1. Cosmology beyond the standard model Multi component dark matter model A. Doroshkevich, Astro-Space Center, FIAN, Moscow, Russia M. Demianski, University of Warsaw, Warsaw, Poland

2. History, three K, second plane, yesterday

3. List of problems 1. Relativistic Astrophysics – black holes 2. Disc accretion – neutron stars 3. Supernova explosions 4. Relic radiation - recombination of the Universe 5. Nonlinear gravitational instability - Zel’dovich pancakes 6. HDM model of the Universe 7. Magnetic field in the Sun

5. Standard ΛCDM model Analysis of the CMB fluctuations shows that the large scale power spectrum of perturbations is the CDM like one P(k) ~ k n, n ≈ 0.96 ± 0.007 for r >10Mpc, M > 10 13 M  B – mode of polarisation, 1403.3985 We show that this dependence cannot be extended to smaller scales

6. First DM models - HISTORY Doroshkevich et al. 1980 - HDM Bisnovaty-Kogan & Novikov 1980 - HDM Bond, Efstathiou, Silk 1980 – CDM Bond, Szalay 1983 CDM & WDM Blumentale & Primack 1984 – CDM Doroshkevich, Khlopov 1984 – UDM, MDM Turner, Steigman, Krauss 1984 – UDM Doroshkevich, Klypin, Khlopov 1988 – MDM Mikheeva, Doroshkevich, Lukash 2007 Doroshkevich, Lukash, Mikheeva 2012 CHICAGO-2013

7. CMB power spectrum High precision ΛCDM model

8. Popular request – sterile neutrino 10 -19 eV < m dm < 10 13 eV Six reviews during 2013 year: Feng (2013), Boyarsky et al. (2013), Dreves (2013) Kusenko & Rosenberg (2013), Horiuchi et al. (2013), Marcovic & Viel (2013). Three standard problems are discussed: 1. Number of satellites, 2. Core – cusp problem, 3. Ly-α forest. Why they are only qualitative ?

9. Questions and problems 1. Observed satellites: M s ~ 10 5 – 10 7 M , z cr ~ 7 –15 Typical mass resolution in simulations M ~ 10 8 M, MW-28, A-13 2.Cusp – in simulations of clusters with M > 10 13 M , NFW Core – in LBG – galaxies with M < 10 9 M  Impact of baryonic component in clusters and galaxies. 3. Ly-α forest: x H ~10 -5, UV background

10. Direct and indirect searches DAMA – Bernabei, 2008, 2010 Super CDMS – Agnese 2013 NEGATIVE Estimates: m s > 13 – 20 keV for WDM Unstable neutrinos: m s < 3keV LAC ? X-rays 3.5keV – 73 clusters: (Bulbul et al. 1402.2301) Decay of DM particles or Ar recombination line

11. Simulations Maccio 2012 – do not reproduce observations WDM is not a viable solution of the core – cusp and satellite problems Libeskind 2013 – low mass clouds are not stable and are expanding Abel (2013) – artefacts appear, filaments Wang (2013) – unstable DM and Ly- α forest Schultz et al. (1401.3769) – high z Dutton & Maccio (1402.7073) – 17 realizations

12. Models with one type of DM particles

13. OUR APPROACH Process and moment of object formation Both galaxies and clusters are diversified steady – state objects. Global characteristics – mass, angular momentum,.. Periods of anisotropic compression and/or merging After virialization the structure of DM halos is frozen. Therefore we can restore the z of formation Z cr – M vir plane Links with the spectrum of perturbations. Impact of baryonic component

