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

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Nature of Dark Matter and Dark Energy

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。

暗物质成品

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.

On the determination of CP violating Majorana phases

∗ ∗ 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.

Diffuse Ionization in the Milky Way and Sterile Neutrinos

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。

暗物质英文介绍

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.

Evolution of the Fine Structure Constant Driven by Dark Matter and the Cosmological Constan

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

SUSY and Dark Matter Constraints from the LHC

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

Quintessential solution of dark matter rotation curves and its simulation by extra dimensio

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 Dark matter

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 Its Discovery

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.。

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a r X i v :h e p -p h /0410114v 2 14 D e c 2004OUTP-04/17PAsymmetric Sneutrino Dark Matter and the Ωb /ΩDM Puzzle Dan Hooper 1,John March-Russell 2,and Stephen M.West 21Astrophysics Dept.,University of Oxford,Denys Wilkinson Building,Oxford OX13RH,UK 2Rudolf Peierls Centre for Theoretical Physics,University of Oxford,1Keble Road,Oxford OX13NP,UK (October,2004)Abstract The inferred values of the cosmological baryon and dark matter densities are strikinglysimilar,but in most theories of the early universe there is no true explanation of this fact;in particular,the baryon asymmetry and thus density depends upon unknown,and a pri-ori small,CP-violating phases which are independent of all parameters determining the dark matter density.We consider models of dark matter possessing a particle-antiparticle asymmetry where this asymmetry determines both the baryon asymmetry and strongly eﬀects the dark matter density,thus naturally linking Ωb and Ωdm .We show that sneutri-nos can play the role of such dark matter in a previously studied variant of the MSSM in which the light neutrino masses result from higher-dimensional supersymmetry-breaking terms.1IntroductionFor some time it has been apparent that the inferred values of the cosmological baryon and dark matter densities are strikingly similar.For example,the latest WMAP-determined range for the dark matter density,0.129>ΩCDM h2>0.095,is within afactor of a few of the combined WMAP and big-bang nucleosynthesis determined value of the baryon density,0.025>Ωb h2>0.012[1,2].In the vast majority of models of theearly universe,the cosmological baryon and dark matter densities are independently de-termined.The surviving baryon density is set by a baryon asymmetry generated during baryogenesis,and thus depends upon unknown,and a priori small CP-violating phases,as well as unknown baryon-number violating dynamics.In contrast,the dark matter density is set by the‘freeze-out’of the interactions that keep the dark matter in equi-librium,and is independent of the dynamics of baryogenesis.In particular,althoughweakly-interacting massive particles at the TeV-scale naturally have a relic density of O(1)times the critical density,this is not at all the case for baryons.The Boltzmann equations show the size of the baryon relic density in the absence of an asymmetry is O(10−11).Thus the comparative closeness of the baryon and dark matter densities poses a puzzle.One possible approach to this problem is to more closely integrate the dynam-ics of baryogenesis with that of the origin of dark matter.In particular,it is natural to consider models where the dark matter and baryon sectors share a quantum number, either continuous or discrete,which provides a relation between their surviving number densities and thus energy densities.1Speciﬁcally,in this letter we consider models of dark matter possessing a particle-antiparticle asymmetry where this asymmetry strongly eﬀects the dark matter density, and through the electroweak(EW)anomaly,determines the baryon asymmetry,thus naturally linkingΩb andΩCDM.