PROCEEDINGS Nuclear Physics B (Proc. Suppl.) 35 (1994) 28-43 SUPPLEMENTS North-Holland

Baryogenesis

A.D. Dolgov 1

The Randall Laboratory of Physics, University of Michigan, Ann Arbor, MI 48109-1120

Abstract: A review on the present state of the baryogenesis is given with an emphasis on electroweak baryogenesis. Technical details of the numerous models considered in the literature are not elaborated but unresolved problems of the isssue are considered. Different logically possible alternatives of the electroweak scenarios are presented. A possible impact of baryogenesis on the is discussed.

Baryogenesis is a process of generation of antibaryons, No >> NB. The magnitude of an excess of over antibaryons of the is characterized by the which presumably took place at an early ratio of the baryonic number density to the stage of the Universe evolution. Two ques- number density of in cosmic mi- tions immediately arise in this connec- crowave background radiation: tions: first, why do we need that and, sec- ond, if baryogenesis is obligatory or one t3 = NB/N.~ = 10 -9- 10 -10 (1) can make the observed Universe without it and the existence of baryogenesis at an This small number means in particular early stage (or stages) is only one of several that the size of the charge asymmetry possible alternatives in cosmology. In my (which is practically 100% now) was tiny opinion baryogenesis is not only possible at high temperatures, T > AQCD ,~ and natural in the frameworks of modern 100 MeV. At these temperatures an- physics but is also necessary for the cre- tibaryons were practically equally abun- ation of the observed Universe at least at dant in the primeval plasma and corre- the same level as . spondingly (NB -- Nt~ / ( NB + NB ) -.~ ~ << 1. Still this number, though very small, is not The idea of baryogenesis emerged from the easy to obtain and the main goal of the- observations that the Universe at some oretical models is to get this number as distance scale lo around us is practi- large as possible. cally 100% charge asymmetric with number density very much exceeding that There are three important problems re- lated to the scale of the asymmetry IB: 1 Permanent address: ITEP, 113259, Moscow, Russia. - 1. What is the magnitude of IB? Is it 0920-5632/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved. SSDI 0920-5632(94)00428-X A.D. Dolgov/ Baryogenesis 29

infinite or, what is practically the same, formulated by Sakharov are the following: larger that the present-day horizon, IB >

lu '~ 101° years? May it be rather small, - 1. Baryonic charge nonconservation. say, like a few × 10 Mpc? In the first case - 2. Asymmetry in particle- the whole Universe or at least the vis- interactions (breaking of C- and CP- ible part is baryon dominated while in invariance). the second case there may be a consider- - 3. Deviation from thermal equilib- able amount of antibaryons which can be rium. in principle observed by their interaction with on the boundaries. Still since It can be shown that neither of these condi- the distance is fairly large the gamma-flux tions are obligatory (see ref. [4]) but coun- from the would be sufficiently terexample are rather exotic. A nice fea- low. ture of these three conditions is that they - 2. May the Universe be charge asym- are perfectly natural in the frameworks metric only in our neighbourhood, never of the present-day particle physics. Bary- mind how large it is (even larger than the onic charge nonconservation, which was horizon), and be charge symmetric as a the most problematic 25 years ago, now is whole? The last possibility is aesthetically predicted by grand unification models and appealing since particle-antiparticle sym- what's more by the standard electroweak metry is restored on large. theory. Unfortunately these are only theo- - 3. Is the amplitude of the asymmetry retical arguments and the remains a constant or may it be a function of stable despite very strong efforts to dis- space points ~ = ~(x, y, z)? The last case cover its decays. The only "experimental" corresponds to the so called isocurvature evidence in favor of baryonic charge non- density fluctuations which may be very in- conservation is given now by cosmology. teresting for the structure formation in low On the contrary C- and CP-violation are Universe. observed experimentally in particle physics and we may be sure that particles and an- The idea that the dominance of baryons tiparticles are indeed different. Still theo- over antibaryons can be explained dynam- retically this phenomenon is not well un- ically was first proposed by Sakharov [1] in derstood: there are many models for CP- 1967. Before it was a common belief that a violation and we do not yet know which nonzero baryonic charge of the Universe is one is true. As for deviation from ther- a result of mysterious initial conditions. At mal equilibrium it is provided by the uni- the present day there are several hundred verse expansion and always exists for mas- papers on the subject discussing different sive particles with the relative magnitude possible scenarios of the generation of the of the order (m2/T2)(H/F) where T is the of the Universe. The temperature of the primeval plasma, H is history of the problem as well as long lists the Hubble parameter characterizing the of references can be found in the review pa- expansion rate, and F is the reaction rate. pers [2-5]. Three very well known by now This expression is valid for m < T and conditions of the baryogenesis which were is typically rather small. For m > T the 30 A.D. Dolgov/Baryogenesis contribution of the particles with the mass tion of state p = -p corresponds to anti- m is usually exponentially suppressed so gravitating medium creating expansion. in both cases deviations from equilibrium are small. This smallness is not crucial for Of course inflationary models have their scenarios of baryogenesis at grand unifi- own problems like very small strength of cation