14. For central regions of the DM halo (Klypin et al. 2011) z cr -M vir plane p c =p c (z cr M 0.1 )

15. Walker et. al, 2009, ApJ, 704, 1274 - 28 dSph objects name r sig_v +/- Mhalf +/- +/- (1 +zcr)/10 +/- kpc km/s 10^6M_o M_o/pc^3 Carina 0.14 6.60 1.20 3.40 1.40 0.320 0.12 1.2 0.53 Draco 0.22 9.10 1.20 11.00 3.00 0.230 0.06 1.1 0.32 Fornax 0.34 11.70 0.90 27.00 0.50 0.160 0.03 1.0 0.04 LeoI 0.13 9.20 1.40 6.50 2.10 0.660 0.21 1.2 0.44 LeoII 0.12 6.60 0.70 3.10 0.90 0.400 0.12 1.2 0.39 Sculptor 0.09 9.20 1.10 4.60 1.70 1.300 0.50 1.3 0.55 Sextant 0.29 7.90 1.30 11.00 4.00 0.100 0.03 1.0 0.39 UMi 0.15 9.50 1.20 7.80 2.20 0.550 0.150 1.2 0.37 CVen I 0.56 7.60 0.40 19.00 2.00 0.025 0.003 0.8 0.10 Coma 0.08 4.60 0.80 0.90 0.35 0.490 0.180 1.3 0.56 Hercules 0.33 3.70 0.90 2.60 1.40 0.017 0.009 0.9 0.53 Leo T 0.18 7.50 1.60 5.80 2.80 0.250 0.120 1.1 0.59 Segue 1 0.03 4.30 1.20 0.31 0.19 3.010 0.800 1.7 1.06 UMa I 0.32 11.90 3.50 26.10 6.00 0.200 0.120 1.0 0.29 UMa II 0.14 5.70 1.40 2.60 1.40 0.230 0.120 1.2 0.68 AndII 1.23 9.30 2.70 62.00 36.00 0.008 0.005 0.7 0.45 Cetus 0.59 17.00 2.00 99.00 23.00 0.110 0.020 0.9 0.22 Sgr^c 1.55 11.40 0.70 120.00 60.00 0.008 0.001 0.7 0.35 Tucana 0.27 15.80 3.60 40.00 19.00 0.460 0.220 1.1 0.57 Bootes 1 0.24 6.50 2.00 5.90 3.70 0.100 0.060 1.0 0.70 Cven II 0.07 4.60 1.00 0.90 0.40 0.530 0.250 1.3 0.65 Leo IV 0.12 3.30 1.70 0.73 0.73 0.110 0.110 1.1 1.26 Leo V 0.04 2.40 1.90 0.14 0.14 0.450 0.450 1.4 1.57 Segue 2 0.03 3.40 1.80 0.23 0.23 1.310 0.300 1.6 1.59 AndIX 0.53 6.80 2.50 14.00 11.00 0.023 0.017 0.8 0.73 AndXV 0.27 11.00 6.00 19.00 2.00 0.230 0.250 1.0 0.22 ----------------------------------------------------------------------------------------------- mns 1.6 0.35 sig 2.3 0.33 Problems of detection and description r corresponds to L(r)=Ltot/2

16. 28 dSph galaxies (Walker et al. 2009) 13 And galaxies (Tollerud et al. 2013) = 15/M 6 0.1 (1 ± 0.12)=3/M 13 0.1 (1 ± 0.12) = 11/M 6 0.1 (1 ± 0.12) = 2.2/M 13 0.1 (1 ± 0.12) For And XVI z cr ~14 For Segue I z cr ~17 For Sgr c z cr ~7

17. 23 dSph 9 SPT-clusters

18. CLS – 83 dSph

19. Summary For 44 SPT – clusters 1 < M 13 < 300 ≈ 36(1 ± 0.37)eV/cm 3, S b ≈ 185(1 ± 0.9)keV cm 2 For 9 SPT - clusters 10 < M 13 < 80 ≈ 34(1 ± 0.25)eV/cm 3, S b ≈ 200(1 ± 0.7)keV cm 2 ≈ 3.2(1 ± 0.04)M 13 -0.1 For 9 REXCESS clusters 10 < M 13 < 70 ≈ 25(1 ± 0.5)eV/cm 3, S b ≈ 320(1 ± 0.3)keV cm 2 ≈ 2.2(1 ± 0.1) For 41 dSph galaxies 10 -7 < M 13 < 10 -4, 0.1 < M 6 < 100 ≈ 28(1 ± 0.8)eV/cm 3, ≈ 3.4(1 ± 0.15)M 13 -0.1

