Asymmetric Sneutrino Dark Matter and the Omega(b)Omega(DM) Puzzle

Nature of Dark Matter and Dark Energy Alexander Alexandrovich Antonov【期刊名称】《现代物理（英文）》【年(卷),期】2017(8)4【摘要】The most complicated problems to solve in science are multidisciplinary problems, which include the problem of explaining of physical reality and physical essenceofimaginary numbers discovered more than five hundred years ago. However, the authors of the special relativity theory created more than a hundred years ago, were trying to unprovenly claim that they have solved this problem and that the imaginary numbers are not physically real with a principle of non-exceeding the speed of light. And physical experiments MINOS at the Tevatron collider and OPERA at the Large Hadron Collider were even seem to confirm such an assertion, since they could not refute the principle of non-exceeding the speed of light. However, since mathematics is the universal language of all exact sciences, the principle of the physical reality of imaginary numbers was still proven, but proven otherwise—with the theoretical and experimental studies of the vibrational processes in linear electric circuits that can be repeated and verified in any radioelectronic and electrical laboratory. And that is why they are definitely reliable and conclusive. Using the very general scientific principle of the physical reality of imaginary numbers allowed to correct the relativistic formula of special relativity theory and onthis basis to cre-ate a theory of hidden Multiverse containing more than two mutually invisible parallel universes. The nature of their invisibility is explained. It is proven that the existence of these unseen parallel universes explains the phenomenon of dark matter and dark energy. Using data obtained by the spacecrafts WMAP and Planck led to the discovery of quaternion structure of the hidden Multiverse and show that our hidden Multiverse is not the only one in nature.【总页数】16页(P567-582)【关键词】Imaginary;Numbers;Complex;Numbers;Hypercomplex;Numbers;Dark;Matte r;Dark;Energy;Antimatter;Special;Relativity;Theory;Multiverse;Hyperverse 【作者】Alexander Alexandrovich Antonov【作者单位】Research Centre of Information Technologies “TELAN Electronics”, Kiev, Ukraine【正文语种】中文【中图分类】O1【相关文献】1.Development of Matter and Testable Negative Matter as Unified Dark Matter and Dark Energy [J], Yi-Fang Chang2.Clues to the Fundamental Nature of Gravity, Dark Energy and Dark Matter [J], Eugene Terry Tatum;U. V. S. Seshavatharam3.The Nature of Dark Matter and of Dark Energy [J], Jacob Schaf4.The basic blocks of the universe matter: Boltzmann fundamental particle and energy quanta of dark matter and dark energy [J], MuradShibli;Sohail Anwar5.On the Nature of Dark Matter and Dark Energy [J], Baurov Yury Alexeevich;Malov Igor Fedorovich因版权原因，仅展示原文概要，查看原文内容请购买。

What is dark matter?
About 65 years ago, the first time that evidence of the existence of dark matter. At that time, Fulizizha Popovich found a large cluster of galaxies in the galaxy has a very high velocity, unless the quality of galaxy clusters is based on the number of calculations in which stars are more than 100 times the value, or cluster of galaxies can not bound lives of these galaxies. After decades of observation and analysis confirmed this. Although the nature of dark matter is still unknown, but by 80 years, accounting for about 20% of the energy density of dark matter to be widely accepted.
What is dark matter?
now we know that dark matter has become an important part of the universe. The total mass of dark matter is ordinary matter, 6.3 times the energy density in the universe, accounting for 1 / 4, but also important is that dark matter dominated the formation of cosmic structures. Now the nature of dark matter remains a mystery, but assuming it is a weak interaction of subatomic particles, then the resulting large-scale structure of the universe is consistent with the observations. Recently, however, the structure of galaxies and galaxy subanalysis shows that this assumption and the difference between observations, which at the same time provide a variety of possible dark matter theory was useless. Small-scale structure through the density, distribution, evolution and its environment studies can distinguish between these potential dark matter model for the nature of dark matter to bring a new dawn.

∗ ∗ Jγk = Uαi Uβj Uαj Uβi ; (α, β, γ and i, j, k cyclic),
(5)
or of the products of Jγk . For three generations, there are nine of such invariants Jγk but the unitarity of U makes all of them have the same imaginary component including the sign Im [Jγk ] = J = c1 c2 c2 3 s1 s2 s3 sin δ. (6)
The phase δ can be determined once one knows J and the mixing angles. Recently there have been many studies [5] where extracting J from the long-baseline three-flavour neutrino oscillations experiments is discussed. Existing 2 neutrino anomalies imply [6] three different scales of neutrino mass squared differences δm2 ≡ (m2 j − mk ):
On the determination of CP violating Majorana phases
M K Samal∗
Institute of Physics, Sachivalaya Marg, Bhubaneswar 751 005, India. The determination of CP violating phases in the Majorana neutrino mixing matrix using phenomenological constraints from neutrino oscillations, neutrinoless double beta decay, (µ− , e+ ) conversion and few other processes is discussed. We give the expressions for the phases in terms of the mixing angles and masses consistent with the recent data from Kamiokande.