scale but may be very important the inflaton interactions and the absence for lower temperatures. Fortunately there of a natural inflationary scenario in the is another way to break the equilibrium frameworks of the simplest gauge theo- by the first order . In that ries of particle interactions which is an case one may expect a low energy baryo- argument against inflation. On the other genesis, T << TOUT ~ 1016 GeV. Anyhow hand the prediction of inflationary mod- some deviations from thermal equilibrium els of approximately flat spectrum of den- always exist in the cosmological plasma sity perturbations is in a reasonable agree- and this provides the third necessary con- ment with the COBE data (see the talk by dition for baryogenesis. J.Silk at this Conference). Slightly tilted spectrum of density fluctuations may bet- We see that baryogenesis might happen in ter describe the Universe structure forma- the course of the Universe evolution and tion and fortunately there exist inflation- now I would like to argue that it indeed ary models which can give this prediction took place. The crucial point is that in- (see e.g. [6]). Another quantitative predic- flation is impossible without baryogenesis. tion of inflation that the density parame- One may argue that the existence of in- ter f~ is most probably equal to one may flation could also be questioned. Strictly be in agreement with observations but the speaking this is true since we do not have latter are very inaccurate and one cannot rigorous proof that the Universe, as we make a decisive conclusion here. Plenty of see it, cannot be created without infla- people would be happy if f~ is considerably tion. Moreover this proof can never be pre- smaller than one. In that case we may not sented. However inflation is the only sce- need nonbaryonic and in view nario which solves in a simple way many of the recent announcements by the ex- cosmological problems which cannot be perimental groups EROS and MACHOS of addressed in any other known cosmological possible microlensing events (see the talks scenario. Among them are the problems of by A. Milsztajn and B. Sadoulet at this Conference) one may think that all the - 1) flatness; the Universe should be fiat dark matter in the Universe is baryonic. with the accuracy 10 -~5 during primordial The claim that there is some baryonic dark nucleosynthesis, matter in the Universe is supported by the -2) horizon, homogeneity, and iso- primordial nucleosynthesis theory which tropy, gives ~s ~ O.05(H/5Okm/sec/Mpc) -2 [7] - 3) generation of the primordial den- while the contribution of the visible bary- sity fluctuations, onic matter is FtB ~ 0.01. However purely - 4) initial push which gave rise to the baryonic universe encounters serious diffi- Universe expansion; the inflationary equa- culties in large scale structure formation AID. Dolgov/Baryogenesis 31

especially because of very small fluctua- SU(3) x SU(2) x U(1)-model (MSM). A tions of the microwave background tem- strong indication of the validity of the perature. From this point of view nonbary- grand unification is the crossing of all three onic dark matter and large (close to 1) fl gauge coupling constants of supersymmet- are very desirable. Taken together with the ric extension of MSM at the same point nice inflationary solution of the basic cos- near EGUT = 1016 GeV. It is rather diffi- mological problems this gives a very strong cult to believe that there are no new parti- argument in favor of inflationary scenario. cles and interactions in the region between electroweak or low energy For successful solution of the flatness and scale and grand unification scale but if the horizon problems duration of inflationary essential quantity is the logarithm of en- stage should be sufficiently large, H1tr > ergy the distance between these two scales 65 - 70. If baryonic charge were conserved is not too big and one may hope that MSM it would be diluted during inflation by a or supersymmetric version of it is the ul- huge factor e 21° - e 195. Unnatural by itself timate truth in low energy physics (up to it does not exclude initial conditions with ECVT). One more argument in favor of low a very big baryonic charge density. But energy supersymmetry is provided by cos- nonzero baryonic charge density implies si- mology, namely, if one demands in accor- multaneously nonzero energy density asso- dance with the theory of large scale struc- ciated with it. Inflation could be achieved ture formation that the bulk of matter in only if energy density in the Universe is the universe is in the form of cold dark a constant or slowly varying function of matter and assumes that the cross-section the scale factor a. This is not true for the of the annihilation of the latter is given by energy density associated with baryonic a = a2/m 2 then the mass m should be charge, PB. It varies as 1/a 3 for nonrela- in the region 100 GeV - 1 TeV. It is just tivistic particles and as 1/a 4 for relativis- the scale of low energy supersymmetry (for tic ones. From the value of ~ (1) we may more details see e.g. ref. [8]) conclude that at high temperature stage pB ~ lO-lOptot. It means that the total en- A strong objection against GUT baryo- ergy density could be approximately con- genesis is a low heating temperature af- stant for the period not larger than 6 Hub- ter inflation. It is typically 4-5 orders of ble times which is too little for a successful magnitude below EavT. It means that the inflation. Thus inflation demands noncon- GUT era possibly did not exist in the servation of baryons. early Universe. A very interesting alterna- tive to the GUT baryogenesis is the elec- Historically first papers on baryogenesis troweak one (for the review see refs. [4,5]). which were based on a well defined parti- Electroweak theory provides all the neces- cle physics model were done in the frame- sary ingredients for baryogenesis including works of the grand unification theories (for baryon nonconservation (see below) so one the review and the literature see [2,3]). may hope to get some baryon asymmetry Grand unification models present a beau- of the Universe even in the frameworks of tiful extension of the minimal standard the MSM. A very interesting question is 32 A.D. Dolgov/Baryogenesis if it is possible to get the right magnitude ternal gauge field. The calculation which of the asymmetry in MSM or baryogene- can be found in many textbooks gives sis demands an extension of the minimal model. (9~,j~L = Ns ( g2__22 WITV g~ YY) 32r 32~r2 One may say in support of the second pos- (3) sibility that cosmology already demands Here N.