(A noteworthy early attempt along these lines which shares some features with our model is contained in Ref.[5].)The shared quantum number clearly requires that the dark matter particle not be it’s own antiparticle,so the putative dark matter candidate cannot be the standard LSP neutralino of the broken Minimal Supersymmetric Standard Model(MSSM).In fact,we will show in sections3 and4that sneutrinos can play the role of such dark matter in a previously studied variant of the MSSM in which the light neutrino masses result from higher-dimensional supersymmetry-breaking terms[6,7,8,9,10].This model preserves all the successes of the MSSM,such as stability of the weak scale and uniﬁcation of gauge couplings,while being,at least in part,testable at the LHC.Before we proceed to the calculation of the relic dark matter and baryon densities and the details of our model,it is useful to consider some aspects of the idea of a shared quantum number determining the ratio of baryon to dark matter.First,consider the simpliﬁed case in which,to a very good approximation,the dark matter and baryon sectors cannot exchange their conserved quantum number after itsﬁrst production.As an example,consider the situation in which the asymptotic baryon number B=1states of the Standard Model(SM)have global charge,q,while the lightest asymptotic states(with mass m dm)in a hidden sector carry charge,Q.Then conservation of global charge implies that q(n b−n dm),where the n’s are the number densities of the indicated(anti)particles.Further assume that interactions in both sectors are strong enough such that almost all antiparticles are eliminated by annihilation with their particles(assuming Q/q<0for simplicity).This impliesn b=cn dm with c=|Q/q|,(1)which in turn leads toΩbm dm n bm dm.(2)Thus the energy densities are indeed related,but the ratio is only naturally O(1)if the ratio of the baryon to dark matter masses is not too small.It is important to note that this disfavours models of the above type where the dark matter candidate is a‘hidden sector’particle and favours a particular class of models where the dark matter candidate has weak scale mass,its mass arising either from electroweak symmetry breaking,or from the dynamics which drives electroweak breaking,such as supersymmetry softly broken at the weak-scale.2As a consequence,the naive statement of Eq.(1)alsorequires modiﬁcation as theapproximation of negligible interactions between the two sectors,and thus negligible ex-change of the shared conserved quantum number,does not hold in realistic models.In this situation,the ratio of the conserved quantum number stored in the two sectors,c, is not simply given by Q/q,but is determined by the‘chemical’equilibrium conditions between the two sectors just before the freeze-out of the relevant interactions.We will further discuss this point in section2.Moreover,two other alterations to the naive re-lation Eq.(2)can be present.First,the shared quantum number may only be conserved modulo n,in which case‘self’annihilations may occur,and second,it is not always the case that dark matter interactions are eﬃcient enough such that n2In extensions of the SM such as the MSSM where many gauge-non-neutral fermionic and scalar states also gain mass at this scale,the beta-function coeﬃcient for SU(3)QCD sharply increases as energies are reduced below the weak scale,and the conﬁnement scale and thus baryon mass is naturally not very much smaller than m weak.a neutralino LSP with negligible coannihilations with other SUSY particles.In such a case,the resulting relic density is simplyΩh2∼=1.04×109√(a+3b/xF ),(3)where M Pl is the Planck mass,x F is the WIMP’s mass over the freeze-out temperature, g∗is number of relativistic degrees of freedom available at freeze-out and a and b are related to the WIMP’s self-annihilation cross section byσv=a+bv2+O(v4),v being the relative velocity of the annihilating WIMPs.For a weakly interacting relic,x F is generally about20and varies only mildly with changes in the cross section or mass.If we instead consider a dark matter candidate and its antiparticle,the calculation becomes somewhat diﬀbeling these species1and2,we now have each particle’s self-annihilation cross section,σ11=σ22,and the particle-antiparticle annihilation cross section,σ12=σ21.In the limit thatσ12is much smaller thanσ11,we simply get two decoupled species which each provide the relic density of Eq.