a r X i v :h e p -p h /9811446v 2 30 N o v 1998UMD-PP-99-053Diffuse Ionization in the Milky Way and Sterile NeutrinosRabindra N.Mohapatra 1,and Dennis W.Sciama 2(1)Department of Physics,University of Maryland,College Park,MD-20742,USA.(2)SISSA and ICTP,Trieste and Dept.of Physics,University of Oxford,UK Abstract We propose the radiative decay of sterile neutrinos which fill a fraction of the halo dark matter with a mass of 27.4eV and lifetime of ∼1022sec.as a way to explain the observed diffuse ionization in the Milky Way galaxy.Since the sterile neutrino number density in the present universe can be adjusted by arranging its dynamics appropriately,the resulting hot dark matter contribu-tion to Ωm can be small as required by many scenarios of structure formation.On the other hand a 27.4eV neutrino could easily be the partial halo dark matter.One realization of this idea could be in the context of a mirror uni-verse theory where the gauge and matter content of the standard model are completely duplicated in the mirror sector (except for an asymmetry in the weak scale);the three mirror neutrinos can mix with the known neutrinos via some strongly suppressed mechanism such as the gravitational or heavy right handed neutrino mediated forces.Two of the mirror neutrinos (say ν′µand ν′τ)could play the role of the above sterile neutrino.The interstellar medium of the Milky Way galaxy is known to contain ionized hydrogen gas with properties which seem to defy common astrophysical explanations[1]. Similar problems also seem to exist for other galaxies studied.One solution that proposes to use a decaying dark matter neutrino was suggested by Sciama[1].Ac-cording to this idea,if the relic tau neutrinos which are supposed to pervade the cosmic background with a density of≈113(cm)−3have a mass of27.4eV and decay to one of the other two lighter neutrinos plus a photon with a lifetime of about2×1023sec.then they could provide enough ionizing photons on galaxy scale heights of nearly a kilopersec to solve this problem.The reason for this is that the decay photon has an energy of13.7eV and so would be able to ionize hydrogen-the lifetime is chosen to ensure that the resulting photonflux would produce the ob-served electron density.With these parameters the tau neutrino could be the dark matter needed to account for theflat rotation curve of the galaxy.Despite the at-tractiveness of this suggestion,the fact that a27.4eV neutrino must provide100% of the dark matter of the universe runs into trouble with the standard scenarios for structure formation.Also the fact that this scenario implies that theΩm=1may be in conflict with high z type Ia supernova data[2]as well as data from clusters[3], which suggest thatΩm may be considerably less than unity.Although one could use cosmic strings to get out of thefirst difficulty,it is tempting to look for alternative proposals that may keep the basic ingredients of the idea and yet not force us into a100%HDM-full universe.In order to set the stage for our suggestion,let us note that the reason why an active neutrino of mass27.4eV constitutes nearly100%of the dark matter in the universe is that its normal weak interaction allows it to remain in equilibrium until the universe is a second old.After it decouples,the annihilation of e+e−to photons increases the temperature of the universe slightly leaving the neutrinos unaffected.1Thus at the present epoch their number density becomes somewhat lower than that of the photons yielding about113neutrinos of each type per cm3.For the Hubble parameter h of about0.5,this leads toΩν=1.On the other hand if we had a sterile neutrino of mass27.4eV,its present number density will be controlled by its interactions with the standard model particles which by virtue of its being sterile are much weaker.This makes it decouple earlier from the cosmic soup(say at T≥200 MeV),thus making its number density much smaller(since the number of degrees of freedom contributing to the energy density of the universe changes drastically below the QCD phase transition temperature which happens to be around200MeV).Their contributions toΩis therefore much smaller.These relic sterile neutrinos will be uniformly distributed thoughout the universe and will eventually concentrate into the halos of galaxies after they form constituting a fraction of the halo dark matter (which could be about10%or so).If its lifetime to photonic decay is proportionally reduced,then it could explain the problem of diffuse ionization in our Galaxy while at the same time avoiding being the dominant dark matter constituent.In this letter we elaborate on this proposal,seek gauge theories where this proposal can be realized and suggest some tests.I.The sterile neutrino mass and lifetime implied by the solution to thediffuse ionization problemTo introduce the requirements for the sterile neutrino to solve the diffuse ion-ization problem,let us recapitulate some of the basic issues involved[1].The major problem that needs a solution is the observed diffuse ionization in the Milky Way, specifically its scale height of nearly670pc and its rather uniform distribution in different directions.Suggestions involving the cosmic rays have been ruled out by observations[4]and any local sources for hydrogen ionizing radiation must overcome2the problem of opacity due to neutral hydrogen HI,that makes it difficult to un-derstand the magnitude of the scale height.On the other hand if an all pervading medium of relic neutrinos decay to photon with an energy of13.7eV,it easily evade all these problems.The key formula for our purpose is the one that dictates the equilibrium be-tween the process of hydrogen ionization by the photons from neutrino decay and recombination of free electron with proton to form neutral hydrogen back.Ifαis assumed to denote the recombination rate of e−+p→H,the equilibrium condition is given by:nντν∼2×10−16 cm−3sec−1.If we now assume that the neutrino lifetime is2×1023sec.this is then consistent with the various constraints from supernova1987A observations[6].This requires the halo density of neutrinos to be about4×107cm−3.As has been shown by Sciama,within a simple approximation of isothermal and isotropic distribution of halo dark matter[5]of neutrinos,the above number density emerges quite naturally.A simple way to see this is to note that the halo density is known fromfits to the galaxy rotation curves to be aboutρ∼.3GeV cm−3.The formulaρ∼nνmνthen yields the above number for the halo density of tau neutrinos.This discussion can be translated to the case of sterile neutrinos,for whom the relic density will be given by:nν′(2)g∗(200MeV)where g∗(T)is the number of degrees of freedom of the particle species in equilibrium with electrons at the temperature,T.If we assume that the QCD phase transition3temperature is below200MeV,then we get g∗(200MeV)=261m3ν′(4)8πUsing the afore mentioned values for the parameters in the above expression,we get a lifetime for the sterile neutrinoτν′≃1022sec.for the choice ofµ23≃10−12µB forθ≃0.01.Thus we get the desired radiative lifetime to solve the diffuse ionization problem.Since we have quite reasonable values for all the necessary parameters involved in our mechanism,we feel that this is a viable solution to the problem at hand.A point that needs to be noted here is that the supernova bound for the radiative lifetime for the eV neutrinos need not apply to our case since we are considering a sterile neutrino and not an active one.Its production in the supernova will be different from the active neutrino case.This brings us to raise the two key particle physics issues that we must address:is it possible to have a viable model for a sterile neutrino whose mass of 27.4eV is not unnatural and how does it fit into the full neutrino picture that accomodates the observations or indications of neutrino oscillations in solar,atmospheric as well as the LSND data.We address these questions in the next section.II.The Complete Scenario for Neutrino Puzzles:There are various scenarios for neutrino masses that can be constructed to fit a radiatively decaying 27.4eV sterile neutrino.For simplicity of presentation,we focus on a variation of the following six neutrino picture that emerges in the context of the mirror universe model for particle physics[12]and assume the following patternfor the neutrino masses:m 2ν′e −m 2νe≃10−5eV 2;m νµ≃m ντ∼√The27.4eVν′µ,τwill play the role in solving the diffuse ionization problem.Next, we present a gauge model where the radiative decay with the required lifetime can emerge.The basic idea is that we must generate a reasonable transition magnetic moment between the activeνµandντ.For this we can choose a version of MSSM with R-parity violating interactions as in Ref.[7].Whereas we have chosen this particular model for the purpose of illustration,one could use any other model that generates a large neutrino magnetic moment while at the same time keeping the mass small[8].Let us consider the gauge group of the model to be G⊗G′where G and G’are identical groups with G operating on the visible sectorfields which contain the standard model particles and G’operating on the mirror sectorfields which have an identical spectrum as the visible sector.We choose G≡G′=SU(3)c⊗SU(2)L⊗U(1)Y.(All groups in the mirror sector will be denoted by a primed symbol).The spectrum of matter and Higgsfields for each sector is same as in the MSSM.The mirror sectorfields will be denoted by a prime on the abovefields.The basic idea of the class of models we will be interested in is that they will generate a transition magnetic momentµ23∼10−12µB while at the same time keeping all neutrino masses ≤1eV.For the superpotential,we choose,W=h u QH u u c+h d QH d d c+LH d e c+MH u H d++f(LµL eµc+LτL eτc)+f1LµLτe c+L e H d e chµ(LµH dµc+LτH dτc)(5)Note that this superpotential has an SU(2)H symmetry between the Lµand Lτ(as between(µc,τc)).We break this symmetry softly in the supersymmetry breaking sector by the slepton mass terms being different.As in Ref.[7],this model gives rise6to a large transition magnetic moment for theµandτneutrinos without simulta-neously giving them large masses.The value ofµ23is given byµ23≃ff1e M2ln M2mτF(M2,M′2,δ,δ′)(7)16π2where M,M′,δ,δ′are parameters characterising the supersymmetry breaking sector of the second and the third generation.It is not impossible to arrange these pa-rameters to get this mixing mass to be in the few eV range,since all one needs to do is to have F≈0.1.The key point here is that in the limit of the exact SU(2)H symmetry,F=0whereasµ23=0.This property enables us to maintain a degree of naturalness in generating the small neutrino masses.Note that this mass matrix gives rise to a maximal mixing pattern for theνµ−ντsector as required by the atmospheric neutrino data.The mass splitting between them must come from alter-7native sources.One way for example is to put in a doubly chargedfield∆⊕¯∆which is an SU(2)L singlet with a coupling in the superpotential∆e c e c and a symmetry violating term in the soft breaking term of type˜m˜µc˜µc˜∆.This generates a neutrino mass of typeνµνµat the two loop level.Its value can be estimated to be of ordermνµνµ≃f2M(8)so that the above diagonal term is of order0.03eV which is in the right range for the atmospheric neutrino data.This model leads to a one loop contribution to theνe mass given bymνe≃f2m2˜l(9)which is easily in the eV range if we require that f∼10−4.Thus the understand-ing of the solar neutrino problem would require veryfine tuned vacuum oscillation between theνe−ν′e.This would require that the soft slepton masses must be asym-metric between the normal and the mirror sector so that mνe≃mν′e.The mirror sector of the model in the limit of exact gauge symmetry and supersymmetry is assumed to be a complete duplicate of the visible sector.After electroweak symmetry breaking,we will choose the symmetry breaking vev v′wk to be much larger(about a factor of30)than the v wk.Similarly the slepton masses which result from supersymmetry breaking will also be required to be different in the two sectors.The mixing between the normal and mirror sector arise via the higher dimensional operators such as LµH u Lµ′H′u/M P l etc as in Ref.[12]and as demonstrated there,one can have eV range masses for theνµ,τand30eV mass for theν′τ,enabling our mechanism to operate.Coming to theνe sector,similar arguments also imply a mixing mass of order10−3eV and if mνe≃0.1eV,this gives sin22θνe−ν′e≃10−2which is in the right range for the MSW solar neutrino oscillation via the small angle oscillation.8We thus see that it is possible to construct plausible particle physics models for our proposal.It is worth pointing out that the large transition magnetic moment betweenνµandνtau which is an essential ingredient of our proposal has other applications.It has been suggested[14]that it can provide a mechanism to revive the stalled shock in supernovae.Another application is its usefulness in understanding pulsar velocities using resonant spinflavor transition[15]in the neutrino sphere of supernovae2).In conclusion,we have presented a modified version of the original tau neutrino radiative decay model for understanding the diffuse ionization in the Milky Way and other galaxies.The model avoids difficulties with structure formation.One particle physics realization of the idea is presented in the context of the already proposed mirror universe idea for neutrino puzzles.The work of R.N.M.is supported by the National Science Foundation grant No.PHY-9802551.References[1]For a review of the problem as well as the radiative neutrino decay solution,seeD.W.Sciama,Modern Cosmology and the Dark Matter Problem,CambridgeUniversity Press,1993.[2]S.Perlmutter et al.Nature391,51(1998).[3]V.Eke,S.Cole,C.S.Frenk and J.P.Henry,astro-ph/9802350;for a review ofthe situation,see J.A.Primack and M.A.K.Gross,astro-ph/9810204. [4]P.Meszaros,Ap.J.185,L41(1973).[5]J.A.R.Caldwell and J.P.Ostriker,Ap.J.251,61(1981).[6]E.W.Kolb and M.Turnner,Phys.Rev.Lett.62,509(1989);F.von Feilitzschand L.Oberauer,Phys.Lett.B200,580(1988);S.Dodelson and J.Jubas, Phys.Rev.D45,1076(1992).[7]K.S.Babu and R.N.Mohapatra,Phys.Rev.Lett.64,1705(1990).[8]K.S.Babu and R.N.Mohapatra,Phys.Rev.Lett.63,228(1989);G.Ecker,W.Grimus and H.Neufeld,Phys.Lett.B232,217(1990);D.Chang,W.Keung and G.Senjanovi´c,Phys.Rev.D42,1599(1990);N.Marcus and M.Leurer,Phys.Lett.B237,81(1990).[9]For a review,see S.Sarkar,Rep.Prog.Phys.59,1493(1996).[10]K.Enquist,K.Kainulainen and M.Thompson,Nucl.Phys.B373,498(1992).[11]R.Foot and R.Volkas,hep-ph/9811067and references therein.[12]Z.Berezhiani and R.N.Mohapatra,Phys.Rev.D52,6607(1995);R.Footand R.Volkas,Phys.Rev.D52,6595(1995).[13]D.Caldwell and R.N.Mohapatra,Phys.Rev.D48,3259(1993);J.Peltoniemiand J.W.F.Valle,Nucl.Phys.B406,409(1993).[14]E.K.Akhmedov,nza,S.T.Petcov and D.W.Sciama Phys.Rev.D55,515(1997).[15]E.K.Akhmedov,nza,D.W.Sciama,Phys Rev D56,617(1997).[16]A.Kusenko and G.Segre,Phys.Lett.B396,197(1997).10。

Detection
Direct detection experiments
Indirect detection experiments
DETECTION
If the dark matter within our galaxy is made up of Weakly Interacting Massive Particles (WIMPs), then thousands of WIMPs must pass through every square centimeter of the Earth each second.[84][85] There are many experiments currently running, or planned, aiming to test this hypothesis by searching for WIMPs. Although WIMPs are the historically more popular dark matter candidate for searches,[9] there are experiments searching for other particle candidates; the Axion Dark Matter eXperiment (ADMX) is currently searching for the dark matter axion, a well-motivated and constrained dark matter source. It is also possible that dark matter consists of very heavy hidden sector particles which only interact with ordinary matter via gravity.

2
Physics Department, McGill University, 3600 University St, Montreal,Quebec H3A 2T8, Canada
D´ epartement de Physique, Universit´ e du Qu´ ebec ` a Montr´ eal C.P. 8888, Succ. Centre-Ville, Montr´ eal, Qu´ ebec, Canada, H3C 3P8
1
Introduction
Speculations that fundamental constants may vary in time and/or space go back to the original idea of Dirac [1]. Despite the reputable origin, this idea has not received much attention during the last fifty years for the two following reasons. First, there exist various sensitive experimental checks that coupling constants do not change (See, e.g. [2]). Second, for a long time there has not been any credible theoretical framework which would predict such changes. Our theoretical mindset, however, has changed since the advent of the string theory. One of the most interesting low-energy features of string theory is the possible presence of a massless scalar particle, the dilaton, whose vacuum expectation value defines the size of the effective gauge coupling constants. A change in the dilaton v.e.v. induces a change in the fine structure constant as well as the other gauge and Yukawa couplings. The stabilization of the dilaton v.e.v., which usually renders the dilaton massive, represents one of the fundamental challenges to be addressed before string theory can aspire to describe the observable world. Besides the dilaton, string theory often predicts the presence of other massless or nearly massless moduli fields, whose existence may influence particle physics and cosmology and may also change the effective values of the coupling constants as well. Independent of the framework of string theory, Bekenstein [3] formulated a dynamical model of “changing α”. The model consists of a massless scalar field which has a linear −1 φFµν F µν , where M∗ is an associated coupling to the F 2 term of the U (1) gauge field, M∗ mass scale and thought to be of order the Planck scale. A change in the background value of φ, can be interpreted as a change of the effective coupling constant. Bekenstein noticed that F 2 has a non-vanishing matrix element over protons and neutrons, of order (10−3 − 10−2 )mN . This matrix element acts as a source in the φ equation of motion and naturally leads to the cosmological evolution of the φ field driven by the baryon energy density. Thus, the change in φ translates into a change in α on a characteristic time scale comparable to the lifetime of the Universe or larger. However, the presence of a massless scalar field φ in the theory leads to the existence of an additional attractive force which does not respect Einstein’s weak universality principle. The extremely accurate checks of the latter [4] lead to a firm lower limit on M∗ , M∗ /MPl > 103 that confines possible changes of α to the range ∆α < 10−10 − 10−9 for 0 < z < 5 [3, 5]. This range is five orders of magnitude tighter than the change ∆α/α ≃ 10−5 indicated in the observations of quasar absorption spectra at z = 0.5 − 3.5 and recently reported by Webb et al. [6]. Given the potential fundamental importance of such a result, one should remain cautious until this result is independently verified. Nevertheless, leaving aside the issue regarding the reliability of the conclusions reached by Webb et al. [6], it is interesting to explore the possibility of constructing a dynamical model, including 1