¢ is the number of fermionic fla- physics beyond the standard model. It vors, gl,2 are the gauge coupling constants should be invoked for realization of in- of U(1) and SU(2) groups, W and Y flation, for the generation of the primor- are the gauge field strength tensors for dial density perturbations, for nonbary- SU(2) and U(1) respectively, and tilde onic dark matter, etc. A drastic change means dual tensor, W "~ = d'~'aW~,a/2. in the standard physics may be neces- The products of the gauge field strength sary for the solution of the cosmological Wff" and Y~" can be written as diver- term problem. (There is a hope however gences of vector quantities, that it may be solved by infrared instabil- ity of quantum gravity in De Sitter back- WfV = O.K; (4) ground, see e.g. refs. [9,10].) So we have already a strong evidence that there is physics beyond the standard model and Y? =o K; (5) thus baryogenesis should not be confined to the MSM. Still the possibility of real- where istic baryogenesis in the minimal model is K~ = #'~aY,.,o,Y~ (6) extremely appealing and moreover it gives K¢ = - 1 the unique possibility to express the mag- gg W WoW ) nitude of the baryon asymmetry fl through (7) parameters of the standard model mea- Here Yv and W~, are gauge field poten- sured in direct experiments. tials of abelian U(1) and nonabelian SU(2) groups respectively. Usually total deriva- Baryonic charge nonconservation in the tives are unobservable since they may be electroweak theory was discovered by 't integrated by parts and disappear. This Hook [11]. It is a very striking phe- is true for the contribution into K ~ from nomenon. Classically baryonic current, as the gauge field strength tensors Y.~ and inferred from the electroweak Lagrangian, W.~ which should sufficiently fast vanish is conserved at infinity. However it is not obligatory for the potentials for which the integral over ,Jbar~onic = 0, (2) infinitely separated hypersurface may be nonzero. Hence for nonabelian groups the but the conservation is destroyed by the current nonconservation induced by quan- quantum corrections. The latter are given tum effects becomes observable. by the very well known as- sociated with triangle fermionic loop in ex- Because of conditions (3,4,7) the variation of A.D. Dolgov/Baryogenesis 33

the baryonic charge can be written as topological charge is called the instanton. As in the usual quantum mechanics action AB = m Amcs (8) evaluated on this trajectory gives the prob- ability of the barrier penetration [12]: where Ncs is the so-called Chern-Simons number characterizing topology in the F ,-, exp (4~w) ,~ 10 -17° (11) gauge field space. It can be written as a space integral of the time component of where aw = gg/4r. This number is so the vector K": small that it is not necessary to present a preexponential factor. Ncs = g~ [ d3xK t (9) 32rr 2 d Expression (11) gives the probability of the Though Ncs is not a gauge invariant quan- baryonic charge violation at zero energy. tity its variation We know from quantum mechanics that the probability of the barrier penetration ANcs = Ncs(t)- Ncs(O) rises with rising energy. Moreover in the system with nonzero temperature a parti- is. cle may classically go over the barrier with the probability determined by the Boltz- In vacuum the field strength tensor W,~ mann exponent, exp(-E]T). This analogy should vanish while the potentials are not let one think that a similar phenomenon necessarily zero but can be the so called may exist in so that purely gauge potentials: the processes with baryonic charge viola- i tion are not suppressed at high tempera- W~, - U(x)cgvU-X(x) (10) g2 ture. One should not of course rely very much on this analogy since there may be There may be two classes of gauge trans- a serious difference between quantum me- formations keeping W,~ = 0: one that chanics which is a system with a finite does not change Ncs and the second that number of degrees of freedom and quan- changes Ncs. The first one can be real- tum field theory which has an infinite (con- ized by a continues transformation of the tinuous) number of degrees of freedom. potentials while the second cannot. If one Still in a detailed investigation of this phe- tries to change Ncs by a continuous vari- nomenon convincing arguments have been ation of the potentials one has to pass the found that baryonic charge nonconserva- region where W,~ is nonzero. It means that tion at high temperature may be strong vacuum states with different topological and that baryogenesis by electroweak pro- charges Ncs are separated by the poten- cesses may be possible. A good introduc- tial barriers. The probability of the barrier tion to the theory of the electroweak (B + penetration can be calculated in quasiclas- L)-violation at high temperature can be sical approximation. The trajectory in the found in lectures [13]. field space in imaginary time which con- nects two vacuum states differing by a unit The first paper where this idea was se- 34 A.D. Dolgov/Baryogenesis riously considered belongs to Kuzmin, suppressed at high temperatures. Rubakov, and Shaposhnikov [14] (for the earlier papers see ref. [4]). They argued The situation is not so simple however and that the probability of baryonic charge there are a few problems which should be nonconservation at nonzero