20. B(z cr ) – M 12, observations

21. Power spectrum of MDM model

22. M dmp ≈10 7 M o /m s 3 (keV)

23. Two composite MDM models P=0.3P cdm +0.7P wdm (50eV), P=0.1P cdm +0.65P wdm (50eV)+0.25P wdm (10keV) Press, Schechter 1974, Bond et al. 1991

24. RESULTS According to this criterion CDM model is rejected The WDM model with P=P WDM is consistent with observations when α w ≈ 1, m w ≈ 3keV For MDM model with P=0.3P CDM +0.7P WDM f CDM ≈ 0.8, f WDM ≈ 0.2, m w ≈ 50eV For MDM model with P=0.1P CDM +0.65P WDM1 +0.25P WDM2 with m w1 ~ 50eV, m w2 ~ 10keV FINAL ANSWER - SIMULATIONS

27. The end

28. Small scale perturbations Linear evolution

29. 28 dSph galaxies

30. CLS-83

31. Problems of detection and description r corresponds to L(r)=L tot /2 name r sig_v +/- Mhalf +/- +/- (1 +z cr )/10 +/- kpc km/s 10^6M_o M_o/pc^3 Carina 0.14 6.60 1.20 3.40 1.40 0.320 0.120 0.12E01 0.53 Draco 0.22 9.10 1.20 11.00 3.00 0.230 0.06 0.11E01 0.32 Fornax 0.34 11.70 0.90 27.00 0.50 0.160 0.03 0.99E00 0.04 LeoI 0.13 9.20 1.40 6.50 2.10 0.660 0.210 0.12E01 0.44 LeoII 0.12 6.60 0.70 3.10 0.90 0.400 0.120 0.12E01 0.39 Sculptor 0.09 9.20 1.10 4.60 1.70 1.300 0.500 0.13E01 0.55 Sextant 0.29 7.90 1.30 11.00 4.00 0.100 0.030 0.99E00 0.39 UMi 0.15 9.50 1.20 7.80 2.20 0.550 0.150 0.12E01 0.37 CVen I 0.56 7.60 0.40 19.00 2.00 0.025 0.003 0.84E00 0.10 Coma 0.08 4.60 0.80 0.90 0.35 0.490 0.180 0.13E01 0.56 Hercules 0.33 3.70 0.90 2.60 1.40 0.017 0.009 0.89E00 0.53 Leo T 0.18 7.50 1.60 5.80 2.80 0.250 0.120 0.11E01 0.59 Segue 1 0.03 4.30 1.20 0.31 0.19 3.010 0.800 0.17E01 1.06 UMa I 0.32 11.90 3.50 26.10 6.00 0.200 0.120 0.10E01 0.29 UMa II 0.14 5.70 1.40 2.60 1.40 0.230 0.120 0.12E01 0.68 AndII 1.23 9.30 2.70 62.00 36.00 0.008 0.005 0.71E00 0.45 Cetus 0.59 17.00 2.00 99.00 23.00 0.110 0.020 0.90E00 0.22 Sgr^c 1.55 11.40 0.70 120.00 60.00 0.008 0.001 0.68E00 0.35 Tucana 0.27 15.80 3.60 40.00 19.00 0.460 0.220 0.11E01 0.57 Bootes 1 0.24 6.50 2.00 5.90 3.70 0.100 0.060 0.10E01 0.70 Cven II 0.07 4.60 1.00 0.90 0.40 0.530 0.250 0.13E01 0.65 Leo IV 0.12 3.30 1.70 0.73 0.73 0.110 0.110 0.11E01 1.26 Leo V 0.04 2.40 1.90 0.14 0.14 0.450 0.450 0.14E01 1.57 Segue 2 0.03 3.40 1.80 0.23 0.23 1.310 0.300 0.16E01 1.59 AndIX 0.53 6.80 2.50 14.00 11.00 0.023 0.017 0.84E00 0.73 AndXV 0.27 11.00 6.00 19.00 2.00 0.230 0.250 0.10E01 0.22 ----------------------------------------------------------------------------------------------- mns 0.16E01 0.35 sig 0.23E00 0.33 Walker et. al, 2009, ApJ, 704, 1274 - 28 dSph objects