(3).Otherwise,the eﬀective cross section becomesσ11+σ12for each species.For the two species together,a density ofΩh2∼=2×1.04×109√(a11+a12+3(b11+b12)/x F)(4)is produced.This case is essentially the calculation of the density of a relic with the coannihilation of a degenerate particle[12].If an asymmetry exists between the number density of particles and antiparticles in the early universe,again this calculation becomes modiﬁed.The most well known exam-ple of this is the baryon-antibaryon asymmetry which leads to the current baryon density of the universe despite the very large baryon-antibaryon annihilation cross section.In such a case,where the particle-particle and antiparitcle-antiparticle annihilation cross sections(σ11andσ22)are zero,or negligibly small,the minimum relic density can be related to the magnitude of the particle-antiparticle asymmetry:Ωh2min=Ωh2bary Am bary,(5)whereΩh2bary is the current density of baryons in the universe,A and A bary are the particle-antiparticle asymmetries of our relic and of baryons,deﬁned by A=(n−M Pl x Fg∗1andΩ2h2∼=1.04×109√(a22,eﬀ+a21,eﬀ+3(b22,eﬀ+b21,eﬀ)/x F),(7)where the eﬀective cross sections are given bya11,eﬀ=a11,a12,eﬀ=x F ∞x F a12e−x+A dx, a22,eﬀ=a22,a21,eﬀ=x F ∞x F a12e−x dx, b11,eﬀ=b11,b12,eﬀ=2x2F ∞x F b12e−x+A dx, b22,eﬀ=b22,b21,eﬀ=2x2F ∞x F b12e−x dx.(8)The factor,e−x/(e−x+A),is the depletion of the second species due to the asymmetry at a temperature,T=m/x.The eﬀect of this depletion depends on the size of the asymmetry and the cross sections involved.If the estimate of Eq.(5)is considerably less than the standard two-species result of Eq.(4),then the asymmetry has little impact and the sum of Eqs.(6)and(7)is nearly equal to Eq.(4).If,however,the estimate of Eq.(5)is larger than the standard two-species result,the relic density moves from the value found with Eq.(4)towards that of Eq.(5).Ifσ11/σ12is small,then the result will be closer to Eq.(5).Ifσ11/σ12is large,then the density will be less modiﬁed.Note that in some cases,the eﬀect of an asymmetry can be to lower the density of a relic by up to a factor of two.This occurs whenσ11andσ12are comparable thus eﬃciently deplete the second species while leaving theﬁrst largely uneﬀected.Although these eﬀects are rather model dependent,the net eﬀect can be large regions of parameter space which predict the observed density of dark matter for a WIMP with a mass near m∼m pΩWMAP h2/Ωbary h2,for a matter-antimatter asymmetry similar to that for baryons.For concreteness,we consider a speciﬁc example of such a model in the following section.3An Example:Mixed Sneutrino Dark MatterWithin the context of the Minimal Supersymmetric Standard Model(MSSM),sneutrinos do not make a very appealing dark matter candidate.They annihilate quite eﬃciently, resulting in a relic density smaller than the observed dark matter density for sneutrinos lighter than about500GeV.Furthermore,their elastic scattering cross section is suﬃ-ciently large to be easily observed by direct dark matter experiments.Thus it is natural that in contrast to other supersymmetric dark matter candidates,sneutrino dark matter has received considerably less attention[13].Looking beyond the vanilla MSSM,however,it is quite easy to construct a viable model for sneutrino dark matter.For example,sneutrinos could mix through A-terms with a singlet forming a mixed sneutrino state.This would reduce the annihilation cross section,potentially providing the appropriate quantity of dark matter,as well as reduce the elastic scattering cross section to experimentally acceptable levels.In fact,such ascenario has previously been discussed as a way to reconcile the results of the direct dark matter detection experiments DAMA and CDMS [8].These models have light sneutrino mass eigenstates which are mixtures of left-handed ‘active’sneutrinos,and right-handed ‘sterile’sneutrinos.Such mixing naturally arises in models in which the light neutrino masses are gen-erated by supersymmetry breaking eﬀects [6,7,9,10].The importance to us of these models is that the light sneutrino states share a non-anomalous (B −L )-symmetry with the baryons which is only