T is deter- resolved before a definite conclusion can mined by the expression be made. They mostly stem from the dif- ference between finite dimensional system F ~exp ( UT~x) (12) like quantum mechanics and infinitely di- mensional field theory. The first question where Um~x is the potential energy at the is what is the probability of the processes saddle point separating vacua with differ- with the change of topology in the gauge ent topological charges. The field configu- field space. Such processes proceed in pre- ration corresponding to this saddle point sumably multiparticle collisions through is called . It was originally found formation of the classical field configu- in ref. [15] and later rediscovered in paper ration with the coherent scale which is [16]. In the last paper the relation of this much larger than inverse temperature. If solution to the topology changing transi- these processes are not fast enough the tions and baryonic charge nonconservation may be not in thermal equi- was clearly understood. Quantum mechan- librium and possibly far below the equi- ical analogue of the sphaleron is a single librium so that the expression (12) would point in the phase space, i.e. the position not be applicable. At the present day we of particle sitting at the top of the barrier. do not know a reliable analytical way to The energy of the sphaleron is address this problem. Numerical simula- tion of the analogous problem made in 1+1 dimensions [19] showed that the creation U~a=U(¢,phat~o,~(x)) - 2Mwf(~)o~w of soliton-antisoliton pairs are indeed fast (13) enough to maintain the equilibrium value where A is the self-interaction coupling and this is one the strongest arguments in constant of the Higgs field, f is a func- favor of efficient baryon nonconservation in tion which can be calculated numerically, electroweak processes. However such pro- f = O(1), and Mw is the mass of the W- cesses in one dimensional space may pro- bosom At zero temperature 2Mw/c~w ceed much easier than those in three space 10 TeV. However at high temperatures dimensions simply because in D = 1 the close to the electroweak phase transition change of topology means just a jump the Higgs condensate is gradually de- from one constant value of the Higgs field stroyed and the height of the barrier de- to another while in D = 3 much more creases together with the mass of W- fine tuning in every space point is neces- M~(T) = M~w(1- T2/T~) [17,18] where sary. Unfortunately numerical simulation Tc = O(1TeV - IOOGeV) is the critical in 3 + 1 case is much more difficult and cor- temperature of the transition. Thus one respondingly much less reliable. So strictly may expect that the processes with bary- speaking the probability of the sphaleron onic charge nonconservation are indeed un- transitions is not known and a better un- A.D. Dolgov/Baryogenesis 35 derstanding of it is very much desirable be washed out and a new one cannot be though it seems plausible that they are generated. This conclusion can be avoided not too much suppressed so that thermal however if deviations from thermal equi- equilibrium with respect to the topology librium existed at the time when baryonic changing transitions was achieved in the charge nonconservation was still effective. early universe. This can be realized in particular if elec- troweak phase transition is of the first or- Another question related to the proba- der. However it is still an open question bility of the processes with AB # 0 is what is the type of the phase transition de- what is the of the sphalerons or pending in particular on the value of the in other words what is the preexponential mass. factor in expression (12). This factor char- acterizes the width of the potential near One more comment may be in order the saddle point in the directions orthog- here. We spoke before only about bary- onal to the trajectory over potential bar- onic charge nonconservation. In fact elec- rier and was calculated in ref. [20]. With troweak interactions break equally bary- this factor taken into account the proba- onic and leptonic charges so that (B- L) is bility of electroweak processes with bary- conserved. With this correction in mind all onic charge nonconservation in the phase the previous statements remain true with with broken electroweak symmetry can be the substitution of (B + L) instead of B. evaluated as Thus the following logical possibilities ex- ist for the electroweak baryogenesis(we simply enumerate them here and discuss in (14) some more detail giving recent references where H is the Hubble parameter charac- below): terizing the rate of the Universe expansion. - I. Change of the field topology is At temperatures above electroweak phase suppressed in three-dimensional space. transition the rate of baryonic charge non- Sphalerons are never abundant and elec- conservation is given by [20,21] troweak nonconservation of (B + L) is in- ~ a~T (15) effective. In that case we should return ei- ther to GUT baryogenesis or to some other Recall that expressions (14) and (15) are more recent proposals described in review valid only if sphalerons are in thermal equi- paper [4]. librium. If this is true then FAB/H >> 1 at - II. Sphaleron transitions are not sup- high temperatures and then abruptly falls pressed above and near the electroweak down with falling temperatures. Thus pro- phase transition and so (B + L) is strongly cesses with baryonic charge nonconserva- nonconserved at these temperatures. If tion are in equilibrium at high T and at this is true the following two possibilities some point are instantly switched off. Thus are open: any preexisting baryon asymmetry would - II.1. The electroweak phase transition 36 A.D. Dolgov/Baryogenesis is of the second order and so the baryon minimal standard model is the magnitude nonconserving processes, which were with of the Higgs boson mass. For a large value a very good accuracy in thermal equilib- of the latter the phase