1 Non–Baryonic Dark Matter V. Berezinsky1, A. Bottino2,3 and G. Mignola3,4 1INFN, Laboratori Nazionali del Gran Sasso, 67010 Assergi (AQ), Italy 2Universit`adi 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- most naturally τ-neutrino. Many new particles ment) were suggested as CDM candidates. The structure formation in Universe put strong Presence of dark matter (DM) in the Universe restrictions to the properties of DM in Universe. is reliably established. Rotation curves in many Universe with HDM plus baryonic DM has a galaxies provide evidence for large halos filled by wrong prediction for the spectrum of fluctuations nonluminous matter. The galaxy velocity distri- as compared with measurements of COBE, IRAS bution in clusters also show the presence of DM in and CfA. CDM plus baryonic matter can ex- intercluster space. IRAS and POTENT demon- plain the spectrum of fluctuations if total density strate the presence of DM on the largest scale in Ω0 ≈ 0.3. the Universe. There is one more form of energy density in the The matter density in the Universe ρ is usually Universe, namely the vacuum energy described parametrized in terms of Ω = ρ/ρc, where ρc ≈ −29 2 3 by the cosmological constant Λ. The correspond- 1.88 · 10 h g/cm is the critical density and 2 ing energy density is given by ΩΛ = Λ/(3H0 ). h is the dimensionless Hubble constant defined −1 −1 Quasar lensing and the COBE results restrict the as h = H0/(100km.s .Mpc ). Different mea- vacuum energy density: in terms of ΩΛ it is less surements suggest generally 0.4 ≤ h ≤ 1. The than 0.7. arXiv:astro-ph/9601188v1 31 Jan 1996 recent measurements of extragalactic Cepheids in Contribution of galactic halos to the total den- Virgo and Coma clusters narrowed this interval to sity is estimated as Ω ∼ 0.03 − 0.1 and clusters 0.6 ≤ h ≤ 0.9. However, one should be cautious give Ω ≈ 0.3. Inspired mostly by theoretical mo- about the accuracy of this interval due to uncer- tivation (horizon problem, flatness problem and tainties involved in these difficult measuremets. the beauty of the inflationary scenarios) Ω0 = 1 Dark Matter can be subdivided in baryonic is usually assumed. This value is supported by DM, hot DM (HDM) and cold DM (CDM). IRAS data and POTENT analysis. No observa- The density of baryonic matter found from nu- 2 tional data significantly contradict this value. cleosynthesis is given [1] as Ωbh =0.025 ± 0.005. There are several cosmological models based on Hot and cold DM are distinguished by velocity the four types of DM described above (baryonic of particles at the moment when horizon crosses DM, HDM, CDM and vacuum energy). These the galactic scale. If particles are relativistic they models predict different spectra of fluctuations to are called HDM particles, if not – CDM. The nat- be compared with data of COBE, IRAS, CfA etc. ural candidate for HDM is the heaviest neutrino, They also produce different effects for cluster- 2 2 cluster correlations, velocity dispersion etc. The also predicts ΩCDM h ≈ 0.15 with uncertainties simplest and most attractive model for a cor- 0.1. Finally, we shall mention that the CDM with rect description of all these phenomena is the Ω0 =ΩCDM =0.3 and h =0.8, which fits the ob- so-called mixed model or cold-hot dark matter servational data, also gives Ωh2 ≈ 0.2. Therefore 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- 2 tralino parameter space. Ω h =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 . This com- 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>= fP Q results in the ΩΛ < 0.7 and the age of Universe one obtains production of massless Goldstone boson. Though ΩCDM ≥ 0.3 and h < 0.7. Thus this model fP Q is a free parameter, in practical applications 3 10 12 it is assumed to be large, fP Q ∼ 10 − 10 GeV stars. The upper limit from SN 1987A was re- and therefore the PQ-phase transition occurs in considered taking into account the nucleon spin very early Universe. At low temperature T ∼ fluctuation in N +N → N +N +a axion emission. ΛQCD ∼ 0.1 GeV the chiral anomaly of QCD There are three known mechanisms of cosmo- induces the mass of the Goldstone boson ma ∼ logical production of axions. They are (i)thermal 2 ΛQCD/fP Q . This massive Goldstone particle is production, (i) misalignment production and (iii) the axion. The interaction of axion is basically radiation from axionic strings. determined by the Yukawa interactions of field(s) The relic density of thermally produced axions φ with fermions. Triangular anomaly, which pro- is about the same as for light neutrinos and thus −2 vides the axion mass, results in the coupling of for the mass of axion ma ∼ 10 eV this compo- the axion with two photons. Thus, the basic for nent is not important as DM. cosmology and astrophysics axion interactions are The misalignment production is clearly ex- those with nucleons, electrons and photons. plained in ref.[5]. Numerically, axion mass is given by At very low temperature T ≪ ΛQCD the mas- sive axion provides the minimum of the potential −3 10 ma =1.9 · 10 (N/3)(10 GeV/fP Q) eV, (3) at value θ = 0,which corresponds to conservation 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 proportional to fP Q and thus are determined by various casually disconnected regions of the Uni- the axion mass.