Introduction: The Dark Matter ProblemModels for Dark MatterAxionsInert HiggsSterile NeutrinoSupersymmetric Dark MatterSupersymmetric particlesKaluza-Klein Particles in Universal Extra DimensionsModels with Enhanced Annihilation RatearXiv:0903.4849v2 [hep-ph] 30 Mar 2009Dark Matter CandidatesLars Bergstr¨omThe Oskar Klein Centre for Cosmoparticle PhysicsDepartment of Physics, Stockholm UniversityAlbaNova, SE-10 6 91 Stockholm, SwedenE-mail: [email protected]. An overview is g iven of various dar k matter candidates. Among themany suggestions given in the literature, axions, inert Higgs doublet, sterile neutrinos,supe rsymmetric particles and Kaluza-Klein particles are discussed. The situationhas recently become very interesting with new results on antimatter in the cosmicrays having dark matter as one of the leading possible explanations. Problems ofthis explanation and possible solutions are discussed, and the importance of newmeasurements is emphasized. If the explanation is indeed dark matter, a whole newfield of physics, with unusual although not impossible mass and interaction propertiesmay soon open itself to discovery.Dark Matter Candidates 21. Introduction: The Dark Matter ProblemThe dark matter problem has been a part of a strophysics for at least 75 years – sinceZwicky’s observation of a large velocity dispersion of the members of the Coma galaxycluster [1 ]. Similarly, the problem of galactic rotation curves - the stars rotate “toofast” to be bound by Newtonian gravity if all matter is visible - can be traced back toBacbcock’s measurements of the Andromeda galaxy 1939 [2]. It took, however, severaldecades before it was recognized as a real problem, and in its modern form it goesback to the late 1970’s and early 19 80’s when the so -called cold dark matt er paradigmappeared [3] (in this context, cold means matter moving with non-relativistic velocitieswhen structure fo r med in the universe). Today, a wealth of impressive data f r om studiesof the microwave background radiation, supernova distance measurements, and large-scale galaxy surveys have together solidified the Standard Model of cosmology, wherestructure formed through gravitational amplification of small density perturbations withthe help of cold dar k matter. Without the existence o f dark matter the density contrastseen in the universe today could not have for med, given the small amplitude of densityfluctuations inferred from anisotropies of the cosmic microwave background.Present-day cosmology of course also has another, mysterious component: acosmological constant Λ or a similar agent (such as time-varying quintessence exertingnegative pressure such that the expa nsion of the universe is today accelerating). Forthe purp ose of this article, however, this dark energy plays little role other than tofix the background metric and thus influencing late-time structure formation. Infact, most large-scale n-body simulations are now carried out in this cosmologicalStandard Model, the ΛCDM model. Modern models of cosmology contain a brief periodof enormously accelerated expansion, inflation, which gives a nearly scale-invariantspectrum of primordial fluctuations, which together with the fact that the universeobservationally appears to be very fla t (i.e., the tota l energy density is equal to t hecritical density) are cornerstones of the Standard Model of cosmology.There exist several extensive reviews of particle dark matter [4, 5, 6, 7] as wellas a recent book [8], in particular covering the prime candidate which has becomesomething of a template for dark matter, namely the lightest supersymmetric particle.In this review, I will focus mainly on recent developments. I will also discuss someof the less often mentioned possibilities, like axion dark matter and sterile neutrinos,and also some new interesting - though speculative, types of dark matter models thatmay perhaps explain the suprising new measurements of a large flux of positrons in thecosmic rays [9, 10]. The enhanced cross sections needed in these models, in particularthe so- called Sommerfeld enhancement , will also be discussed.1.1. Models for Dark MatterAlmost all current models of dark matter use the standard concept of quantum fieldtheory to describe the properties of elementary particle candidates (for exceptions, seefor instance [11, 12]). This means that they can be cha r acterized by the mass and spinDark Matter Candidates 3Table 1. Properties of various Dark Matter CandidatesType Particle Spin Approximate Mass ScaleAxion 0 µeV-meVInert Higgs Doublet 0 5 0 GeVSterile Neutrino 1/2 keVNeutralino 1/2 10 GeV - 10 TeVKaluza-Kle in UED 1 TeVof the dark matter particle. The mass of proposed candidates spans a very large range,as illustrated in Table 1.The density of cold dark matter (CDM) is now given to an accuracy of a fewpercent. With h being the Hubble constant today in units of 100 kms−1Mpc−1, thedensity derived fron the 5-year WMAP data [13] isΩCDMh2= 0.1131 ± 0.0034, (1)with the estimate h = 0.705 ± 0.0134.Using the simplest type of models of thermally produced dark matter (reasonablyfar away from thresholds and branch cuts) this corresponds to an average of theannihilation rate at the t ime of chemical decoupling of [4]hσAvi = 2.8 · 10−26cm3s−1. (2)The fact that this corresponds to what one gets with a weak interaction cross section forparticles of mass around the electroweak scale around a few hundrd GeV is sometimescoined the “WIMP miracle” (WIMP standing for Weakly Interacting Massive Particle),but it may of course be a coincidence. However, most of the detailed models proposedfor the dark matter are in fact containing WIMPs as dark matter particles.The rat e in Eq. (2) is a convenient quantity to keep in mind, but it has t o beremarked that this is the va lue needed at the time of freeze-out, when the t emperaturewas typica lly of the or der of (0.05 − 0.1 )MX(with MXthe mass of t he dark matterparticle) and the velocity v/c ∼ 0.2 − 0.3. There are now publicly available computercodes [14, 15] that solve the Boltzmann equation numerically, taking various effects intoaccount, such as co-annihilations which may change the effective average annihilationcross section appreciably if there are other states than the one giving the dark matterparticle which are nearly degenerate in mass. There are also computer packagesavailable (e.g., [16]) that can perform joint Bayesian likelihood analysis o f the