transition is sec- rium above the phase transition, would be ond order and for a small one it is first instantly completely switched off below it. order. To illustrate this statement let us In this case any preexisting (B + L) would consider the following temperature depen- be washed out and we again meet two pos- dent effective potential for the Higgs field ¢ sibilities: (temperature dependent terms appear due - la. The observed asymmetry might to interactions of the field ¢ with the ther- arise from an earlier generated (B - L) ei- mal environment of the cosmic plasma): ther by (B - L) nonconserved processes which exist e.g. in higher rank grand uni- U(¢, T) = m2(T)¢2/2 -t- (A¢4)ln(¢2/a2)/ fication groups or by charge non- 4 + ~,(T)¢ 3 + ... (16) conservation in decays of heavy Majorana fermion. Notations here are selfexplanatory. The - lb. Baryogenesis should take place at temperature dependence of the effective low energies below which mass is roughly speaking the following for sure demands new low energy weak m2(T) = -m~ + AT ~ where the con- physics. stant A is usually positive. (It is positive - II.2. Electroweak phase transition is in MSM.) Logarithmic dependence on ¢ first order so thermal equilibrium was came from one-loop quantum perturbative strongly broken when both phases coex- corrections to the potential. At high tem- isted. If this is the case (B+ L)-asymmetry peratures the potential has the only mini- could be generated in electroweak pro- mum at T = 0, cesses at temperatures near 1TeV. An im- of the ¢ is zero, and the electroweak sym- portant subdivision in this situation is: metry is unbroken. At smaller tempera- - 2a. The standard model is able to give tures a deeper minimum is developed at a correct magnitude of the baryon asym- nonzero ¢ and mass of the field near this metry of the Universe so that baryogenesis minimum is rn~t ~ 2m02 (we neglected here does not demand any physics beyond the logarithmic terms in U). One sees that minimal standard SU(3) × SU(2) × U(1)- the larger is m02 (and correspondingly the model (MSM). physical mass m~) the easier is the phase

- 2b. An extension of the minimal stan- transition. There is no consensus in the lit- dard model is necessary. This is not well erature about the value of mH separating defined and may include an introduc- first and second order phase transitions. tion of additional Higgs fields (like in su- While earlier perturbative calculations in persymmetric versions), considerable CP- the MSM [22] give a rather small value violation in the lepton sector, CP-violation mH ,,~ 45 GeV, it was argued that higher in strong interaction, etc. loop effects are essential [23-25]. Moreover since thermal perturbation theory for non- The essential quantity which determines abelian gauge fields suffers from severe in- the character of the phase transition in the frared divergences, nonperturbative effects ,4.D. Dolgov/Baryogenesis 37 might be important acting in favor of the different families because if the quark mass first order phase transition with higher mn matrix and the kinetic term in the La- [26]. It is supported by the recent lattice grangian are simultaneously diagonal then calculations [27,28]. For a more detailed the phase rotation would not change them. discussion and list of references see papers By these reasons the amplitude of CP- [5,29]. Hence we cannot make any rigor- violation in MSM is suppressed by the fac- ous conclusion now about the nature of tor (which is called the Jarlskog determi- the electroweak phase transition though it nant): seems probable that MSM with the exist- ing lower experimental bound on the Higgs A_ ,~ sin 012 sin 0~3 sin 031 sin ~cP - -- mass mH > 62 GeV given by LEP favors -- mo)(mo second order phase transition while in ex- - m )l tended models with several Higgs fields the E '2 (17) transition might be first order. Here Oij are mixing angles between dif- Even if the electroweak phase transition in ferent generations and ~cP is the CP- MSM is first order the generated asymme- odd phase in the mass matrix. The prod- try is expected to be very small. It is con- uct of sin's of these quantities is about nected with a strong suppression of CP- 10 -4 - 10 -5. E is the characteristic en- violating effects at high temperatures. CP- ergy of a process with CP-breaking. In the breaking in the MSM is created by the case considered when the temperature of imaginary part of the quark mass matrix the medium is above 100 GeV, E is of the (Cabibbo-Kobayashi-Maskawa matrix). If same order of magnitude. Correspondingly there are only two quark generations the one should expect that baryon asymmetry imaginary part is not observable because in MSM should be of the order of 10 -~°. the phase may be absorbed in a redefini- tion of the quark wave function. The state- This conclusion was questioned recently ment remains true with more quarks fam- by Farrar and Shaposhnikov [29,30]. They ilies with degenerate masses because the argued that flavor dependent tempera- unit matrix is invariant with respect to ture corrections to the quark masses in unitary transformations. One can see that the vicinity of the domain wall where the minimum number of quark families for the expectation value of the Higgs field which the imaginary part is observable is is changing nonadiabatically, may drasti- three with different masses of quarks with cally enhance efficiency of the electroweak the same value of electric charge. (If we baryogenesis. This effect is especially pro- believe that there is no extension of the nounced at the low energy tail of the quark standard model then the necessity of CP- distribution in the phase space. As a result violation for the generation of the charge the value of the baryon asymmetry may be asymmetry of the Universe justifies the ex- close to the observed one even in the mini- istence of at least three fermionic families.) mal standard model. This very interesting Moreover the amplitude of