particles can be present we which depends a bit on collision energy and geometry need to find additional constraints. These arise from re- condition does not change the fact that the micro-bang actions between different components. For any reaction radius is 29 orders of magnitude smaller compared to ν f A f = 0, where ν f are the reaction equation coeffi- Eq.(27). cients of the chemical species A f , chemical equilibrium occurs when ν f µ f = 0, which follows from minimizing 5. Antimatter annihilation the Gibbs free energy. Here µ f are chemical potentials which we now consider. 5.1. Evolution constraints In the early Universe when the hadron matter phase 5.2. Chemical potentials emerges from the QGP we have both matter and anti- In a system of non-interacting particles, the chemi- matter present present in large abundance, and as the cal potential µ f of each species f is independent of the 5 Johann Rafelski / Nuclear Physics B Proceedings Supplement 00 (2018) 1–8 6

chemical potentials of other species, resulting in a large 5 150 S/B = 4.5 x 10 6 number of free parameters. Reactions between compo- S/B = 4.5 x 10 7 nents result in reaction equilibrium. In the early Uni- S/B = 4.5 x 10 8 125 S/B = 4.5 x 10 verse and in particular in the hadronic epoch following 9 S/B = 4.5 x 10 10 on the QGP hadronization three different equilibrium S/B = 4.5 x 10 100 11 conditions are recognized given differences in pertinent S/B = 4.5 x 10 12 S/B = 4.5 x 10 reaction cross sections: 13 S/B = 4.5 x 10 1) The kinetic equilibrium (also called thermal equilib- 75 T (MeV) rium): particles equipartition energy by means of col- lisions that do not change particle number or undergo 50 changes akin to chemical reactions. This type of in- teraction assures that particles have the Bose or Fermi 25 (Boltzmann) momentum distribution. Their number can differ from naive expectation. 0 -6 -4 -2 0 2 2) Relative chemical equilibrium is specific to hadron 10 10 10 10 10 µ (MeV) world: individual quarks can flow between hadrons but d quark pairs are not produced. In relative chemical equi- Figure 1. The chemical potential µd evolves towards common value librium, the chemical potential of hadrons is equal to µd ≃ m/3 for any value of S/b [18]. the sum of the chemical potentials of their constituent quarks. For example, Σ0(uds) has chemical potential Reactions between particles expressed in terms of µΣ0 = µu + µd + µs = 3 µd − ∆µl. 3) (Absolute) chemical equilibrium: quark-antiquark equilibrium chemical conditions supplemented by con- pair production processes are fast enough to assure that servation conditions always close the system of chemi- the yields of hadrons are in equilibrium. This equi- cal rate equations. Thus one can find a unique solution librium also addresses the weak or electromagnetic in- and obtain all particle abundances present. For the early teraction process that connects hadrons with leptons. Universe these equations were for the first time estab- When pairs are in equilibrium, i.e., the reaction f + f¯ ⇋ lished and solved numerically in Ref.[8]. Some of these results were presented for the first time in recent survey 2γ proceeds freely in both directions. Therefore, µ f = − Ref.[9]. We recall a few important results: Strangeness, µ f¯ whenever chemical and thermal equilibrium is at- tained. present in kaons, persists down to T = 10 MeV. Pion It turns out that only weak interactions are weak and muon evolve in chemical equilibrium as we briefly enough in the early Universe to freeze-out and this oc- discuss in next section 6, their density falling below den- ≃ curs relatively late, beyond our current interest. When sity of nucleons only below T 6 MeV. the system is chemically equilibrated with respect to In order to describe the low net baryon density weak interactions [17]: Eq.(25) the value of the baryon chemical potential just before the phase transition is a tiny 10−10 fraction of the 3 µu = µd − ∆µl, µs = µd, µB ≡ (µd + µu) (30) temperature 2 +0.11 µB = 0.33−0.08 eV. (33) where As temperature decreases µd approaches (weighted) ∆µl = µi − µν , i = e,µ,τ. (31) i one-third the nucleon mass (2mn − mp)/3 = 313.6 MeV and neutrino oscillations imply that neutrino number is reflecting the dominance of protons and neutrons in exchanged between flavors νe ⇋ νµ ⇋ ντ and hence their classical Boltzmann limit T ≪ m f , see Fig. 1. The different lines step each by an order of magnitude µ = µ = µ ≡ µ . (32) νe νµ ντ ν the value of entropy per baryon Eq.