weakly broken by the Majorana neutrino masses.In analogy to the Giudice-Masiero mechanism for the Higgs µ-term there exists a global symmetry that forbids a direct mass,M R NN ,and neutrino Yukawa coupling,λLNH u ,involving the SM singlet right-handed neutrino superﬁeld N ,but allows non-renormalizable couplings to a supersymmetry-breaking hidden-sector ﬁeld T .The right-handed neutrino mass and the neutrino Yukawa coupling,λLNH u ,then only arise from 1/M planck -suppressed terms involving the fundamental supersymmetry breaking scale m I ∼(vM pl )1/2,where v is the weak scale.The relevant terms in the Lagrangian areL = d 4θ h T †M 2N †N +h B T †T T †M LNH u,(9)where all dimensionless couplings g,h ,etc,are taken to be O (1).The structure of the Lagrangian can be enforced by some simple symmetries [6,7,9],including R-parity,which leads to a stable lightest supersymmetric particle (LSP)dark matter candidate.After supersymmetry is broken in the hidden sector at the scale m I ,the F and A components of the ﬁeld T acquire intermediate scale vevs, F T ∼ A T 2∼m 2I .Substituting these vevs into the Lagrangian shows that after SUSY breaking,there arises:(1)a neutrino Yukawa coupling of size ∼10−7−10−8,(2)right-handed neutrino and sneutrino masses at the weak scale ,(3)a weak-scale trilinear scalar A -term,and (4)a right-handed sneutrino lepton-number violating B -term with magnitude B 2∼(few ×100MeV)2.These together lead to two sources of neutrino masses,a tree level see-saw contribution,as well as a dominant 1-loop contribution,leading to a consistent and attractive neutrino phenomenology [6,9].More relevant for us,the sneutrino mass matrix squared is˜ν∗n m 2L 12Av sin β12Av sin βm 2R ˜νn ∗ ,(10)where we have ignored the small lepton number violating B -term for the moment.There-fore mixing between the left-handed ‘active’sneutrino,˜ν,and the right-handed ‘ster-ile’sneutrino,˜n ,occurs,producing the light mass eigenstate ˜ν1=−˜νsin θ+˜n ∗cos θ,where tan 2θ=−√3Note that the size of the A terms is limited by considerations of vacuum stability [10].This can have important consequences for detection,potentially making consistent the DAMA and CDMS experiments depending upon parameters[8].For the purposes of our discussion this splitting is irrelevant.)We now turn to the calculation of the relative asymmetry in the sneutrino and baryon sectors.The method is a simple adaption of the standard‘chemical’equilibriation techniques applied to,for example,the calculation of the ratio B/(B−L)in the SM[15] or MSSM[16]in the presence of anomaly-induced baryon number violating processes in the early universe.For each species of particle we introduce a chemical potential,µA, and for each interaction in equilibrium,say A+B↔C+D there is a corresponding relation among chemical potentialsµA+µB=µC+µD.Note that when in thermal(not necessarily chemical)equilibrium the CP-conjugate speciesA =−µA.Theasymmetry in particle-antiparticle number density for the relevant case ofµ≪T and a species of mass m is given by n−where theﬁrst equality arises from A-term mediated interactions(as the A terms are O(m w)it is simple to show that these are in equilibrium),and the second equality arises from SU(2)w×U(1)Y gaugino interactions.4In terms ofµ0,µu L,andµνL,the condition Eq.(11)is unchanged in the case of the MSSM+k rhd neutrino supermultiplets.Theﬁnal step in the calculation of the relative number densities proceeds by ex-pressing the relevant densities in terms of the independent chemical potentials.For the baryon number density B the result is simplyB=6T2µuL.(13) For the sneutrino asymmetry the result depends upon the mass spectrum of the sneutrino mass eigenstates relative to T c.In the range of parameters of interest to us where the light sneutrino eigenstate˜ν1is the LSP we have m1<T c.On the other hand the heavier eigenstate˜ν2can have m2>T c or m2<T c.If both eigenstates satisfy m<T c then the sneutrino density is(allowing for a possible k such states)S=kT23µνL(14)while if only m1<T c then S is half as large.Finally using the non-perturbative relation Eq.(11)weﬁnd thatAB =k6(15)depending on m2.We view k=1as most likely,so we specialize to that case in the next section.Finally we mention that a full susy-mass-threshold dependent calculation of the relative asymmetries introduces only small corrections to this result(see Ref.