CP-violation is proposal is discussed by Shaposhnikov at proportional to the mixing angles between this Conference so I would not stop on the 38 A.D. Dolgov/Baryogenesis details of the model. a large selection of models the literature, each having a chance to be the right one. Despite all the attractiveness of the possi- A possible exception is the model with a bility of effective baryogenesis in the MSM large CP-violation in the lepton sector [33] it should be excluded if the experimen- which demands a heavy tau-neutrino with tal lower bound on the Higgs boson mass the mass of the order of 10 MeV. However proves to be above the value necessary the recent nucleosynthesis bounds [34-36] for successful first order phase transition. which close the window for u~-mass in the This seems rather probable now and the region 0.5-35 MeV strongly disfavor it. models with several Higgs fields are pos- sibly the next best choice. They may give In the case if the phase transition is sec- a larger CP-violation and what's more in ond order, baryon asymmetry could not these models both experimental and the- be generated by electroweak processes but, oretical bounds on the Higgs boson mass if sphalerons are effective, the latter may are much less restrictive. be very good for erasure of any preexist- ing (B + L)-asymmetry. A nonzero initial The generic feature of all scenarios of elec- (B - L)i-asymme,try is conserved by elec- troweak baryogenesis is a coexistence of troweak interactions and the subsequent two phases in one of which baryonic charge sphaleron processes would result in equal is strongly nonconserved, the correspond- baryon and lepton asymmetry B I = Lj = ing reactions are well in equilibrium, and (B - L)i/2. Assuming that this is indeed no asymmetry can be generated, while in the case one can derive a bound on the the second phase baryonic charge is prac- strength of (B - L)-nonconserving inter- tically conserved and the asymmetry also actions at lower temperatures when (and cannot be generated though by an op- if) (B + L)-erasure is effective. (One should posite reason. So the only place where keep in mind however that all these bounds baryon asymmetry may be produced are are valid only if there is no baryogenesis at the boundaries between the phases. The electroweak or lower temperature range.) outcome of such a process strongly de- If the rate of (B + L)-nonconserving spha- pends upon the interaction between the leron transitions is given by eqs.(14, 15), high temperature cosmic plasma and the the sphaleron processes are in equilibrium domain walls and in particular upon the in the temperature range velocity of the wall propagation in plasma. These problems are addressed in several 10 2 -- 10 3 < T < 1012 (GeV) (18) papers (for the recent ones see e.g. refs. [31,32]) but still more work in this field is For successful baryogenesis the processes desirable. with (B - L)-nonconservation should not be in equilibrium in this range. This idea Despite all these uncertainties the elec- was first used in ref.[37], where the model troweak baryogenesis is presently the most of baryogenesis through the decay of heavy fashionable scenario of creation of the Majorana fermion has been proposed, to building blocks of our Universe. There is put a bound on the Majorana mass of A.D. Dolgov/Baryogenesis 39 light neutrinos, rnM(u ) < 50 KeV. Neu- many possible forms of the interaction and trinos with a larger Majorana mass to- theoretical models giving rise to them so gether with sphalerons would destroy both that their more detailed description is out- baryon and lepton asymmetry. There ex- side the scope of the present talk and one ists a large literature on the subject (the should be addressed to original literature references can be found in the review pa- on the subject. per [4]) where the bounds on different types of (B- L)-nonconserving interac- Now I would like to turn to some more ex- tions are obtained. I would like to men- otic cases. The first one is a possibility of tion here only a recent paper [38] where it a large lepton asymmetry together with a was argued that lepton asymmetry stored normal small baryon asymmetry. Though in right-handed electrons, which are sin- the data gives a rather accurate value of glets with respect to nonabelian part of (within an order of magnitude), the value the electroweak group and due to that do of the lepton asymmetry is practically un- not interact with sphalerons, might be pre- known. The best limits follow from the served for the temperature down to ap- primordial nucleosynthesis which permits proximately 10 TeV. Below that the Higgs muonic and taonic lepton asymmetry close would effectively transform right- to unity while electronic lepton asymme- handed electrons into left-handed ones and try cannot exceed 1% (see [4] for the list subsequently sphalerons would convert the of references). The bound on the chemical lepton asymmetry in the sector of right- potential associated with electronic charge handed electrons into baryon asymmetry. is stronger because it would directly shift The creation of the initial lepton asymme- proton- equilibrium in weak reac- try could be favored by a rather strong vi- tions like n + u~ ~ p + e-, while u u and olation of leptonic charge conservation. All u~ influence n/p-ratio only through the to- other (B- L)-breaking interactions should tal energy density. Thus even in the most be out of equilibrium above 10 TeV while restricted case the value of lepton asym- the usual demand is that they are out of metry may be as large as 10 -2. equilibrium at much higher temperatures where either sphalerons come into equilib- A large lepton asymmetry could only be rium or where the initial (B - L) is pro- realized if the sphaleron processes were not duced. This invalidates some of the con- effective or if the asymmetry was gener- clusions obtained in the earlier papers (not ated below electroweak scale. Even if this quoted here) of