(18), and we see a The strong and electromagnetic interactions remain significant variance in behavior. However, such a large always faster than the expansion of the Universe. The range of S/B requires a considerable change in baryon situation is grossly different in the micro-bang. The or entropy content prior to BBN which occurs at the fi- weak and electromagnetic interactions are entirely de- nal convergence point in Fig. 1. coupled from the micro-bang. The expansion of QGP is fast enough to worry about detailed study of hadron re- 5.3. QGP–HG transformation and distillation action decoupling and chemical non-equilibrium among The conversion of QGP to hadrons can proceed by hadrons. formation of separate domains of both phases. The is- 6 Johann Rafelski / Nuclear Physics B Proceedings Supplement 00 (2018) 1–8 7 sue is that in HG the entropy density is lower than it is Comparing relaxation time for this reaction τπ to τu ≡ in QGP and the transition from QGP to HG in chemical 1/H shows that π0 remains in chemical equilibrium equilibrium can only occur if in conversion from QGP even as its thermal number density gradually decreases, to HG the volume occupied by HG is much larger. Thus consistently with falling thermal production rates. This the total volume will grow while the ambient tempera- phenomenon can be attributed to the high population of ture remains practically unchanged. While this is occur- photons, within which it remains probable to find pho- ring distillation of the quantities we needed to conserve tons of high enough energy to fuse into π0, and as the and in particular the baryon and charge density can oc- number of high energy photons decreases, described by cur. photons’ Planck distribution, so does the number of π0 Considering that matter-antimatter symmetry has which need to be maintained. been very slightly broken, as a function of fHG(t) there Two-to-two reactions maintain equilibrium within will in general be further asymmetry developing e.g. in and between charged pion populations [20] the baryon distribution, which is different in two phases 0 0 + − + − for same statistical parameters. To date nobody has car- π + π ⇋ π + π , γ + γ ⇋ π + π (37) ried out a realistic study of the dynamical Universe evo- and lepton populations lution allowing for proper distillation of the physical properties between the phases, along with annihilation e+ + e− ⇋ µ+ + µ−, γ + γ ⇋ l+ + l−, (38) of the high initial matter antimatter content. This re- π+ + π− ⇋ l+ + l−, (l = µ, e). mains an interesting research task for the near future. A first insight [8, 9] is obtained considering the total The chemical relaxation times of each of these reactions partition function parametrized as are faster than the expansion of the Universe.

ln Ztot = fHG ln ZHG + (1 − fHG) ln ZQGP, (34) 7. Conclusions in which fHG(t) represents the fraction of total volume occupied by the HG phase. In a model we can assume Today we can look back in the history of the Uni- that fHG evolves linearly in time and that the total dura- verse by observing free-streaming photons created at tion of the phase transformation is e.g. 10 µs, the actual Tr = 0.26eV (about 3000 K) when electrons and nu- dynamics of the transition is beyond the current discus- clei recombined. The Universe was about 1000 times sion scope. Note that Eq.(28) is now generalized as smaller in size. The next snapshot comes from study of the abundances of light isotopes made in the period Q = 0 = nQGP V + nHG V , (35) Q QGP Q HG of the big-bang nucleosynthesis when temperatures are − QGP HG another factor 10,000 times greater, at T = 30keV = Vtot (1 fHG) nQ + fHG nQ . h i and more. Looking beyond this we can not ‘see’ any- and analogous expressions hold for Eqs.(29) applies. thing until we get to the QGP, recreated in the micro- For each fHG the net charge per baryon nQ/nB is cal- bang, corresponding to an era when the Universe was culated in each phase as a function fHG, which is in- 10,000 hotter and smaller in size: the QGP hadronized dependent of the additional assumptions. Protons and 12 at T ≃ 150MeV at zh = 0.9 × 10 , see section 4 and neutrons being the lowest excitations in the HG phase, Eq.(24). The big-bang QGP is tiny: in size scale we the HG takes on a positive charge as soon as the trans- are missing 29 orders of magnitude. Even if we assume formation begins. The QGP therefore takes on a nega- a point-like initial condition for the big-bang QGP, the tive charge density, which is initially tiny since it occu- size of the Universe would be 10km [7] and the scale pies the larger volume, yet it can cause large variation of big-bang still differs by 18 orders of magnitude from in local electric potentials, a point needing much future the micro-bang. attention. It is a big question if from the tiny micro-bang lab- oratory model of the early Universe we can learn ev- 6. Pion and lepton equilibration: 50 & T & 2 MeV erything we need to know about the big-bang QGP and hadron phases. In the QGP micro-bang we only see a It is importantto realize that hadronsalways are a part tiny piece of the Universe and as our discussion shows of the evolving Universe, a point not much discussed. there are many differences to overcome, before we can The reaction allowing presence of hadrons in a ‘cold’ connect with the big-bang. However, we create QGP in evolving Universe is [19] the laboratory and we can take time and effort to under- π0 ⇋ γ + γ, (36) stand and generalize what we learned, so as to be able to 7 