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

History, three K, second plane, yesterday

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

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 ± for r >10Mpc, M > M  B – mode of polarisation, We show that this dependence cannot be extended to smaller scales

First DM models - HISTORY Doroshkevich et al HDM Bisnovaty-Kogan & Novikov 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

CMB power spectrum High precision ΛCDM model

Popular request – sterile neutrino eV < m dm < 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 ?

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 > 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

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 ) Decay of DM particles or Ar recombination line

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. ( ) – high z Dutton & Maccio ( ) – 17 realizations

Models with one type of DM particles

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

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 )

Walker et. al, 2009, ApJ, 704, dSph objects name r sig_v +/- Mhalf +/- +/- (1 +zcr)/10 +/- kpc km/s 10^6M_o M_o/pc^3 Carina Draco Fornax LeoI LeoII Sculptor Sextant UMi CVen I Coma Hercules Leo T Segue UMa I UMa II AndII Cetus Sgr^c Tucana Bootes Cven II Leo IV Leo V Segue AndIX AndXV mns sig Problems of detection and description r corresponds to L(r)=Ltot/2

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

23 dSph 9 SPT-clusters

CLS – 83 dSph

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 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 < M 13 < 10 -4, 0.1 < M 6 < 100 ≈ 28(1 ± 0.8)eV/cm 3, ≈ 3.4(1 ± 0.15)M

B(z cr ) – M 12, observations

Power spectrum of MDM model

M dmp ≈10 7 M o /m s 3 (keV)

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

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 WDM P WDM2 with m w1 ~ 50eV, m w2 ~ 10keV FINAL ANSWER - SIMULATIONS

The end

Small scale perturbations Linear evolution

28 dSph galaxies

CLS-83

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 E Draco E Fornax E LeoI E LeoII E Sculptor E Sextant E UMi E CVen I E Coma E Hercules E Leo T E Segue E UMa I E UMa II E AndII E Cetus E Sgr^c E Tucana E Bootes E Cven II E Leo IV E Leo V E Segue E AndIX E AndXV E mns 0.16E sig 0.23E Walker et. al, 2009, ApJ, 704, dSph objects