Furthermore, in order to be consistent with the observed structure of the universe, WMAP favours cold dark matter, or matter comprised of particles that are non-relativistic when galaxy formation starts. This naturally leads one to conclude that some sort of weakly interacting massive particle, or WIMP, is providing this dark contribution to our universe, and it is here that exciting astrophysics suddenly evolves into challenging and captivating particle physics! The Large Hadron Collider (LHC) at CERN in Geneva will start taking data next year and the purpose of this talk is to look at how much the LHC will be able to say about the dark matter problem, from the direct production and observation of WIMP candidates. Given the
In SUSY theories, all existing particles of the standard model have partners with opposite spin statistics called sparticles. Furthermore, one can impose a symmetry called R-parity under which the standard model particles are even whilst the SUSY particles are odd. This has two important phenomenological consequences: 1. We will pair produce sparticles at the LHC. 2. The lightest sparticle (LSP) is absolutely stable. Thus, the LSP is a natural WIMP candidate, and any consideration of SUSY models is highly relevant to the search for dark matter. It is noted that in different regions of the SUSY parameter space, one obtains different LSP’s, with possible options including the gluino, sneutrino, gravitino and the lightest neutralino. The last particle in this list is an admixture of the superpartners of the neutral SM gauge bosons, and remains the subject of the majority of studies. Thus, it is the only SUSY candidate to be considered from now on. 2.2 Reconstructing SUSY Models at the LHC

a r X i v :g r -q c /0303031v 3 7 A p r 2003Quintessential solution of dark matter rotation curves andits simulation by extra dimensionsV.V.KiselevState Research Center ”Institute for High Energy Physics”Protvino,Moscow region,142281RussiaFax:+7-0967-744739,E-mail:kiselev@th1.ihep.suAbstract On the base of an exact solution for the static spherically symmetric Einstein equations with the quintessential dark matter,we explain the asymptotic behavior of rotation curves in spiral galaxies.The parameter of the quintessence state,i.e.the ratio of its pressure to the density is tending to −1/3.We present an opportunity to imitate the relevant quintessence by appropriate scalar fields in the space-time with extra 2dimensions.1IntroductionThe rotation curves in spiral galaxies,i.e.the dependence of rotation velocity on the distance from the center of galaxy,as observed astronomically are typically given by the profile represented in Fig.1.This picture shows that the contribution determined by the visible matter (the dotted line)is falling down beyond the optical size of the galaxy (R opt )in agreement with the behavior expected from the Newton’s law for the gravity force of point-like mass,while in the central disk of galaxy this term is decreased with the decrease of mass involved in the interaction.The observed curves prove the presence of dark halo causing the flat,non-falling character of rotation curves in the asymptotic region beyond the optical size.The corresponding term shown by the dashed line begins to dominate at large distances.The described superposition of two contributions allows a phenomenological description in terms of universal rotation curves [2].The dark matter review can be found in [3].As for the explanations of the halo dominated contribution [4],we emphasize the attempt of[5]to build the dynamics in terms of scalar fields of the quintessence kind [6],so that the flat rotation curves were found to be the results of quintessence with the pressure-to-density ratio close to −1/3.Figure1:The characteristic rotation curve taken from[1].In this paper we apply our recent result on the exact solution of spherically symmetric static Einstein equations with the perfectfluid of quintessence[7]to the problem of rotation curves in the asymptotic region of dark-matter-halo dominance.This class of solutions agrees with the common consideration of static metrics given in[8].Wefind an exact description of asymptotic behavior in terms of the quintessence and give its interpretation by the scalarfields in extra2 dimensions.2Exact resultsIn this section,we,first,derive the relation between the metric components and the rotation velocity.Second,we show how the quintessential solution reproduces the asymptotic behavior of rotation curves in the halo dominant region.Third,we explore the adiabatic approximation in order to describe some variation in the pre-asymptotic region.Fourth,we give the interpretation of obtained results in terms of scalarfields in the extra dimensions.2.1Rotation equationsWe describe the rotation curves in the halo dominated region in the framework of Hamilton–Jacobi formalism.So,let us consider the equation for the motion of a test particle with a mass m in the gravitationalfield,gµν∂µS∂νS−m2=0(1) with the metric yielding the interval1d s2=g tt(r)d t2−where E and M are the conserved energy and rotational momentum,respectively.Then,from (1)we deduce∂S g 2tt E 2−1r 2+m 2 ,(3)which results in S =r (t )r 0d r 1E 2−V 2(r ),(4)where V 2is an analogue of potential,V 2(r )=g tt (r ) M 2∂E =const =−t +r (t )r 0d r 1∂M =const =θ−r (t ) r 0d r 1g ttr 2 rv M ,(9)relating the energy and the rotational momentum,where we have introduced the velocityv def =r ˙θ.The points of return are determined by˙r =0,⇒E 2−V 2=0,⇒M 2=m 2r 2v 2∂λ=∂r∂r =g tt∂∂λ 2=E 2−V 2,(10)so that the stability of circular motion implies the stability of potential,∂V 22d g tt (r )2dg tt (r )r ,which reproduces the exact result of(12).Introducing a re-scaled velocity with respect to the proper time,v 2=12d ln g tt (r )r 3w n +1,(13)where r n are positive constants,andg rr =−1r k r k +B n δi j ,(15)so that the averaging givesT [n ]i j =−p n (r )δi j ,independently of the parameter B .However,the Einstein equations are satisfied at the appro-priate value of B n =−3w n +1r 3w n +1=⇒ n T [n ]µν,so that we can get various exact spherically symmetric static solutions of Einstein equations by combinations of relevant terms.Let us consider the limit of quintessence with the state parameter w q =−1/3+ǫ→−1/3+0.Then,the metric component ˜g tt =1−αrǫ−1 tends to ˜g tt =1+αlnr 2α,(18)describing the asymptotic behavior at large distances,i.e.in the halo dominated region.Thus,the quintessential solution describes the asymptotic rotation curves with the metric(17)for the dark matter.Numerically,the quantity αis of the order of 10−6,which implies that the inner horizon is posed at a distance many orders of magnitude less than the parameter r q .The energy-momentum tensor for the quintessence is given by the expressionT [q ]t t =T [q ]r r =ρq (r )=−αr q+1 ,(19)T [q ]θθ=T [q ]φφ=−α3 1+1r q +1 ,(21)which has a singular point at ln r/r q =−1(see Fig.2).0.20.40.60.81 1.2-4-224r/r qw q w 0q =−1/3Figure 2:The parameter of state equation for the quintessence.To the same moment we can isolate two parts in the energy density,i.e.the logarithmic contribution and the 1/r 2-term,so that their state parameters are equal tow ln =−13,respectively.However,this separation is not unique,and any arbitrary redefinition of r q pa-rameter will result in the rearrangement.For example,introducing a large scale ln ˜r q /r q ,we get ˜w ln =−132+ln ˜r q /r q 3,at ln ˜r q /r q →∞,which is the case we have been going to consider with no singularity of the constant w .The spatial part of energy-momentum tensor for the logarithmic term is purely radial,while the 1/r 2-term is tending to the radial form with the small contribution isotropic over the angles.Thus,we can draw a conclusion on the dark matter described by the quintessence with a negative pressure at w q =−1/3corresponds to the asymptotically flat rotation curves,so that the exact solution of static spherically symmetric Einstein equations allows the superposition of various terms such as the Schwarzschild black hole surrounded by the quintessence.2.3Adiabatic modificationLet us consider a phenomenologically motivated variation of the parameter determining the pre-asymptotic behavior of the term contributing to the star velocities due to the dark matter halo,α=α0r 2∂α∂α∂r.In the metric under study we get∂ln αr q +1r q .The phenomenological parametrization of αgives2a 2r q +1r q ,so that the adiabatic approximation is sound at r ≫a ,while at r ∼a we deduce the conditionr q ∼a,which implies that the quintessence-term parameter r q is determined by the optical size of the galaxy,if we desire to incorporate the observed decrease of the dark matter contribution into the rotation curves within the description suggested above.We present the dependence of angle 0.51 1.52 2.53-0.4-0.3-0.2-0.1r/r qα−1T [q ]θθFigure 3:The adiabatic regularization of the angle component in the energy-momentum tensor of quintessence at a =r q (the solid curve)in comparison with the constant α(the dashed line).component for the energy-momentum tensor of the quintessence under the adiabatic change of the parameter αin Fig.3.Thus,the decrease of rotation velocity at the distances less than the optical size of galaxy as caused by the dark matter can be included in the offered mechanism by the small adiabatic change of the solution parameter.2.4InterpretationThe quintessential state with the negative pressure is usually considered as a perfect fluid approx-imation of a scalar field with an appropriate potential.So,let us start with a general contribution of the scalar field.A scalar field ϕwith the lagrangian equal toL =1generates the energy-momentum tensorTµν=∂µϕ∂νϕ−gµν 1g tt(r)d r2−r2[dθ2+sinθ2dφ2]+κ(y−1)d y2−1−κ(y4)d y24,(26) and the4dimensional(4D)interval is given by the conditiond y2−1=d y24.Introduce two scalarfields by the following definitions:¯ϕ=e y−1,(27) which is the isotropic function,and the tripletϕ(1)=e y4sinθcosφ,(28)ϕ(2)=e y4sinθsinφ,(29)ϕ(3)=e y4cosθ,(30) depending on the angles.Then,under the condition ofκ(y extra(r))=r2,for the metric components restricted to the4D world,wefind for the energy-momentum tensors the following expressions:¯T t t =¯T r r=¯Tθθ=¯Tφφ=−L(¯ϕ)=−12r2e2y4+V(ϕ(i)),(32)Tθθ=Tφφ=1The 4D space-time is considered aty −1=y 4,(34)so that at ¯V =V we can easily get that the scalar fields simulate the energy-momentum tensor of quintessence,if we put¯ϕ2= ϕ(i ) 2=−αr q +1 ,(35)2V =−αα¯ϕ2 =−α162ln r 4r 2q exp 1−4ˆ¯ϕ2 =−α4 2ln r 1The ghosts have negativesign in front of the kinetic term in the lagrangian.On a relevance of tachyons in the modern theory see review in [10].equations are satisfied,and hence,χ’s do not contribute to the4D Einstein equations,while their derivatives are adjusted in order to make the Einstein equations valid in the extra dimensions. In that case the extra-dimensional components of energy-momentum tensor are proportional to the metric,i.e.the situation in extra dimensions looks like the vacuum solution with the curvature depending on the3D distance as a parameter.So,the scalarfield equations are topics of separate investigations.Thus,we claim only that the extra-dimensional scalarfields with appropriate exponential potentials simulate the quintessential solution for the rotation curves.By the way,once we have encountered the problem of ghosts in the treatment with extra dimensions,we have to note that equations equivalent to(38)–(40)can be replicated in the4D space-time,so that the only difference is the overall negative sign of the lagrangian for the triplet field2.The change of normal phase to the ghost for the scalarfield is spectacular,since it is closely related to the variation of sign for the energy density.Both these facts are irrelevant in the case of adiabatic growth of the parameterαat ln r/r q≈0.The ghost phase is essential in the asymptotic region of large distances,if we do believe in the constant velocity of rotation in infinity.On another side,the negative value of kinetic energy is familiar from the quantum mechanics if the particle enters the classically forbidden region under the potential barrier.3ConclusionIn this paper we have found a quintessential solution for the problem on the asymptotic behav-ior of the rotation curves in spiral galaxies in the region of dark-matter-halo dominance.The explanation is constructed on the base of new class of metrics,describing the perfectfluid with a negative pressure in the static spherically symmetric gravitationalfield.This class satisfies the principle of superposition for various kind of matter contributions,and,hence,it does not destroys the Schwarzschild metric by adding some amount of exotic or ordinary matter.The quintessence with the state parameter w q=−1/3exactly results in theflat limit of rotation curves.Its energy-momentum tensor is simulated by scalarfields in extra dimensions with appropriate exponential potentials.The author thanks Prof.R.Dzhelyadin for the possibility to collaborate with the LHCB group at CERN,where this work has been done.I am grateful to Prof.S.S.Gershtein for useful discussions and valuable remarks,and to members of Russian team in LHCB for a kind hospitality.This work is supported in part by the Russian Foundation for Basic Research,grants01-02-99315,01-02-16585,and00-15-96645.References[1]K.A.Olive,arXiv:astro-ph/0301505.[2]M.Persic,P.Salucci and F.Stel,Mon.Not.Roy.Astron.Soc.281,27(1996)[arXiv:astro-ph/9506004].[3]S.Khalil and C.Munoz,Contemp.Phys.43,51(2002)[arXiv:hep-ph/0110122];P.J.Peebles and B.Ratra,arXiv:astro-ph/0207347.[4]R.H.Sanders and S.S.McGaugh,arXiv:astro-ph/0204521;A.Arbey,J.Lesgourgues and P.Salati,Phys.Rev.D65,083514(2002)[arXiv:astro-ph/0112324],Phys.Rev.D64,123528(2001)[arXiv:astro-ph/0105564], arXiv:astro-ph/0301533;U.Nucamendi,M.Salgado and D.Sudarsky,Phys.Rev.Lett.84,3037(2000) [arXiv:gr-qc/0002001],Phys.Rev.D63,125016(2001)[arXiv:gr-qc/0011049].[5]T.Matos, F.S.Guzman and D.Nunez,Phys.Rev.D62,061301(2000)[arXiv:astro-ph/0003398];T.Matos,F.S.Guzman,L.A.Urena-Lopez and D.Nunez,arXiv:astro-ph/0102419;T.Matos,F.S.Guzman and L.A.Urena-Lopez,Class.Quant.Grav.17,1707(2000) [arXiv:astro-ph/9908152];F.S.Guzman,T.Matos,D.Nunez and E.Ramirez,arXiv:astro-ph/0003105.[6]T.Chiba,Phys.Rev.D60,083508(1999)[arXiv:gr-qc/9903094];N.A.Bahcall,J.P.Ostriker,S.Perlmutter and P.J.Steinhardt,Science284,1481(1999) [arXiv:astro-ph/9906463];P.J.Steinhardt,L.M.Wang and I.Zlatev,Phys.Rev.D59,123504(1999) [arXiv:astro-ph/9812313];L.M.Wang,R.R.Caldwell,J.P.Ostriker and P.J.Steinhardt,Astrophys.J.530,17 (2000)[arXiv:astro-ph/9901388];V.Sahni,Class.Quant.Grav.19,3435(2002)[arXiv:astro-ph/0202076].[7]V.V.Kiselev,Class.Quant.Grav.20,1187(2003)[arXiv:gr-qc/0210040].[8]S.Mignemi and D.L.Wiltshire,Class.Quant.Grav.6,987(1989);S.Mignemi and D.L.Wiltshire,Phys.Rev.D46,1475(1992);S.J.Poletti and D.L.Wiltshire,Phys.Rev.D50,7260(1994)[Erratum-ibid.D52,3753 (1995)][arXiv:gr-qc/9407021];K.G.Zloshchastiev,Phys.Rev.D64,084026(2001)[arXiv:hep-th/0101075].[9]S.Chandrasekhar,Mathematical Theory of Black Holes(Oxford Science Publications,Ox-ford,1983).[10]G.W.Gibbons,arXiv:hep-th/0301117;A.Sen,JHEP0207,065(2002)[arXiv:hep-th/0203265].11。