Johann Rafelski / Nuclear Physics B Proceedings Supplement 00 (2018) 1–8 8 use it to understand the hadron Universe once it emerges [3] J. Kapusta, B. Muller and J. Rafelski, Quark-Gluon Plasma: from the EW transition beginning e.g. at 0.1ns passing Theoretical Foundations, (Elsevier Science, 2003) 836pp through the QGP hadronization near 30µs and reaching [4] H. Satz, Statistical Mechanics Of Quarks And Hadrons Proceed- ings of International Symposium, Bielefeld, Germany, August BBN at a few seconds of age. 24-31, 1980, (Elsevier Science Ltd 1981) 479pp We have discussed that hadrons remain in chemical [5] M. Jacob and J. Tran Thanh Van, Quark Matter Formation And equilibrium throughout the evolution of the Universe. Heavy Ion Collisions, Proceedings of Rencontres de Moriond 1981, Phys. Rept. 88 (1982) 325pp. The same mechanism that allows π0 to rapidly decay [6] A. D. Dolgov and Y. .B. Zeldovich, “Cosmology and Elemen- in reaction Eq.(36) is present when two photons col- tary Particles,” Rev. Mod. Phys. 53 (1981) 1. lide in the thermally equilibrated Universe, and photon [7] J. Letessier and J. Rafelski, Hadrons and quark - gluon plasma, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 18, (2002) 1. ‘fusion’ reactions fill any missing π0 [19, 20]. Given [8] M. J. Fromerth and J. Rafelski, “Hadronization of the Quark that hadron chemical equilibrium is maintained, one can Universe,” astro-ph/0211346. use methods of hadro-chemistry to study particle abun- [9] M. J. Fromerth, I. Kuznetsova, L. Labun, J. Letessier and dances. We have shown how to compute the values of J. Rafelski, “From Quark-Gluon Universe to Neutrino Decou- the quark and lepton chemical potentials that yield the pling: 200¡T¡2MeV,” Acta Phys. Polon. B 43 (2012) 12, 2261 [arXiv:1211.4297 [nucl-th]]. observed matter–antimatter asymmetry in the early Uni- [10] M. Petran, J. Letessier, V. Petracek and J. Rafelski, “Hadron verse after hadronization and equilibration of the HG. production and QGP Hadronization in Pb-Pb collisions at LHC,” The non-zero chemical potentials drive charge distil- arXiv:1303.2098 [hep-ph]. lation during the phase transformation, with the QGP [11] M. Petran and J. Rafelski, “Universal hadronization condition from RHIC to LHC,” arXiv:1303.0913 [hep-ph]. and HG having negative and positive charge densities, [12] P. Huovinen and P. V. Ruuskanen, “Hydrodynamic Models for respectively. Large Coulomb fields may be present Heavy Ion Collisions,” Ann. Rev. Nucl. Part. Sci. 56 (2006) 163 across phase boundaries in case electrons and positrons [nucl-th/0605008]. must be part of the neutralization process, these very [13] S. Hamieh, J. Letessier and J. Rafelski, “Quark gluon plasma fireball,” Phys. Rev. C 62, 064901 (2000) [hep-ph/0006085]. low mass particles cannot follow the sharp hadronic [14] G. Steigman, “Neutrinos and big-bang nucleosynthesis,” phase boundaries precisely. Appearance of strong arXiv:1208.0032 [hep-ph]. Coulomb fields can play a significant role in amplifying [15] J. Birrell, C. -T. Yang, P. Chen and J. Rafelski, “Fugacity and Reheating of Primordial Neutrinos,” arXiv:1303.2583 [astro- pre-existent baryon asymmetry, thus a much smaller net ph.CO]. baryon asymmetry could be amplified to values we see, [16] J. Beringer et al. (Particle Data Group), [1528 pages]Review of a point that certainly needs much further study. Particle Physics Phys. Rev. D 86, (2012) 010001, see Section To finish, we note there three pillars of the field of 21. [17] N. K. Glendenning, Compact stars: Nuclear physics, particle QGP: the creation, observation, exploration of QGP, a physics, and general relativity, (Springer New York 2000) 390 p very dense new phase of matter; the study of confine- [18] M. Fromerth, and J. Rafelski, unpublished. ment of quarks; and the creation of matter from energy, [19] I. Kuznetsova, D. Habs and J. Rafelski, “Pion and muon produc- that is hadronization. These topics as we have discussed tion in e-, e+, gamma plasma,” Phys. Rev. D 78, 014027 (2008) [arXiv:0803.1588 [hep-ph]]. here connect directly the experimental relativistic heavy [20] I. Kuznetsova and J. Rafelski, “Unstable Hadrons in Hot Hadron ion program with the physics of the early Universe. The Gas in Laboratory and in the Early Universe,” Phys. Rev. C 82, study of QGP in the laboratory is today the only ex- 035203 (2010) [arXiv:1002.0375 [hep-th]]. perimentally accessible approach to improve the under- standing of the early Universe at a temperature that is a billion times greater than the ion-electron recombina- tion condition at Tr ≃ 0.25 eV.

Acknowledgments I thank J. Birrell for discussions about size of the Universe and point-like initial condi- tions considered in [7]. This work has been supported by a grant from the U.S. Department of Energy, DE- FG02-04ER41318.

References [1] B. V. Jacak and B. Muller, “The exploration of hot nuclear mat- ter,” Science 337 (2012) 310. [2] Z. Fodor, “Selected results in lattice quantum chromodynam- ics,” PTEP 2012 (2012) 01A108. 8