Non–Baryonic Dark Matter V. Berezinsky1 , A. Bottino2,3 and G. Mignola3,4 1INFN, Laboratori Nazionali del Gran Sasso, 67010 Assergi (AQ), Italy 2Universit`a di Torino, via P. Giuria 1, I-10125 Torino, Italy 3INFN - Sezione di Torino, via P. Giuria 1, I-10125 Torino, Italy 4Theoretical Physics Division, CERN, CH–1211 Geneva 23, Switzerland (presented by V. Berezinsky) The best particle candidates for non–baryonic cold dark matter are reviewed, namely, neutralino, axion, axino and Majoron. These particles are considered in the context of cosmological models with the restrictions given by the observed mass spectrum of large scale structures, data on clusters of galaxies, age of the Universe etc. 1. Introduction (Cosmological environ- The structure formation in Universe put strong ment) restrictions to the properties of DM in Universe. Universe with HDM plus baryonic DM has a Presence of dark matter (DM) in the Universe wrong prediction for the spectrum of fluctuations is reliably established. Rotation curves in many as compared with measurements of COBE, IRAS galaxies provide evidence for large halos filled by and CfA. CDM plus baryonic matter can ex- nonluminous matter. The galaxy velocity distri- plain the spectrum of fluctuations if total density bution in clusters also show the presence of DM in Ω0 ≈ 0.3. intercluster space. IRAS and POTENT demon- There is one more form of energy density in the strate the presence of DM on the largest scale in Universe, namely the vacuum energy described the Universe. by the cosmological constant Λ. The correspond- The matter density in the Universe ρ is usually 2 ing energy density is given by ΩΛ =Λ/(3H0 ). parametrized in terms of Ω = ρ/ρc,whereρc ≈ Quasar lensing and the COBE results restrict the 1.88 · 10−29h2 g/cm3 is the critical density and vacuum energy density: in terms of ΩΛ it is less h is the dimensionless Hubble constant defined than 0.7. −1 −1 as h = H0/(100km.s .Mpc ). Different mea- Contribution of galactic halos to the total den- . h surements suggest generally 0 4 ≤ ≤ 1. The sity is estimated as Ω ∼ 0.03 − 0.1 and clusters recent measurements of extragalactic Cepheids in give Ω ≈ 0.3. Inspired mostly by theoretical mo- Virgo and Coma clusters narrowed this interval to tivation (horizon problem, flatness problem and 0.6 ≤ h ≤ 0.9. However, one should be cautious the beauty of the inflationary scenarios) Ω0 =1 about the accuracy of this interval due to uncer- is usually assumed. This value is supported by tainties involved in these difficult measuremets. IRAS data and POTENT analysis. No observa- Dark Matter can be subdivided in baryonic tional data significantly contradict this value. DM, hot DM (HDM) and cold DM (CDM). There are several cosmological models based on The density of baryonic matter found from nu- 2 the four types of DM described above (baryonic cleosynthesis is given [1] as Ωbh =0.025 ± 0.005. DM, HDM, CDM and vacuum energy). These Hot and cold DM are distinguished by velocity models predict different spectra of fluctuations to of particles at the moment when horizon crosses be compared with data of COBE, IRAS, CfA etc. the galactic scale. If particles are relativistic they They also produce different effects for cluster- are called HDM particles, if not – CDM. The nat- cluster correlations, velocity dispersion etc. The ural candidate for HDM is the heaviest neutrino, simplest and most attractive model for a cor- most naturally τ-neutrino. Many new particles rect description of all these phenomena is the were suggested as CDM candidates. so-called mixed model or cold-hot dark matter 1 model (CHDM). This model is characterized by Ωh2 ≈ 0.2 can be considered as the value common following parameters: for most models. In this paper we shall analyze several candi- ΩΛ =0,Ω0 =Ωb+ΩCDM +ΩHDM =1, dates for CDM, best motivated from the point of −1 −1 H0 ≈50 kms Mpc (h ≈ 0.5), view of elementary particle physics. The motiva- ΩCDM :ΩHDM :Ωb ≈0.75 : 0.20 : 0.05, (1) tions are briefly described below. Neutralino is a natural lightest supersymmetric where ΩHDM ≈ 0.2 is obtained in ref.