The mysteries of the universe DarkmatterDark matter is one of the most enigmatic and perplexing concepts in the field of astrophysics and cosmology. It is a substance that makes up a significantportion of the universe, yet it remains largely elusive and mysterious to scientists. The existence of dark matter was first proposed in the 1930s by Swiss astronomer Fritz Zwicky, who observed that the visible matter in the Coma galaxy cluster could not account for the gravitational forces that were holding thecluster together. This led him to hypothesize the presence of unseen "dark" matter that was responsible for the gravitational effects. Since then, numerous observations and experiments have provided compelling evidence for the existenceof dark matter, but its true nature continues to elude researchers. One of the most compelling lines of evidence for dark matter comes from the study of the rotation curves of galaxies. When astronomers measure the velocities of stars and gas in a galaxy as a function of their distance from the galactic center, theyfind that the velocities do not decrease as expected with increasing distance. Instead, the velocities remain constant or even increase, indicating the presence of additional unseen mass that is providing the gravitational pull to keep thestars and gas in their orbits. This discrepancy between the observed motion of galactic objects and the visible matter in galaxies has led scientists to conclude that there must be a significant amount of dark matter present in galaxies, outweighing the visible matter by a factor of about six to one. Another piece of evidence for dark matter comes from the study of the large-scale structure of the universe. Observations of the cosmic microwave background radiation, the afterglow of the Big Bang, have revealed subtle patterns in the distribution of matter onthe largest scales. These patterns can be explained by the presence of dark matter, which exerts gravitational forces to shape the distribution of galaxies and galaxy clusters in the universe. Additionally, the gravitational lensing of distant galaxies by intervening mass concentrations, such as galaxy clusters, provides further evidence for the presence of dark matter. The bending of light from these distant galaxies can only be explained by the gravitational influence of unseenmass, which is consistent with the properties of dark matter. Despite the overwhelming evidence for the existence of dark matter, its true nature remains a profound mystery. Dark matter does not emit, absorb, or reflect light, making it invisible to telescopes and other instruments that rely on electromagnetic radiation for detection. This has made it incredibly challenging for scientists to directly observe and study dark matter, leading to a wide range of theoretical and experimental efforts to uncover its properties. One of the leading candidates for the identity of dark matter is a type of particle that interacts only weakly with ordinary matter and electromagnetic forces, known as a weakly interacting massive particle (WIMP). WIMPs are a theoretical class of particles that arise in extensions of the standard model of particle physics, and they are thought to have been produced in the early universe in sufficient quantities to account for the observed abundance of dark matter today. Numerous experiments around the world are dedicated to detecting WIMPs through their rare interactions with ordinary matter, such as through the recoil of atomic nuclei in underground detectors or the production of secondary particles in particle accelerators. Another potential explanation for dark matter is the existence of primordial black holes, which are hypothesized to have formed in the early universe from the gravitational collapse of overdense regions. These black holes would not emit significant amounts oflight or other radiation, making them difficult to detect directly. However, their gravitational influence on surrounding matter could betray their presence, and ongoing observational campaigns are searching for the signatures of primordial black holes in the universe. In addition to these particle-based and astrophysical explanations, some scientists have proposed modifications to the laws of gravity as an alternative to dark matter. These modified gravity theories seek to explain the observed gravitational effects in galaxies and galaxy clusters without invoking the presence of additional unseen mass. While these theories have had some success in reproducing certain observational data, they have yet to provide a comprehensive and consistent explanation for the full range of evidence for dark matter. The search for dark matter continues to be a vibrant and active area of research in astrophysics and particle physics. New generations of experiments are pushing the boundaries of sensitivity and precision in the huntfor dark matter particles, while astronomers are mapping the distribution ofmatter in the universe with ever-increasing detail. The discovery of dark matter would represent a profound breakthrough in our understanding of the fundamental constituents of the universe and the forces that govern its evolution. It would also have far-reaching implications for our understanding of the cosmos, from the formation of galaxies and galaxy clusters to the ultimate fate of the universe itself. The quest to unravel the mysteries of dark matter is not just ascientific endeavor, but also a deeply human one. It speaks to our innatecuriosity about the nature of the universe and our place within it. Therealization that the majority of the matter in the universe is invisible and fundamentally different from the matter we interact with on a daily basis is both humbling and awe-inspiring. It challenges our preconceived notions of the cosmos and forces us to confront the limits of our current understanding. The search for dark matter is a testament to the human spirit of exploration and discovery, as we strive to push the boundaries of knowledge and unlock the secrets of the universe. In conclusion, dark matter remains one of the most captivating and tantalizing mysteries in modern science. Its existence is supported by a wealth of observational evidence, yet its true nature continues to elude us. Whether it is composed of exotic particles, primordial black holes, or a modification of thelaws of gravity, the discovery of dark matter would revolutionize our understanding of the cosmos and our place within it. The ongoing quest to uncover the secrets of dark matter is a testament to the enduring human spirit ofcuriosity and exploration, as we continue to push the boundaries of knowledge and strive to unlock the mysteries of the universe.。