stronger bounds on (B - is true, the majority of models naturally L)-nonconservation. Still the assumption give L ~ B but there are some examples that baryogenesis proceeds through trans- permitting L >> B (see e.g. [39,4]). In this formation of an initial (B - L)-asymmetry case we would have at our disposal an ex- into B-asymmetry permits to deduce in tra free parameter for the theory of primor- some cases more interesting bounds on dial nucleosynthesis, namely the chemical e.g. L-nonconservation than that follow- potential of . What's more the char- ing from direct experiments. There are too acteristic scale of spatial variation of the leptonic charge density IL might be much 40 A.D. Dolgov/Baryogenesis smaller than IB and if the former is in the that the distribution of baryons in the Uni- range lg~ < IL < Iv one may observe that verse would be in the form: by spatial variation of the abundances of F/2 light nuclei and in particular of 4He. NB ~ NBo + N1 cos --lB (19)

The relatively strong isocurvature fluctu- where ff is an arbitrary unit vector. The ations in leptonic sector with a possibly scale IB of the fluctuations is given by nonflat spectrum may be also interesting the exponentially stretched Compton wave for the theory of the large scale structure length of ¢ and could easily be as large as formation with a single dominant compo- 100 Mpc as was indicated by the observa- nent of hot dark matter. Usually one con- tions [42]. An interesting picture emerges if siders isocurvature perturbations in bary- No = 0 and the Universe consists of alter- onic sector which are stronger bounded by nating baryonic and antibaryonic layers. the isotropy of the cosmic microwave back- ground. Another unusual picture of the Universe, the so called island universe model may be Returning to the isocurvature fluctuations realized with the specific though not too in baryonic sector one may find plenty complicated model of baryogenesis [40]. In baryogenesis scenarios (see [4]) providing this model our Universe is a huge bary- very interesting perturbations with the onic island with the size large or about 10 l° spectrum varying from the flat one to that years (or z = 5 - 10), while floating in the having a prominent peak at a particular see of dark matter which is more or less wave length. The last case corresponds to uniformly distributed. There are two inter- a periodic in space distribution of bary- esting features of this model which may be onic matter. It may be naturally realized relevant to the structure formation. First, if three rather innocent assumptions are the background radiation comes to us from satisfied: the baryon empty regions so that the fluc- tuations in its temperature is not directly - 1.There exists a complex scalar field related to the density perturbations inside ¢ with the mass which is small in compar- the island. Second, our noncentral posi- ison with the Hubble parameter during in- tion inside the island would give rise to flation. The latter may be as large as 1014 intrinsic dipole, d ,,~ 10 -3, in the angu- GeV so one does not need a really light lar distribution of the microwave radiation scalar field. which is not related to our motion. The - 2. The potential of the field ¢ contains quadrupole asymmetry in this case would nonharmonic terms like )t[¢14. be rather small, q ,,~ d 2 ,-, 10 -6. It may - 3.A condensate of ¢ was formed dur- make easier structure formation in the cold ing inflationary stage which was a slowly dark matter model. (This point was em- varying function of space points. phasized to me by J. Silk.) Without in- trinsic dipole and with the fiat spectrum If these conditions are fulfilled then it can of perturbations more complicated models be proven (for the details see refs. [40,41] of the structure formation are necessary, A.D. Dolgov/Baryogenesis 41 like e.g. a mixture of hot and cold dark assuming that the only massive stable par- matter [43] or a model with cold dark mat- tides in the Universe are and ter and nonzero vacuum energy (cosmolog- electrons [45] and all the dark matter is ical constant). Both these models demand made of the normal baryonic staff. To some fine tuning which is not well under- do that one has to develop a scenario in stood today. The first one needs the en- which baryogenesis proceed much more ef- ergy density of hot and cold dark matter ficiently in relatively small space regions to be the same within the factor of 2 while giving/~ = 1 - 0.01 while it goes normally the other demands p~,c which is normally outside. The regions with that huge baryon time independent constant to be close to- number density mostly form black holes day to the critical energy density which is with the mass distribution time dependent, pc "~ rn~pt/t 2. The latter may be explained if the smallness of the ~[A~ ~' exp -'7 (20) cosmological constant is ensured by the so called adjustment mechanism (for the re- Parameters 3' and M0 cannot reliably view see [44]). Though these two possibili- found in the model but one reasonably ex- ties are more conservative than the island pect that 7 = O(1) and M0 is close to model still they are not the most economic the solar mass. These black holes might ones. Proliferation of the universe compo- be the objects observed in the microlensing nents from the purely baryonic universe to search reported here. If there are no other the mixed baryonic and hot dark matter massive stable particles one has to build or later on to baryonic and cold dark mat- a theory of the structure formation with ter and now to the mixture of all three these black holes which behave as normal of them (baryonic+cold+hot) with close cold dark matter. At the tail of the distri- energy densities is rather mysterious. On bution in mass there should be very heavy the other hand there are stable neutrinos black holes with masses like 106 - 10 9 solar which are very likely to be massive and masses which may serve as seeds for the it is also