[16]for a similar analysis in the MSSM case).In the end the vital point is that independent of whatever dynamics at scales E>T c produces an asymmetry in either the baryon sector,or in the neutrino or sneutrino sector,the(B+L)-anomaly-induced interactions together with EW gaugino and A-term interactions automatically distributes the asymmetry between the baryons and the light sneutrino states,with a predictable A/A bary ratio.The asymmetry could originate from, e.g.a GUT-based baryogenesis mechanism,or maybe more interestingly in the context of the sneutrino dark matter model there is the possibility that it could arise via a resonant leptogenesis mechanism at the TeV-scale as discussed in Ref.[10].The end result is that we expect1/3>∼A/A bary>∼1/6independent of the source of the asymmetry.4Asymmetric sneutrino and baryon abundancesWe will now apply the formalism of section2to the sneutrino model.Given the value of 1/3>∼A/A bary>∼1/6,we expect the role of the matter-antimatter asymmetry to be mostimportant for sneutrinos with masses on the order of m∼few×m pΩWMAP h2/Ωbary h2≃30GeV.For this reason,we will focus on the mass range of about10to80GeV.In this range,the most important annihilation channel is s-channel Z-exchange to fermions. This is a p-wave amplitude,and has no a-term in the expansion in v2(see section2). This is also only a sneutrino-antisneutrino process(i.e.σ11,22,notσ12,21).Other channels include t-channel neutralino and chargino exchanges to neutrinos and charged leptons. The channel to charged leptons includes both a and b terms in the v2expansion.Addi-tionally,sneutrino-sneutrino pairs(or antisneutrino-antisneutrino pairs)can annihilate via t-channel neutralino exchange to neutrino pairs of the sameﬂavor.This is the only contribution toσ12,21in this model.The annihilation cross sections for the neutralino and chargino exchange processes depend on the masses and mixings of these exchanged particles,although the Z-exchange channels do not.We have adopted the parameters M1=300GeV,M2=300GeV,µ=600 GeV and tanβ=50throughout our calculation.Additionally,there is the mixing angle between the sneutrino and the singlet which can be varied.This quantity has the eﬀect of reducing all electroweak couplings of the sneutrino eigenstate by a factor of sin2θ,i.e. reducing the annihilation cross sections by a factor of sin4θ.Finally,one can consider the s-channel exchange of Higgs bosons to bb.In the right frame,a matter-antimatter asymmetry of A/A bary≃1/6was included.To further illustrate this eﬀect,we show the result of this calculation across one value of sinθinﬁgure2.Below about30GeV,the matter-antimatter asymmetry has little eﬀect on the calculation and the solid and dot-dashed lines fall nearly on top of each other.In the range of roughly30-70GeV,however,the asymmetry pulls the relic density above the standard symmetric result into the range favored by WMAP.Above this range,sneutrino-antisneutrino annihilation decreases,leading to larger relic densities for the case with no asymmetry.The relic density for the asymmetric case,however,is largely determined by the sneutrino-sneutrino annihilation cross section in this region, so does not increase as rapidly,therefore resulting in a relic density much closer to the preﬀered value,even for m˜ν>70GeV.5Indirect DetectionSneutrinos in the mass range we have studied here annihilate dominantly through s-channel Z exchange in the early universe.This annihilation channel consists of a b-termFigure1:The regions of parameter space which provide the quantity of mixed sneutrinocold dark matter measured by WMAP,0.129>ΩCDM h2>0.095.In the left frame,the standard calculation with no matter-antimatter asymmetry is used.In the center framethe eﬀect of a matter-antimatter asymmetry with A/A bary≃1/6is included,while in the right frame a matter-antimatter asymmetry A/A bary≃1/3is assumed.Notice the much larger regions of acceptable parameter space in cases with asymmetry.We use thefollowing parameters:M1=300GeV,M2=300GeV,µ=600GeV,tanβ=50and m h=115GeV.The region above the solid line is excluded by measurements of the invisible Z decay width[14].in the