The Science of Dark Matter and ItsDiscoveryIntroductionDark matter is an elusive substance that makes up about 27% of the universe. It neither emits nor absorbs light, making it invisible to telescopes. Scientists have been studying dark matter for decades, and its discovery is considered one of the greatest mysteries of modern physics. In this article, we will delve into the science of dark matter, its properties, and the research that has led to its discovery.What is Dark Matter?Dark matter is a hypothetical substance that does not interact with light or any other form of electromagnetic radiation. It is invisible to telescopes, but its presence is inferred from its gravitational effects on objects that emit light. Dark matter is thought to be five times more abundant than visible matter, which is what stars, planets, and galaxies are made of.The Properties of Dark MatterAlthough scientists have yet to observe dark matter directly, they have been able to infer its properties from its gravitational effects. Dark matter is thought to be cold, meaning that its particles move relatively slowly. It is also believed to be non-interacting, meaning that it does not interact with other particles except through the force of gravity.Dark matter is widely thought to be made up of weakly interacting massive particles (WIMPs), which are particles that interact with each other only through the weak force and gravity. Other proposed candidates for dark matter particles include axions and sterile neutrinos, but these have not been observed directly.The Search for Dark MatterThe search for dark matter has been ongoing for several decades. One of the most promising methods for detecting dark matter involves looking for the energetic particles that result from the annihilation of dark matter particles. This method is called indirect detection and involves searching for gamma rays, neutrinos, or cosmic rays that are produced by the decay or annihilation of dark matter particles.Another way to detect dark matter is through the direct detection method, which involves looking for the recoil of atomic nuclei in a detector after they have been struck by dark matter particles. This method requires a sophisticated detector that can detect even the slightest signal. Several experiments are currently underway to detect dark matter particles using these methods.Discovery of Dark MatterThe discovery of dark matter can be traced back to the 1930s when Swiss astronomer Fritz Zwicky observed that the visible matter in the Coma cluster of galaxies was not enough to hold the cluster together. He hypothesized the presence of invisible matter that was holding the cluster together, which he called dark matter.Over the years, other scientists have provided evidence for the existence of dark matter. In the 1970s, Vera Rubin and Kent Ford studied the rotation curves of galaxies and found that the observed mass could not account for the observed rotation speeds. They concluded that there must be more mass in the form of dark matter that was holding the galaxies together.More recently, the European Space Agency’s Planck satellite produced a detailed map of the cosmic microwave background radiation, which is thought to be leftover radiation from the Big Bang. The map provided strong evidence for the existence of dark matter and its abundance in the universe.ConclusionThe discovery of dark matter is one of the most exciting and challenging areas of modern physics. Scientists continue to search for dark matter using a variety of methods, including indirect and direct detection. Although dark matter has yet to be observeddirectly, its presence and properties can be inferred from its gravitational effects on visible matter. As we continue to unravel the mysteries of dark matter, we are sure to gain new insights and a deeper understanding of the universe we inhabit.。

a rXiv:h ep-ph/992267v18Fe b1999BARI-TH/324-98Super-Kamiokande data and atmospheric neutrino decay G.L.Fogli,E.Lisi,A.Marrone,and G.Scioscia Dipartimento di Fisica and Sezione INFN di Bari,Via Amendola 173,I-70126Bari,Italy Abstract Neutrino decay has been proposed as a possible solution to the atmospheric neutrino anomaly,in the light of the recent data from the Super-Kamiokande experiment.We investigate this hypothesis by means of a quantitative analy-sis of the zenith angle distributions of neutrino events in Super-Kamiokande,including the latest (45kTy)data.We find that the neutrino decay hypothesis fails to reproduce the observed distributions of muons.PACS number(s):13.35.-r,13.35.Hb,14.60.PqTypeset using REVT E XThe Super-Kamiokande(SK)experiment has confirmed,with high statistical significance, the anomalousflavor composition of the atmospheric neutrinoflux.Such anomaly is found in all SK data samples,including(in order of increasing energy)sub-GeV e-like andµ-like events(SG e and SGµ)[1],multi-GeV e-like andµ-like events(MG e and MGµ)[2],and upward through-going muons(UPµ)[3].In particular,all muon event samples(SGµ,MGµ, and UPµ)show significant distortions of the observed zenith angle distributions,as compared with standard expectations.The recent muon data from the MACRO[4]and Soudan-2[5] experiments,as well as from thefinalized Kamiokande sample[6],are also consistent with the Super-Kamiokande data.The observed dependence of the muon deficit on both energy and direction can be beau-tifully explained via neutrinoflavor oscillations in theνµ→ντchannel[7].Transitions into sterile states are also consistent with the data[8,9],as well as subdominant oscillations in theνµ→νe channel[10].Determing theflavor(s)of the oscillating partner(s)of the muon neutrino will represent a crucial test of such explanation(s).In the meantime,it is useful to challenge the oscillation hypothesis and to investigate possible alternative scenarios[11].Neutrino decay has been recently proposed[12]as a possible solution to the atmospheric neutrino anomaly.In a nutshell,the muon neutrinoνµis assumed to have an unstable (decaying)componentνd,cosξ≡ νµ|νd =0,(1) with mass and lifetime m d andτd,respectively.In the parameter range of interest,theνµsurvival probability reads[12]Pµµ≃sin4ξ+cos4ξexp(−αL/E),(2) whereα=m d/τd,and L/E is the ratio between the neutrino pathlength and energy.The possible unstable component ofνe is experimentally constrained to be very small[12,13],so one can take P ee≃1.For large values of cosξand forα∼O(D⊕/1GeV)(D⊕=12,800km),the exponential term in Eq.(2)can produce a detectable modulation of the muon-like event distributions[12].In particular,the expected modulation seems to be roughly in agreement[12]with the reconstructed L/E distribution of contained SK events[7].However,the L/E distribution is not really suited to quantitative tests,since it is affected by relatively large uncertainties, implicit in backtracing the(unobservable)parent neutrino momentum vector from the(ob-served)final lepton momentum.Moreover,the L/E distribution includes only a fraction of the data(the fully contained events),and mixes low-energy and high-energy events,making it difficult to judge how the separate data samples(SG,MG,and UP)arefitted by the decay solution.Therefore,we think it worthwhile to test the neutrino decay hypothesis in a more convincing and quantitative way,by using observable quantities(the zenith distributions of the observed leptons)rather than unobservable,indirect parameters such as L/E.To this purpose we use,as described in[10],five zenith-angle distributions of neutrino-induced lepton events in Super-Kamiokande,namely,SG e and SGµ(5+5bins),MG e and MGµ(5+5bins),and UPµ(10bins),for a total of30data points.The data refer to the preliminary45kiloton-year sample of Super-Kamiokande,as taken from[8,9].The theoret-ical calculations are performed with the same technique as in[10],but theflavor survival probability refer now toνdecay[Eq.(2)]rather thanνoscillations.As in[10],conservative errors are assumed not only for the overall normalization of the expected distributions,but also for their shape distortions.The(dis)agreement between data and theory is quantified through aχ2statistic,which takes into account the strong correlations between systematics.Figure1shows the results of ourχ2analysis in the plane(cosξ,α),withαgiven in unit of GeV/D⊕.The regions at90and99%C.L.are defined byχ2−χ2min=4.61and 9.21,respectively.As qualitatively expected,the data preferα≃1and large cosξ,in order to produce a large suppression ofνµ’s coming from below.However,the absolute χ2is always much higher than the number of degrees of freedom,N DF=28(30data points−2free parameters).In fact,it isχ2min=86.2at the best-fit point[reached for (cosξ,α)=(0.95,0.90)].The very poor globalfit indicates that the zenith distributions cannot be accounted for by neutrino decay,contrarily to the claim of[12],which was based on reduced and indirect data(the L/E distribution).This situation should be contrastedwith theνµ↔ντoscillation hypothesis,which givesχ2min/N DF∼1both in two-flavor[7]and three-flavor scenarios[10].Even using“older”Super-Kamiokande data(i.e.,the published 33kTy sample[1–3]),we getχ2min∼65for theνdecayfit,still much higher than N DF.Basically,neutrino decay fails to reproduce the SK zenith distributions for the following reason:The lower the energy,the faster the decay,the stronger the muon deficit—a pattern not supported by the data.This can be better appreciated in Fig.2,which shows the SK data(45kTy)and the expectations(at the“best-fit”point)for thefive zenith angle(θ) distributions considered in our analysis.In each bin,both the observed and the expected lepton rates R are normalized to the standard values in the absence of decay R0,so that “no decay”corresponds to R/R0=1.The data are shown as dots with1σerror bars,while the decay predictions are shown as solid lines.The predictions are affected by strongly correlated errors(not shown),as discussed in Appendix B of[10].In Fig.2,the muon data show significant deviations from the reference baseline R/R0= 1,most notably for MGµevents.Theνdecay predictions also show some(milder)deviations, but their agreement with the data is poor,both in normalization and in shape.Neutrino decay implies a muon deficit decreasing with energy,at variance with the fact that the overall(θ-averaged)deficit is about the same for both SGµ’s and MGµ’s(−30%).The shape distortions of the muon zenith distributions are also expected to be exponentially weaker at higher energies(i.e.,for slower neutrino decay).This makes it impossible tofit at the same time the distorted muon distributions observed at low energy(SGµ)and at high energy(UPµ),and to get a strong up-down asymmetry at intermediate energy(MGµ)as well.Notice in Fig.2that,although the predicted shape of the zenith distribution appears to be in qualitative agreement with the data pattern for SGµ’s,it is not sufficiently up-down asymmetric for MGµ’s,and it is definitely tooflat for UPµ’s,where the muon suppression reaches the plateau Pµµ≃c4ξ+s4ξ,in disagreement with the observed cosθ-modulation[9]. Finally,we remark that the electron neutrinos,despite being“spectators”in theνdecay scenario(flat SG e and MG e distributions in Fig.2),play a role in thefit through the constraints on their overall rate normalization,as in theνµ→ντoscillation case[10].In conclusion,we have shown quantitatively that the neutrino decay hypothesis,although intriguing,fails to reproduce the zenith angle distributions of the Super-Kamiokande sub-GeV,multi-GeV,and upgoing muon data for any value of the decay parametersαand cosξ.Even at the“bestfit”point,data and expectations differ both in total rates and in zenith distribution shapes.Therefore,neutrino decay(at least in its simplest form[12])is not a viable explanation of the Super-Kamiokande observations.The strong disagreement between data and theory was not apparent in[12],presumably because the experimental information used there was rather reduced and indirect.Note added.When this work was being completed,our attention was brought to the recent paper[14],where several scenarios—alternative to neutrino oscillations—are consid-ered,including neutrino decay(for cosξ=1).The authors of[14]find that neutrino decay provides a very poorfit to the Super-Kamiokande data,consistently with our conclusions. As far as the neutrino decay hypothesis is concerned,our work has the advantage of being more general(cosξunconstrained),more refined in the statistical approach,and updated with latest SK data(45kTy)[8,9].REFERENCES[1]Super-Kamiokande Collaboration,Y.Fukuda et al.,Phys.Lett.B433,9(1998).[2]Super-Kamiokande Collaboration,Y.Fukuda et al.,Phys.Lett.B436,33(1998).[3]Super-Kamiokande Collaboration,Y.Fukuda et al.,hep-ex/9812014,submitted to Phys.Rev.Lett.[4]MACRO Collaboration,Phys.Lett.B434,451(1998).[5]Soudan-2Collaboration,W.W.M.Allison et al.,hep-ex/9901024,submitted to Phys.Lett.B.[6]Kamiokande Collaboration,S.Hatakeyama et al.,Phys.Rev.Lett.81,2016(1998).[7]Super-Kamiokande Collaboration,Y.Fukuda et al.,Phys.Rev.Lett.81,1562(1998).[8]M.Messier for the Super-Kamiokande Collaboration,in DPF’99,Proceedings of the1999Meeting of the American Physical Society,Division of Particles and Fields,edited by K.Arisaka and Z.Bern(Library of the University of California at Los Angeles,1999), to appear.Transparencies available at /dpf99.[9]A.Habig for the Super-Kamiokande Collaboration,in DPF’99[8].[10]G.L.Fogli,E.Lisi,A.Marrone,and G.Scioscia,Phys.Rev.D59,033001(1999).[11]J.M.LoSecco,hep-ph/9809499.[12]V.Barger,J.G.Learned,S.Pakvasa,and T.J.Weiler,astro-ph/9810121.[13]Review of Particle Physics,C.Caso et al.,Eur.Phys.J.C3,1(1998).[14]P.Lipari and M.Lusignoli,hep-ph/9901350.FIGURESFIG.1.Fit to the Super-Kamiokande data(45kTy,30data points)in the plane of the neutrino decay parameters cosξ= νµ|νd andα=m d/τd.The solid and dotted lines are defined by χ2−χ2min=4.61and9.21,corresponding to90%and99%C.L.for two variables.The analysis favorsα∼1GeV/D⊕and large cosξ.However,even at the bestfit point there is poor agreement between data and theory(χ2min/N DF=86.2/28=3.1),indicating thatνdecay is not a viable explanation of the Super-Kamiokande observations.FIG.2.Zenith angle distributions of Super-Kamiokande sub-GeV e-like andµ-like events(SG e and SGµ),multi-GeV e-like andµ-like events(MG e and MGµ),and upward-going muons(UPµ). Data:dots with±1σstatistical error bars.Theory(νdecay bestfit):solid curves.In each bin, both theoretical and experimental rates R are normalized to their standard(no decay)expectations R0.The solid curves do not appear to reproduce the muon data pattern.。