very plausible that there is su- structure formation. Still tilted spectrum persymmetry in particle physics so that of the initial perturbations may be desir- there should be a stable heavy particle. able if only cold dark matter is permitted. These two are perfect candidates for the hot and cold dark matter (what's more we Conclusions of the talk reflect to a large may have now dark solar size objects in extend my personal opinion and may not galaxies) so that it would be only natural be shared by everybody or not even by the that these particles participates as build- majority. ing blocks of the Universe. The unresolved question is their interaction strength which I. The best choice for the baryogene- provides very different number densities sis scenario is the dectroweak one and in and similar mass densities for the particles its framework the one based on the mini- of hot and cold dark matter. real standard model is the most appealing. The problems with the electroweak baryo- One may try to make a cosmological model genesis are the unknown probabilities of 42 A.D. Dolgov/Baryogenesis three dimensional reactions with classical References field configurations, which may question the scenario as a whole, and the type of the electroweak phase transition. The knowl- [1] A. D. Sakharov, Pis'ma Zh. Eksp. Tear. edge of the value of the Higgs boson mass Fiz. 5 (1987) 32. could be of great help here. [2] A. D. Dolgov and Ya. B. Zeldovich, Rev. II. If not MSM the low energy SUSY is Mod. Phys. 53 (1981) 1. the next best choice. SSC could be very interesting for that but alas... [3] E. W. Kolb and M. S. Turner, Annu. Rev. III. If electroweak interactions destroy Nud. Part. Sci. 33 (1983) 645. but not generate baryon asymmetry (like [4] A. D. Dolgov, Phys. Repts. 222 (1992) e.g. in the case of the second order phase 311. transition), a very interesting possibil- ity is baryogenesis through . [5] A. G. Cohen, D. B. Kaplan, and A. E. One needs to this end a heavy Majorana Nelson, Annu. Rev. Nucl. Part. Sci. 3 fermion with mass around 1012 Gev (plus- (1993). minus a few orders of magnitude) and cor- [8]F. C. Adams, J. R. Bond, K. Freese, J. respondingly a new physics beyond the A. Frieman, A. V. Olinto, Phys. Rev. D47 standard model. (1993) 426. IV. A very low temperature (below the electroweak scale) baryogenesis is not ex- [7]T. P. Walker, G. Steigman, D. N. cluded but there is no natural particle Schramm, K. A. Olive, and H.-S. Kung, physics model for that. Astrophys. J. 376 (1991) 51. V. Majority of models give lepton and [8]G. L. Kane, C. Kolda, L. Roszkowski, and baryon asymmetry of approximately the J. D. Wells, UM-TH-93-24. same magnitude but one may find scenar- ios giving L >> B with interesting conse- [9] L. Ford, Phys. Rev. D31 (1985) 710. quences for the primordial nucleosynthesis. [10] N. C. Tsamis and R. P. Woodard, Phys. VI. A better understanding of baryoge- Lett. B301 (1993) 351. nesis may be of interest for the theory of the large scale structure formation in par- [11] G. 't Hooft, Phys. Rev. Lett. 37 (1976) 8; ticular because in the process of baryogen- Phys. Rev. D 14 (1976) 3432. esis isocurvature density fluctuations with [12] A. A. Belavin, A. M. Polyakov, A. S. a complicated spectrum might be created. Schwarts, and Yu. S. Tyupkin, Phys. Lett. B 59 (1975) 85. [13] L. McLerran, Lectures presented at ICTP School on High Energy Physics, July 1992, Trieste, Italy; UM-AC-93-02. This work was supported in part by the Department of Physics of University of [141 V. A. Kuzmin, V. A. Rubakov, and M. E. Michigan and by NSF Young Investigator Shaposhnikov, Phys. Lett. B 155, (1985) reward to F. Adams. 36. A.D. Dolgov/Baryogenesis 43

[15]It. Dashen, B. Hasslacher,and A. Neveu, [31] B.-H. Liu, L. McLerran, and N. Turok, Phys. Rev. D 10 (1974)4138. PHys. Rev. D46 (1993) 2668. [16] N. S. Manton, Phys. Rev. D 28 (1983) [32] P. Huet, K. Kajante, R. G. Leigh, B.-H. 2019. Liu, and L. McLerran, Phys. Rev. D48 (1993) 2477. [17]D. A. Kirzhnits, Pis'ma ZhETF, 15 (1972) 745. [33] A. G. Cohen, D. B. Kaplan, and A. E. Nelson, Phys. Lett. B245 (1990); Nucl. [18]A. D. Linde, Repts. on Progress in Phys. B 349 (1990) 727. Physics, 42 (1979) 389. [34] E. Kolb, M. S. Turner, A. Chakravorty, [19]D. Yu. Grigoriev and V. A. Rubakov, and D. N. Schramm, Phys. Rev. Lett. 67 Nud. Phys. B 299 (1988) 67. (1991) 533. [20] P. Arnold and L.McLerran, Phys. Rev. D [35] A. D. Dolgov and I. Z. Rothstein, Phys. 36 (1987) 581. Rev. Lett. 71 (1993) 476. [21] S. Yu. Khlebnikov and [36]M. Kawasaki, P. Kernan, H.-S. Kang, M. E. Shaposhnikov, Nucl. Phys. B 308 R. J. Scherrer, G. Steigman, and T. P. (1988) 885. Walker, OSU-TA-5/93, UPR-0562T. [22] M. E. Shaposhnikov, Nucl. Phys. B 287 [37] M. Fukugita and T. Yanagita, Phys. Lett. (1987) 757. B174 (1986) 45; Phys. Rev. D42 (1990) 1285. [23] M. Dine, It. Leigh, P. Huet, A. Linde, and D. Linde, Phys. Lett. 283B (1992) 319; [38] J. M. Cline, K. Kalnulainen, K. A. Olive, Phys. Rev. D46 (1992) 550. UMN-TH-1201/93; TPI-MINN-93/16T. [24] P. Arnold and E. Espinosa, Phys. Rev. [39]A. D. Dolgov and D. K. Kirilow, J. D47 (1993) 3546. Moscow Phys. Soc. 1 (1991) 217. [25]J. E. Bagnasco and M. Dine, Phys. Lett. [40]A. D. Dolgov, A. F. lllaxionov, N. S. B303 (1993) 308. Kardashev, and I. D. Novikov, Zh. Exp. Teor. Fiz. 94 (1987) 1. [26] M. E. Shaposhnikov, CERN-TH.6918/93 [41] M. V. Chizhov and A. D. Dolgov, Nucl. [27] J. Krifpganz, B. Bunk, E. M. Ilgenfritz, Phys. B372 (1992) 521. and A. Schiller, Phys. Lett. B284 (1992) [42] T. J. Broadhurst, It. S. Ellis, D. C. Koo, 371. and A. S. Szalay, Nature, 343 (1990) 726. [28]K. Kajante, K. gummukainen, and M. [43]J. It. Primack, IV Rencontre de Blois, Shaposhnikov, Nucl. Phys. B407 (1993) Summary talk; SCIPP 92/51. 356. [44] S. Weinberg, Rev. Mod. Phys. 61 (1989) [29] G. R. Faxrar and M. E. Shaposhnikov 1. CEItN-TH.6734/93. [45]A. Dolgov and J. Silk, Phys. Rev. D47 [30]G. R. Farrar and M. E. Shaposhnikov, (1993) 4244. Phys. Rev. Lett. 70 (1993) 2833.