expansionσv=a+bv2+O(v4),and thus is very eﬃcient for annihilations at low velocities which take place in the late universe.At low velocities,the process˜ν˜ν→νν, via t-channel neutralino exchange,is the most important annihilation channel.Given these characteristics,searches for gamma-rays,anti-protons,positrons or other particles produced in sneutrino annihilations in the Galactic halo are quite ineﬃcient. Due to the rather large elastic scattering cross sections of sneutrinos,however,indirect detection techniques involving the capture of dark matter in bodies such as the Sun can be very eﬀective.Neutrino telescopes detect neutrinos produced in dark matter annihilations in the core of the Sun by observing’tracks’of muons generated in charged current interactions. If our sneutrino dark matter candidate is of muon or tauﬂavor,theﬂux of muons gener-ated in this way in a detector at Earth is on the order of10−12cm−2s−1[8],in conﬂict with data from the Super-Kamiokande and MACRO experiments,for example[17].If the sneutrino candidate,however,is of electronﬂavor,these bounds can be easily averted.6ConclusionsIn the standard freeze-out calculation for a weakly interacting dark matter relic,there is little reason to expect a density of dark matter which is similar to the density of baryons,short of anthropic arguments.In this letter,however,we have presented an explanation for the similarity between these two quantities.Our solution introduces an asymmetry between dark matter particles and anti-particles which is related to theFigure2:The thermal relic density as a function of mass for sneutrinos+antisneutrinos with no asymmetry(dot-dash),with a matter-antimatter asymmetry of A/A bary≃1/6 (solid)and the estimate of Eq.(5)(dots).The relic density range favored by WMAP is bound by dashed lines(0.129>ΩCDM h2>0.095).sinθ=0.3,M1=300GeV,M2=300 GeV,µ=600GeV,tanβ=50and m h=115GeV have been used.See text for details.baryon-antibaryon asymmetry.This leads to a natural dark matter relic density of the same order of magnitude as the baryon density.As an example,we considered a mixed sneutrino dark matter candidate which trans-fers its particle-antiparticle asymmetry to the baryons through the electroweak anomaly. We carry out the relic density calculation for such a candidate andﬁnd substantial re-gions of parameter space in which the observations of WMAP can be satisﬁed.With no asymmetry,only a narrow strip of parameter space can provide the observed relic density.References[1]D.N.Spergel et al.,Astrophys.J.Suppl.148(2003)175[arXiv:astro-ph/0302209].[2]S.Eidelman et al.[Particle Data Group Collaboration],Phys.Lett.B592,1(2004).[3]F.Wilczek,arXiv:hep-ph/0408167.[4]G.R.Farrar and G.Zaharijas,arXiv:hep-ph/0406281.[5]D.B.Kaplan,Phys.Rev.Lett.68,741(1992).[6]N.Arkani-Hamed,et al,Phys.Rev.D64,115011(2001)[arXiv:hep-ph/0006312];N.Arkani-Hamed,et al,arXiv:hep-ph/0007001;[7]F.Borzumati and Y.Nomura,Phys.Rev.D64,053005(2001)[arXiv:hep-ph/0007018];F.Borzumati,et al,arXiv:hep-ph/0012118;[8]D.R.Smith and N.Weiner,Phys.Rev.D64,043502(2001)[arXiv:hep-ph/0101138];D.Tucker-Smith and N.Weiner,arXiv:hep-ph/0402065.[9]J.March-Russell and S.M.West,arXiv:hep-ph/0403067.[10]T.Hambye,J.March-Russell and S.M.West,JHEP0407(2004)070[arXiv:hep-ph/0403183];S.M.West,arXiv:hep-ph/0408318.[11]K.Griest and D.Seckel,Nucl.Phys.B283,681(1987)[Erratum-ibid.B296,1034(1988)].[12]K.Griest and D.Seckel,Phys.Rev.D43,3191(1991).[13]T.Falk,K. A.Olive and M.Srednicki,Phys.Lett.B339,248(1994)[arXiv:hep-ph/9409270];L.E.Ibanez,Phys.Lett.B137,160(1984);J.S.Hagelin,G.L.Kane and S.Raby,Nucl.Phys.B241,638(1984);L.J.Hall,T.Moroi andH.Murayama,Phys.Lett.B424,305(1998)[arXiv:hep-ph/9712515];T.Han andR.Hempﬂing,Phys.Lett.B415,161(1997)[arXiv:hep-ph/9708264].[14]T.Hebbeker,Phys.Lett.B470,259(1999)[arXiv:hep-ph/9910326].[15]J.A.Harvey and M.S.Turner,Phys.Rev.D42,3344(1990).[16]T.Inui,T.Ichihara,Y.Mimura and N.Sakai,Phys.Lett.B325,392(1994)[arXiv:hep-ph/9310268].