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迷迭香酸（罗丹酚酸）对H2O2处理过的皮肤黑色素瘤细胞的抗氧化作用Sun Mi Yoo1 and Jeong Ran Kang2*1.韩国光州500-741号东冈大学美容系2.韩国首尔143-701号建国大学生物工程系2009.2.6收到 2009.4.17接收本学科旨在检测迷迭香酸对人工孵育的皮肤黑色素瘤细胞在ROS下的抗氧化作用。

通过XTT比色法，以细胞毒性和抗氧化作用来分析细胞粘附活性，DPPH自由基清除活性以及H2O2处理1-10h和未经处理的两种情况下乳酸脱氢酶的活性。

用20-110 μM 的H2O2处理皮肤黑色素瘤细胞5-7h后，细胞活性的降低呈剂量和时间依赖性。

通过XTT比色法测得H2O2的半抑制浓度（IC50 ）为90μM。

同时H2O2增强了LDH细胞的剂量依赖性。

用50-90μM的H2O2处理8h后测得LDH50为60 μM H2O2。

迷迭香酸能增强细胞活性和DPPH自由基清除活性，降低乳酸盐脱氢酶的活性。

细胞的H2O2处理证实了对人工孵育的皮肤黑色素瘤细胞的强抗氧化作用。

通过H2O2的处理，迷迭香酸能在细胞内能增强细胞活性和DPPH 自由基清除活性，降低乳酸盐脱氢酶的活性。

这被认为是迷迭香酸对ROS（ROS）如H2O2的抗氧化作用。

Key words：DPPH-radical scavenging, LDH, rosmarinic acid, XTT assay关键字：DPPH自由基清除活性，乳酸脱氢酶，迷迭香酸，XTT比色法据研究发现，ROS通过氧化应激对细胞的损伤和一些脑部疾病比如帕金森症或心脏疾病例如心肌梗塞之间有很大的关联[Difazio et al., 1992; Delanty and Dichter, 1998].尤其是研究人员认为ROS是皮肤老化的一个主要的因素后，一直试图从ROS方面研究衰老。

[Yokozawa et al., 1998].据研究表明，ROS的氧化应激会通过萎缩细胞引起各种疾病，例如超氧自由基、H2O2（H2O2）或羟基自由基的巯基蛋白反应中断酶的活性，破坏脱氧RMA（DNA）或RMA（RNA），诱导细胞膜脂质过氧化。

Quintom with Single scalar field Recall single scalar fields like Quintessence , Phantom and Kessence can not cross -1
equivalent to two fields
For
A. B.
II.
Implications in CMB: W. Hu astro-ph/0410680 R. Caldwell and Doran: astro-ph/0501104 G. Zhao, J. Xia, M. Li, B. Feng and X. Zhang: astro-ph/0507482
III. Different from cosmological constant, Quintessence and Phantom in the determination of the evolutions and the fate of the universe A lot of studies on the evolution of UNIVERSE with w across -1 just give one example: Oscillating Quintom
G.Zhao, J. Xia, M.Li, B. Feng and X.Zhang astro-ph/0507482
Oscillating Quintom and the Recurrent Universe: astro-ph/0407432
Bo Feng, Minzhe Li, Yunsong Piao, Xinmin Zhang
Dark Energy and its connections to Neutrinos, Baryogenesis and Dark Matter

Dark Matter versus MONDT. R. Mongan【期刊名称】《现代物理（英文）》【年(卷),期】2017(8)6【摘要】Many physicists believe darkmatter accounts for flat velocity curves in spiral galaxies and find further evidence for dark matter in observations of the colliding “bullet cluster” galaxies 1E0657-56. Others claim a modified law of gravity called MOND (MOdified Newtonian Dynamics) explains galactic velocity curves better than dark matter. Merritt recently argued for MOND (arXiv:1703.02389) by claiming dark matter models cannot account for the MOND acceleration thresholda0&asymp;1.2x10-8cm/sec2 and the (Vobserved/VNewtonian) relation. However, this note shows that the HLSS model involving dark matter accounts for both the MOND acceleration and the(Vobserved/VNewtonian) relation. After this paper was accepted for publication, I learned that Man Ho Chan previously reached the same conclusion (arXiv:1310.6801) using a dark matter based analysis independent of the holographic approach used in this paper.【总页数】4页(P919-922)【关键词】Galactic;Structure;Dark;Matter;MOND;(MOdified;Newtonian;Dynamics)【作者】T. R. Mongan【作者单位】84 Marin Avenue, Sausalito, California, USA【正文语种】中文【中图分类】P1【相关文献】1.A Unifying Theory of Dark Energy, Dark Matter, and Baryonic Matter in the Positive-Negative Mass Universe Pair: Protogalaxy and Galaxy Evolutions [J], Ding-Yu Chung2.Development of Matter and Testable Negative Matter as Unified Dark Matter and Dark Energy [J], Yi-Fang Chang3.New connection between dark matter direct detections,astrophysical and cosmological observations with self-interacting dark matter [J], YiPeng Jing4.Explanation of Dark Matter, Dark Energy and Dark Space: Discovery of Invisible Universes [J], Alexander Alexandrovich Antonov5.The basic blocks of the universe matter: Boltzmann fundamental particle and energy quanta of dark matter and dark energy [J], MuradShibli;Sohail Anwar因版权原因，仅展示原文概要，查看原文内容请购买。

Big-Bang Nucleosynthesis
Thermo-Nuclear Fusion in Early Universe
• Best tested theory of Early Uபைடு நூலகம்iverse
• Baryon-to-photon ratio hnB/ng only parameter
• Neutron decay-anti-decay equilibrium ends when T~1MeV, they decay until they are captured in deuterium
decoupling – Need electrically neutral component
Dark Matter and Dark Energy
Hitoshi Murayama 290E
September 5, 2001
Introduction
• We can’t see neither Dark Matter nor Dark Energy • Then why do we talk about it? • This talk:
• For flat Universe:
r R3(1w)
– Matter-dominated Universe
r R3, R t 2 /3
– Radiation-dominated Universe r R4, R t1/2
– Vacuum-dominated Universe r R0, R eHt
Observational evidence for Dark Matter
Theoretical Arguments for Dark Matter