[2] from particle (LSP) in SUSY. It is stable if R-parity is damped Lyα data. Thus in the CHDM model conserved. Ωχ ∼ ΩCDM is naturally provided by the central value for the CDM density is given by annihilation cross-section in large areas of neu- tralino parameter space. Ω h2 =0.19 (2) CDM Axion gives the best known solution for strong with uncertaities within 0.1. CP-violation. Ωa ∼ ΩCDM for natural values of The best candidate for the HDM particle is τ- parameters. neutrino. In the CHDM model with Ων =0.2 Axino is a supersymmetric partner of axion. It mass of τ neutrino is mντ ≈ 4.7 eV .Thiscom- can be LSP. ponent will not be discussed further. Majoron is a Goldstone particle in spontaneously The most plausible candidate for the CDM par- broken global U(1)B−L or U(1)L. KeV mass can ticle is probably the neutralino (χ): it is massive, be naturally produced by gravitational interac- stable (when the neutralino is the lightest super- tion. symmeric particle and if R-parity is conserved) Apart from cosmological acceptance of DM and the χχ-annihilation cross-section results in particles, there can be observational confirma- 2 Ωχh ∼ 0.2 in large areas of the neutralino pa- tion of their existence. The DM particles can rameter space. be searched for in the direct and indirect experi- In the light of recent measurements of the Hub- ments. The direct search implies the interaction ble constant the CHDM model faces the age prob- of DM particles occurring inside appropriate de- lem. The lower limit on the age of Universe tectors. Indirect search is based on detection of t0 > 13 Gyr (age of globular clusters) imposes the the secondary particles produced by DM particles upper limit on the Hubble constant in the CHDM in our Galaxy or outside. As examples we can −1 −1 model H0 < 50 kms Mpc . This value is in mention production of antiprotons and positrons slight contradiction with the recent observations in our Galaxy and high energy gamma and neu- of extragalactic Cepheids, which can be summa- trino radiation due to annihilation of DM parti- −1 −1 rized as H0 > 60 kms Mpc . However, it is cles or due to their decays. too early to speak about a serious conflict tak- ing into account the many uncertainties and the 2. Axion physical possibilities (e.g. the Universe can be locally overdense - see the discussion in ref.[3]). The axion is generically a light pseudoscalar The age problem, if to take it seriously, can particle which gives natural and beautiful solu- be solved with help of another successful cosmo- tion to the CP violation in the strong interaction logical model ΛCDM. This model assumes that [4] (for a review and references see[5]). Sponta- Ω0 = 1 is provided by the vacuum energy (cos- neous breaking of the PQ-symmetry due to VEV mological constant Λ) and CDM. From the limit of the scalar field <φ>=fPQ results in the ΩΛ < 0.7 and the age of Universe one obtains production of massless Goldstone boson. Though ΩCDM ≥ 0.3andh<0.7. Thus this model fPQ is a free parameter, in practical applications 2 10 12 also predicts ΩCDMh ≈ 0.15 with uncertainties it is assumed to be large, fPQ ∼ 10 −10 GeV 0.1. Finally, we shall mention that the CDM with and therefore the PQ-phase transition occurs in Ω0 =ΩCDM =0.3andh=0.8, which fits the ob- very early Universe. At low temperature T ∼ 2 servational data, also gives Ωh ≈ 0.2. Therefore ΛQCD ∼ 0.1 GeV the chiral anomaly of QCD 2 induces the mass of the Goldstone boson ma ∼ production, (i) misalignment production and (iii) 2 ΛQCD/fPQ . This massive Goldstone particle is radiation from axionic strings. the axion. The interaction of axion is basically The relic density of thermally produced axions determined by the Yukawa interactions of field(s) is about the same as for light neutrinos and thus −2 φ with fermions. Triangular anomaly, which pro- for the mass of axion ma ∼ 10 eV this compo- vides the axion mass, results in the coupling of nent is not important as DM. the axion with two photons. Thus, the basic for The misalignment production is clearly ex- cosmology and astrophysics axion interactions are plained in ref.[5]. those with nucleons, electrons and photons. At very low temperature T ΛQCD the mas- Numerically, axion mass is given by sive axion provides the minimum of the potential −3 10 at value θ = 0,which corresponds to conservation ma =1.9·10 (N/3)(10 GeV/fPQ) eV, (3) of CP. At very high temperatures T ΛQCD where N is a color anomaly (number of quark the axion is massless and the potential does not doublets). depend on θ. At these temperatures there is no All coupling constants of the axion are inversely reason for θ to be zero: its values are different in various casually disconnected regions of the Uni- proportional to fPQ and thus are determined by the axion mass. Therefore, the upper limits on verse. When T → ΛQCD the system tends to go emission of axions by stars result in upper limits to potential minimum (at θ =0)andasare- for the axion mass. Of course, axion fluxes can- sult oscillates around this position. The energy not be detected directly, but they produce addi- of these coherent oscillations is the axion energy tional cooling which is limited by some observa- density in the Universe.