[17]G.Giacomelli[MACRO Collaboration],Braz.J.Phys.33,211(2003)[arXiv:hep-ex/0210006];I.De Mitri[MACRO collaboration],arXiv:hep-ex/0212055.a r X i v :h e p -p h /0410114v 2 14 D e c 2004OUTP-04/17PAsymmetric Sneutrino Dark Matter and the Ωb /ΩDM Puzzle Dan Hooper 1,John March-Russell 2,and Stephen M.West 21Astrophysics Dept.,University of Oxford,Denys Wilkinson Building,Oxford OX13RH,UK 2Rudolf Peierls Centre for Theoretical Physics,University of Oxford,1Keble Road,Oxford OX13NP,UK (October,2004)Abstract The inferred values of the cosmological baryon and dark matter densities are strikinglysimilar,but in most theories of the early universe there is no true explanation of this fact;in particular,the baryon asymmetry and thus density depends upon unknown,and a priori unknown and possibly small,CP-violating phases which are independent of all parameters determining the dark matter density.We consider models of dark matter possessing a particle-antiparticle asymmetry where this asymmetry determines both the baryon asymmetry and strongly eﬀects the dark matter density,thus naturally linking Ωb and Ωdm .We show that sneutrinos can play the role of such dark matter in a previously studied variant of the MSSM in which the light neutrino masses result from higher-dimensional supersymmetry-breaking terms.1IntroductionFor some time it has been apparent that the inferred values of the cosmological baryon and dark matter densities are strikingly similar.For example,the latest WMAP-determined range for the dark matter density,0.129>ΩCDM h2>0.095,is within afactor of a few of the combined WMAP and big-bang nucleosynthesis determined value of the baryon density,0.025>Ωb h2>0.012[1,2].In the vast majority of models ofthe early universe,the cosmological baryon and dark matter densities are independently determined.The surviving baryon density is set by a baryon asymmetry generated dur-ing baryogenesis,and thus depends upon unknown,and a priori unknown and possiblysmall CP-violating phases,as well as unknown baryon-number violating dynamics.In contrast,the dark matter density is set by the‘freeze-out’of the interactions that keep the dark matter in equilibrium,and is independent of the dynamics of baryogenesis.Inparticular,although weakly-interacting massive particles at the TeV-scale naturally have a relic density of O(1)times the critical density,this is not at all the case for baryons.The Boltzmann equations show the size of the baryon relic density in the absence of an asymmetry is O(10−11).Thus the comparative closeness of the baryon and dark mat-ter densities poses a puzzle.One possible approach to this problem is to more closelyintegrate the dynamics of baryogenesis with that of the origin of dark matter.In partic-ular,it is natural to consider models where the dark matter and baryon sectors share aquantum number,either continuous or discrete,which provides a relation between their surviving number densities and thus energy densities.1Speciﬁcally,in this letter we consider models of dark matter possessing a particle-antiparticle asymmetry where this asymmetry strongly eﬀects the dark matter density, and through the electroweak(EW)anomaly,determines the baryon asymmetry,thus naturally linkingΩb andΩCDM.(A noteworthy early attempt along these lines which shares some features with our model is contained in Ref.[9].)The shared quantum number clearly requires that the dark matter particle not be it’s own antiparticle,so the putative dark matter candidate cannot be the standard LSP neutralino of the broken Minimal Supersymmetric Standard Model(MSSM).In fact,we will show in sections3 and4that sneutrinos can play the role of such dark matter in a previously studied variant of the MSSM in which the light neutrino masses result from higher-dimensional supersymmetry-breaking terms[10,11,12,13,14].This model preserves all the successes of the MSSM,such as stability of the weak scale and uniﬁcation of gauge couplings,while being,at least in part,testable at the LHC.Before we proceed to the calculation of the relic dark matter and baryon densities and the details of our model,it is useful to consider some aspects of the idea of a shared quantum number determining the ratio of baryon to dark matter.First,consider the simpliﬁed case in which,to a very good approximation,the dark matter and baryon sectors cannot exchange their conserved quantum number after itsﬁrst production.As an example,consider the situation in which the asymptotic baryon number B=1states of the Standard Model(SM)have global charge,q,while the lightest asymptotic states。