a rXiv:as tr o-ph/95189v118Oct1995.THE NATURE OF THE DARK MATTER KIM GRIEST Physics Department University of California,San Diego,La Jolla CA 920931.Introduction The dark matter problem has been around for decades,and there is now con-sensus that we don’t know what the most common material in the Universe is [1].It is “seen”only gravitationally,and does not seem to emit or absorb substantial electromagnetic radiation at any known wavelength.It dominates the gravitational potential on scales from tiny dwarf galaxies,to large spiral galaxies like the Milky Way,to large clusters of galaxies,to the largest scales yet explored.The universal average density of dark matter determines the ultimate fate of the Universe,and it is clear that the amount and nature of dark matter stands as one of the major unsolved puzzles in science.In this series of talks I will first recall the evidence for dark matter,with empha-sis on the dark matter in our own Galaxy.This overlaps somewhat with Primack’s lecture [these proceedings],so I will be brief.I then turn to the dark matter can-didates and how we might discover which (if any)of them actually exists.Then,Iwill focus in on two of my favorite candidates,the supersymmetric neutralino Wimp candidate,and the baryonic Macho candidate.For the later candidate,I will go into some detail concerning the one particular experiment with which I am involved,and present some results showing,that over a broad range of masses,this candidate has been ruled out as the primary constituent of the dark matter in our Galaxy.For the supersymmetric Wimp and especially the neutrino and axion candidates I will be brief,since there will be talks by Masiero [these proceedings]on these topics.2.Physical Evidence for Dark MatterEvidence for dark matter(DM)exists on many scales,and it is important to remember that the dark matter on different scales may be different–the dark matter in dwarf spirals may not be the dark matter which contributesΩ=1;in fact,the Ω=1dark matter may not exist.This consideration is especially important when discussing dark matter detection,since detection is done in the Milky Way and its environs,and evidence for dark matter outside the Milky Way may not be relevant. So,let me start with an inventory of dark matter in the Universe.The cosmological density of dark matter on different scales is quoted using Ω=ρ/ρcrit,whereρis the density of some material averaged over the Universe,and ρcrit is the critical density.Most determinations of Omega are made by measuring the mass-to-light ratioΥof some system and then multiplying this by the average luminosity density of the Universe:j0=1.9±0.1×108h−1L⊙/M⊙[Kirshner,these proceedings].Here h=0.4−1parameterizes our uncertainty of the Hubble constant. There are methods,such asΩbaryon from big bang nucleosynthesis,and potential reconstruction from bulkflows,which do not use depend upon j0,but methods which involve taking an inventory of material depend upon it.For example,the mass-to-light ratio in the solar neighborhood isΥ≈5,givingΩlum=0.003h−1= 0.003−0.007.If the solar neighborhood is typical,the amount of material in stars, dust and gas is far below the critical value.2.1Spiral GalaxiesThe most robust evidence for dark matter comes from the rotation curves of spiral ing21cm emission,the velocities of clouds of neutral hydrogen can be measured as a function of r,the distance from the center of the galaxy.In almost all cases,after a rise near r=0,the velocities remain constant out as far as can be measured.By Newton’s law for circular motion GM(r)/r2=v2/r,this implies that the density drops like r−2at large radius and that the mass M(r)∝r at large radii.Once r becomes greater than the extent of the mass,one expects the velocities to drop∝r−1/2,but this is not seen,implying that we do not know how large the extended dark halos around spirals are.For example,the rotation curve of NGC3198[2]impliesΥ>30h,orΩhalo>0.017.The large discrepancy between this number andΩlum is seen in many external galaxies and is the strongest evidence for dark matter.It is fortunate that the most secure evidence for dark matter is in spiral galaxies, since searches for dark matter can be made only in spiral galaxies;in fact only in our spiral,the Milky Way.Unfortunately,the rotation curve of the Milky Way is not well constrained,with recent measurements extending only to15to20kpc,and having differing amplitudes and shapes[3,4].This leads to substantial uncertainty in the amount of dark matter in our Galaxy.There are other indicators of the mass2of the Milky Way.By studying the motion of dwarf galaxies(especially Leo I at a distance of230kpc)Zaritsky,et al.[5]find a mass of the Milky Way of M MW= 1.25+0.8−0.3×1012M⊙,forΥMW≈90,andΩMW≈0.054h−1(assuming the Universe is like the Milky Way).A very recent study by Kochanek[6],does a maximum likelihood analysis including constraints from satellite velocities,the distribution of high velocity stars(local escape velocity),the rotation curve,and the tidal effects of M31,tofind a mass of the Milky Way inside50kpc of5.4±1.3×1011M⊙.It is interesting that this value is just what one expects from aflat rotation curve with v=220km/sec out to50kpc,so the Milky Way is very likely a typical spiral with a large dark halo.2.2Clusters of GalaxiesMoving to larger scales,the methods of determiningΩbecome less secure,but give larger values.There is a great deal of new evidence on dark matter in clusters of galaxies,coming from gravitational lensing[7]from X-ray gas temperatures[8] and from the motions of cluster member galaxies.For example,consider the Coma cluster which contains around a thousand galaxies.White et al.[9]recently collated some of the data on the Coma cluster,reporting separate measurements of the amount of mass in stars,hot gas,and in total.Within a radius of1.5h−1Mpc,they giveM star=1.0±0.2×1013h−1M⊙M gas=5.4±1×1013h−5/2M⊙M total=5.7−11×1014h−1M⊙,where the total mass is estimated in two completely different ways.Thefirst method is a refinement of Zwicky’s method of using the radial velocities of the member galaxies,and the assumption of virialization to gauge the depth of the gravitational potential well.The second method makes use of the ROSAT X-ray maps and the assumption of a constant temperature equilibrium to get the same information. Remarkably the two methods give the same mass within errors.Thus with a mass-to-light ratio ofΥ=330−620M⊙/L⊙,onefindsΩ=0.2−0.4,if the inner1.5Mpc of Coma is representative of the Universe as a whole.There is,however,a disconcerting in about the above numbers.As pointed out by White,et al.[9]M baryonto the entire Universe.But,big bang nucleosynthesis limitsΩbaryon<0.015h−2. IfΩtotal=1,the two inequalities are in quite strong disagreement for any value of h.So this is a puzzle.The conclusions of White,et al.,are that eitherΩis not unity,or that big bang nucleosynthesis is not working.However,there are other possible explanations,notably that the measurements of the total mass in clusters by gravitational lensing tend to give larger total mass than the X-ray and virial methods,and that mass and velocity bias may mean that clusters are not representative of the Universe as a whole.The story is clearly not yetfinished. 2.3Large Scale FlowsIt would be best to measure the amount of dark matter on the largest possible scales so that the sample is representative of the entire Universe.Within the past several years a host of large-scaleflow methods have been tried and are giving impressive results[10].These methods have the advantage stated above but the disadvantage that they depend upon assumptions about galaxy formation—that is, they depend upon gravitational instability theory,the assumption of linear biasing, etc.Also,the errors in these measurements are still large and the calculations are complicated,but they do have great promise,and tend to give values ofΩnear unity.A simple example comes from the observation that the local group of galaxies moves at627±22km sec−1with respect to the cosmic microwave background (CMB)(measured from the amplitude of the CMB dipole).If this motion comes from gravity,then the direction of the motion should line up with the direction where there is an excess of mass,and the velocity should be determined by the size of this excess.Thus,taking into account the expansion of the Universe,one hasv∝Ω0.6δρbδnb=0.9±0.2.Thus with the very conservative limit b>0.5,one hasΩ>0.2,and with the reasonable limit b>1,onefindsΩ>0.5.For this method to be reliable,δn/n must be measured on very large scales to ensure that convergence has been reached, and it is not sure that this is the case.4The above technique is only one of many related methods used to determine Ωon large scales.Another example is the detailed comparison of the peculiar velocities of many galaxies with the detailed maps ofδn/n.This should not only determineΩ,but serve as a stringent test for the theory that large-scale structure is formed by gravitational instability.A recent review by Dekel[10]surveys many such methods and concludes that reasonable evidence exists forΩ>0.3.Although these techniques holds much promise,it should be noted that different analyses of the same data sometimes lead to different conclusions.So for the time being,these estimates ofβshould not yet be viewed as robust[12].In conclusion,the observational evidence for large amounts of dark matter on galactic halo scales is overwhelming.On larger scales,the observational evidence for Ωin the0.1to0.2range is strong.On the largest scales,substantial observational evidence exists forΩ>0.3,and some evidence forΩnear unity exists,although this may be in conflict with observations on cluster scales.2.4The Baryonic Content of the UniverseAn important ingredient in the motivation for non-baryonic dark matter comes from big-bang-nucleosynthesis limits on the average baryonic content of the Uni-verse.To agree with the measured abundances of helium,deuterium,and lithium, the baryonic content of the Universe must be between0.01<Ωb h2<0.015[13,14,15]. Given the large uncertainty in h this means0.01<Ωb<0.1.These values are far below unity,so the theoretical predilection forΩtotal=1(or the observational evi-dence forΩ>0.3)forces the bulk of the dark matter to be non-baryonic.The lower limit of this range is actually above the abundance of known stars,gas,etc.,and so there also seems to be evidence for substantial baryonic dark matter as well.However,if one considered only the most secure dark matter,that found in spiral galaxies,then it is completely possible that it is all baryonic.Since this is the only dark matter which is directly accessible to experimental detection,it is crucial to consider the possibility of an entirely baryonic dark halo.2.5Distribution of Dark Matter in the Milky WayWhile we don’t know what the dark matter(DM)is,we have a fairly reasonable idea as to how much of it there is in the Galaxy,how it is distributed,and how fast it is moving.This information comes from the rotation curve of the Milky Way, and is crucial to all the direct searches for dark matter.If we say that the rotation curve of the Milky Way is constant at about v c=220km/sec out to as far as it is measured,then we know that the density must drop as r−2at large distances. This velocity also sets the scale for the depth of the potential well and says that the dark matter must also move with velocities in this range.Assuming a spherical5and isotropic velocity distribution is common,and a usual parameterization isa2+r20ρ(r)=ρ0d3v.π3/2v3cIt should be noted that the specifics of the above models are not very secure. For example,it is quite possible that the halo of our Galaxy isflattened into an ellipsoid,and there may be a component of the halo velocity which is rotational and not isotropic.Also,some(or even most)of the rotation curve of the Milky Way at the solar radius could be due to the stellar disk.Canonical models of the disk have the disk contributing about half the rotation velocity,but larger disks have been envisioned.Recent microlensing results may be indicative of a larger disk as well (see Section7.).Finally,other important points about our Galaxy’s geography include the fact that the nearest two galaxies are the LMC and SMC,located at a distance of50 kpc and60kpc respectively,that the halo of the Milky Way is thought to extend out at least this far,and that the bulge of the Milky Way is a concentration of stars in the center of our Galaxy(8.5kpc away)with a size of about1kpc.3.Brief Survey of Dark Matter CandidatesThere is no shortage of ideas as to what the dark matter could be.In fact, the problem is the opposite.Serious candidates have been proposed with masses ranging from10−5eV=1.8×10−41kg=9×10−72M⊙(axions)up to104M⊙black holes.That’s a range of masses of over75orders of magnitude!It should be clear that no one search technique could be used for all dark matter candidates.Evenfinding a consistent categorization scheme is difficult,so we will try a few. First,as discussed above,is the baryonic vs non-baryonic distinction.The main baryonic candidates are the Massive Compact Halo Object(Macho)class of candi-dates.These include brown dwarf stars,jupiters,and100M⊙black holes.Brown dwarfs are spheres of H and He with masses below0.08M⊙,so they never begin nuclear fusion of hydrogen.Jupiters are similar but with masses near0.001M⊙. Black holes with masses near100M⊙could be the remnants of an early generation of stars which were massive enough so that not many heavy elements were dispersed6when they underwent their supernova explosions.Other,less popular,baryonic pos-sibilities include fractal or specially placed clouds of molecular hydrogen[16].The non-baryonic candidates are basically elementary particles which are either not yet discovered or have non-standard properties.Outside the baryonic/non-baryonic categories are two other possibilities which don’t get much attention,but which I think should be kept in mind until the nature of the dark matter is discovered.The first is non-Newtonian gravity.See Begeman et al.[17]for a provocative discussion of this possibility;but watch for results from gravitational lensing which may place very strong constraints.Second,we shouldn’t ignore the“none-of-the-above”pos-sibility which has surprised the Physics/Astronomy community several times in the past.Among the non-baryonic candidates there are several classes of particles which are distinguished by how they came to exist in large quantity during the Early Universe,and also how they are most easily detected.The axion(Section5)is motivated as a possible solution to the strong CP problem and is in a class by itself.The largest class is the Weakly Interacting Massive Particle(Wimp)class (Sections4and6),which consists of literally hundreds of suggested particles.The most popular of these Wimps is the neutralino from supersymmetry(Section6). Finally,if the tau and/or muon neutrino had a mass in the2eV to100eV range, they could make up all or a portion of the dark matter.This possibility will be discussed by Masiero and also Klypin[these proceedings].Another important categorization scheme is the“hot”vs“cold”classification.A dark matter candidate is called“hot”if it was moving at relativistic speeds at the time when galaxies could just start to form(when the horizonfirst contained about 1012M⊙).It is called“cold”if it was moving non-relativistically at that time.This categorization has important ramifications for structure formation,and there is a chance of determining whether the dark matter is hot or cold from studies of galaxy formation.Hot dark matter cannot cluster on galaxy scales until it has cooled to non-relativistic speeds,and so gives rise to a considerably different primordial fluctuation spectrum[see Klypin,these proceedings].Of the above candidates only the light neutrinos would be hot;all the others would be cold.4.Thermal Relics as Dark Matter(Wimps)Among the particle dark matter candidates an important distinction is whether the particles were created thermally in the Early Universe,or whether they were created non-thermally in a phase transition.Thermal and non-thermal relics have a different relationship between their relic abundanceΩand their properties such as mass and couplings,so the distinction is especially important for dark matter detection efforts.For example,the Wimp class of particles can be defined as those particles which are created thermally,while dark matter axions come mostly from non-thermal processes.7In thermal creation one imagines that early on,when the Universe was at very high temperature,thermal equilibrium obtained,and the number density of Wimps (or any other particle species)was roughly equal to the number density of photons. As the Universe cooled the number of Wimps and photons would decrease together as long as the temperature remained higher than the Wimp mass.When the tem-peraturefinally dropped below the Wimp mass,creation of Wimps would require being on the tail of the thermal distribution,so in equilibrium,the number density of Wimps would drop exponentially∝exp(−m W imp/T).If equilibrium were main-tained until today there would be very few Wimps left,but at some point the Wimp density would drop low enough that the probability of one Wimpfinding another to annihilate would become small.(Remember we must assume that an individual Wimp is stable if it is to become the dark matter.)The Wimp number density would“freeze-out”at this point and we would be left with a substantial number of Wimps today.Detailed evolution of the Boltzmann equation can be done for an accurate prediction[Section6.2],but roughlyΩW imp≈10−26cm3s−1The best example of a non-thermal particle dark matter candidate is the axion [18].Actually,thermal axions are produced in the standard way,but if such axions existed in numbers so as to make up the dark matter,they would have lifetimes too short to still be around in quantity.However,there is another,more important, production mechanism for axions in the early Universe.The axion arises because the QCD Lagrangian contains a term¯θg2L⊃mass,so one scans the frequency spectrum looking for such a resonance signal.Two experiments,one at Florida and one at Brookhaven have already used this technique and reported negative results[20].The sensitivity of thoses early experiments was significantly below the expected signal,however,and it is this new experiment which will for thefirst time have the capability of detecting dark matter axions if in fact they exist.6.Search for Wimp Dark Matter(Neutralinos)Why is it important to actually search for and to identify the dark matter?Of course it is intrinsically interesting to know what the primary constituent of the Universe consists of,but also until we know the dark matter identity,there will always be the doubt that there is no dark matter,and instead there is someflaw in our knowledge of fundamental physics.Unfortunately,no one technique is useful for all the different candidates.The only way to proceed is to pick a candidate and design an experiment specific to that candidate.This is risky proposition,especially for the experimentalist who must spend many years of his or her life developing the technology and performing the search.For this reason,only the best motivated candidates are currently being searched for.There are hundreds of other dark matter candidates that we have not discussed at all.As one goes down the list of popular candidates,asking oneself which candidate is the most likely,I have to admit that“none-of-the-above”comes to mind.However,it is difficult to make any progress searching for an unspecified candidate.After“none-of-the-above”,I think the Wimp candidates,and especially the supersymmetric neutralino candidate,is probably the best bet.It may sound odd to an astrophysically oriented group such as yourselves that my best guess for the dark matter is a specific undiscovered elementary particle based on a theory for which there is no evidence,so I will spend some time describing my somewhat idiosyncratic reasons.Please see the lectures by A.Masiero[these proceedings]for additional in depth discussion of many of the issues covered here.Also see the new Physics Report “Supersymmetric Dark Matter”,by Jungman,Kamionkowski,and myself for more details on everything covered here.6.1Motivation for SupersymmetryFirst,why should astrophysicists take seriously supersymmetry,a theory which requires more than doubling the number of known elementary particles,none of which has yet been detected?When Dirac attempted to make special relativity consistent with quantum mechanics he discovered the Dirac equation.He also discover a disconcerting fact.There was a new symmetry,CPT symmetry,implied10by his equation,and this symmetry required that for every known particle there had exist a charge conjugate,or anti-particle.He resisted the idea of doubling the number of known particles,and initially hypothesized that the CPT partner of the electron was the proton.This idea was soon shown to be impossible,but fortunately the anti-electron and anti-proton were soon discovered,vindicating Dirac’s theory.The situation may be similar with regard to supersymmetry.Many attempts have been made to make general relativity consistent with quantumfield theory, especially within the framework of a theory which combines gravity with the strong and electroweak interactions.It is interesting that in all the most successful at-tempts a new symmetry is required.The powerful Coleman-Mandula theorem states that within the framework of Lie algebras,there is no way to unify gravity with the gauge symmetries which describe the strong and electroweak interactions.So the“super”-symmetry which successfully combines these interactions had to move beyond Lie algebras to“graded”Lie algebras.Graded Lie algebras are just like Lie algebras except they use anti-commutation relations instead of commutation relations.Thus they relate particles with spin particles to without spin.Examples of theories that attempt to combine gravity with the other forces include super-strings and super-gravity,where in both cases“super”refers to the supersymmetry. Thus,if such a symmetry exists in nature,every particle with spin(fermion)must have a related super-symmetric partner without spin(boson),and vice versa.As it now stands,standard quantumfield theory seems to be incompatible with gen-eral relativity.Since the world is unlikely to be incompatible with itself,it seems either quantumfield theory or general relativity must be modified,and of course a new theory which combines gravity with the strong and electroweak interactions would be the most elegant.Thus,one sees why so many particle physicists have become enamored with supersymmetry,and why many thousands of papers have been written on the subject.As in Dirac’s case,this doubling of the number of particles was disconcerting, and it was initially hoped that perhaps the neutrino could be supersymmetric part-ner of the photon.Now it is known that this is impossible,but unlike in Dirac’s case,no discovery of supersymmetric partners has quickly followed.In fact,it is now known that supersymmetry must be a“broken”symmetry,since perfect su-persymmetry requires that the masses of the super-partners be the same as their counterparts.This is easily arranged,but leaves the masses of all the superpartners undetermined.In fact,the masses could be so large that all the superpartners are completely undetectable in current or future accelerators and are therefore mostly irrelevant to current physics or dark matter detection.There are however some very suggestive reasons why the superpartners may have masses in the100GeV to several TeV range.First,there is coupling constant unification.The strength of the strong,weak, and electromagnetic interactions is set by the value their coupling constants,and11these“constants”change as the energy of the interactions increase.For example,theelectromagnetic coupling constantα=1128when electrons arecollided at the LEP machine at CERN.Several decades ago it was noticed that the three coupling constants would meet together at a universal value when the energy of interactions reached about1015GeV.This would allow a“Grand Unification”of the strong,weak,and electromagnetic interactions,and much model building was done.In the past few years,the values of the three coupling constants have been measured much more accurately,and it is now clear that,in fact,they cannot unify at any scale unless many new particles are added to the theory.Suggestively,if the supersymmetric partners exist,and have reasonably low masses they give just the right contribution to force the coupling constants to unify.Next,there is the gauge hierarchy problem.The standard model of particle physics is enormously successful.It accurately predicts the results of hundreds of measurements.In the standard model,fermions such as electrons are intrinsically massless,but develop a mass through interactions with the Higgsfield that is hy-pothesized tofill the Universe.The mass of a fermion then is just proportional to the strength of its coupling to the Higgsfield.The Higgs is thus an essential feature of the standard model.The Higgs also develops a mass through a“bare”mass term and interactions with other particles,but due to is scalar nature,the mass it acquires through interactions are as large as the largest mass scale in the theory.Thus,in any unified model,the Higgs mass tends to be enormous.Such a large Higgs mass cannot be,however,since it would ruin the successful perturba-tion expansion used in all standard model calculations.Thus in order to get the required low Higgs mass,the bare mass must befine-tuned to dozens of significant places in order to precisely cancel the very large interaction terms.At each order of the perturbation expansion(loop-expansion),the procedure must be repeated. However,if supersymmetric partners are included,thisfine-tuning is not needed. The contribution of each supersymmetric partner cancels offthe contribution of each ordinary particle.This works only if the supersymmetric partners have masses below the TeV range.Thus,stabilization of the gauge hierarchy is accomplished automatically,as long as supersymmetric particles exist and have masses in the range100-1000GeV.The enormous effort going into searches for supersymmetric particles at CERN,Fermilab,etc.is largely motivated by this argument.Even though no supersymmetric particles have been discovered,they have all been given names.They are named after their partners.Bosonic ordinary particles have fermonic superpartners with the same name except with the suffix“ino”added, while fermonic ordinary particles have bosonic(scalar)superpartner names with the prefix“s”added.So for example,the photino,Higgsino,Z-ino,and gluino are the partners of the photon,Higgs,Z-boson,and gluon respectively.And the squark, sneutrino,and selectron are the scalar superpartners of the quark,neutrino,and electron respectively.There are several superpartners which have the same quan-12tum numbers and so can mix together in linear combinations.Since these do not necessarily correspond to any one ordinary particle,they are given different names. For example,the photino,Higgsino,and Z-ino can mix into arbitrary combinations called the neutralinos,and the charged W-ino and charged Higgsino combine into particles called charginos.Finally,an interesting feature of most supersymmetric models is the existence of a multiplicatively conserved quantum number called R-parity,in which each superpartner is assigned R=−1,and each ordinary particle is assigned R=+1. This quantum number implies that supersymmetric particles must be created or destroyed in pairs,and that the lightest supersymmetric particle(LSP)is absolutely stable;just as the electron is stable since electric charge is conserved and there is no lighter charged particle into which it could decay.This fact is what makes supersymmetric particles dark matter candidates.If supersymmetry exists and R-parity is conserved,then some LSP’s must exist from the Early Universe.The only question is how many.6.2Relic Abundance in More DetailThe number density of any particle which was once in thermal equilibrium in the Early Universe can be found by solving the relevant set of Boltzmann equations. In most cases only one is neededdnχ=−3Hnχ−(n2χ−n eqχ2) σv annihilation.dtStarting at an early time when all particles were in equilibrium,one integrates this equation either numerically or using the standard“freeze-out”approximation[21]. and obtains the number density at t=0(today).The relic abundance is simply Ωχ=mχnχ/ρcrit,where mχis the mass of the LSP.13。