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**Geheimnis der dunklen Materie**

Topical Seminar Neutrino Physics & Astrophysics 17-21 Sept 2008, Beijing, China The Dark Universe, Neutrinos, and Cosmological Mass Bounds Georg Raffelt, Max-Planck-Institut für Physik, München

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**Thomas Wright (1750), An Original Theory of the Universe**

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**Title Dark Energy 73% (Cosmological Constant) Neutrinos 0.1-2%**

Dark Matter 23% Ordinary Matter 4% (of this only about 10% luminous)

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**Dark Matter in Galaxy Clusters**

Coma Cluster A gravitationally bound system of many particles obeys the virial theorem Velocity dispersion from Doppler shifts and geometric size Total Mass

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**Dark Matter in Galaxy Clusters**

Fritz Zwicky: Die Rotverschiebung von Extragalaktischen Nebeln (The redshift of extragalactic nebulae) Helv. Phys. Acta 6 (1933) 110 In order to obtain the observed average Doppler effect of 1000 km/s or more, the average density of the Coma cluster would have to be at least 400 times larger than what is found from observations of the luminous matter. Should this be confirmed one would find the surprising result that dark matter is far more abundant than luminous matter.

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**Structure of Spiral Galaxies**

Spiral Galaxy NGC 2997 Spiral Galaxy NGC 891

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**Galactic Rotation Curve from Radio Observations**

Observed flat rotation curve Expected from luminous matter in the disk Spiral galaxy NGC 3198 overlaid with hydrogen column density [ApJ 295 (1985) 305] Rotation curve of the galaxy NGC 6503 from radio observations of hydrogen motion [MNRAS 249 (1991) 523]

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**Structure of a Spiral Galaxy**

Dark Halo

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**Expanding Universe and the Big Bang**

Photons Neutrinos Charged Leptons Quarks Gluons W- and Z-Bosons Higgs Particles Gravitons Dark-Matter Particles Topological defects … Hubble’s law vexpansion = H0 distance Hubble’s constant H0 = h 100 km s-1 Mpc-1 Measured value h = 0.72 0.04 Expansion age of the universe t0 H0-1 14 109 years 1 Mpc = 3.26 106 lyr = 3.08 1024 cm

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Big Bang

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**Cosmic Expansion Cosmic Scale Factor Cosmic Redshift**

Space between galaxies grows Galaxies (stars, people) stay the same (dominated by local gravity or by electromagnetic forces) Cosmic scale factor today: a = 1 Wavelength of light gets “stretched” Suffers redshift Redshift today: z = 0

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**Friedman Equation & Einstein’s “Greatest Blunder”**

Density of gravitating mass & energy Curvature term is very small or zero (Euclidean spatial geometry) Newton’s constant Friedmann equation for Hubble’s expansion rate Cosmological constant L (new constant of nature) allows for a static universe by “global anti-gravitation” Yakov Borisovich Zeldovich Quantum field theory of elementary particles inevitably implies vacuum fluctuations because of Heisenberg’s uncertainty relation, e.g. E and B fields can not simultaneously vanish Ground state (vacuum) provides gravitating energy Vacuum energy rvac is equivalent to L

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**Generic Solutions of Friedmann Equation**

of state Behavior of energy-density under cosmic expansion Evolution of cosmic scale factor Radiation p = r/3 r a-4 a(t) t1/2 Dilution of radiation and redshift of energy Matter p = 0 r a-3 a(t) t2/3 Dilution of matter Vacuum energy p = -r r = const Vacuum energy not diluted by expansion Energy-momentum tensor of perfect fluid with density r and pressure p

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**Hubble’s orginal data (1929)**

Hubble Diagram Supernova Ia as cosmological standard candles Apparent Brightness Hubble’s orginal data (1929) z = 0.003 Redshift

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**Hubble Diagram Supernova Ia as cosmological standard candles**

Accelerated expansion (WM = 0.3, WL = 0.7) Decelerated expansion (WM = 1)

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**Latest Supernova Data Kowalski et al.,**

Improved cosmological constraints from new, old and combined supernova datasets, arXiv:

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**Expansion of Different Cosmological Models**

Time (billion years) Adapted from Bruno Leibundgut Cosmic scale factor a -14 M = 0 M = 0.3 L = 0.7 -9 M = 1 -7 M > 1 today

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**Title Dark Energy 73% (Cosmological Constant) Neutrinos 0.1-2%**

Dark Matter 23% Ordinary Matter 4% (of this only about 10% luminous)

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**Neutrino Thermal Equilibrium**

Neutrino reactions Dimensional analysis of reaction rate if T ≪ mW,Z Examples for neutrino processes GF Cosmic expansion rate Friedmann equation Radiation dominates Expansion rate Condition for thermal equilibrium: G > H Neutrinos are in thermal equilibrium for T ≳ 1 MeV corresponding to t ≲ 1 sec

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**Present-Day Neutrino Density**

Neutrino decoupling (freeze out) H ~ G T 2.4 MeV (electron flavor) T 3.7 MeV (other flavors) Redshift of Fermi-Dirac distribution (“nothing changes at freeze-out”) Temperature scales with redshift Tn = Tg (z+1) Electron-positron annihilation beginning at T me = MeV QED plasma is “strongly” coupled Stays in thermal equilibrium (adiabatic process) Entropy of e+e- transfered to photons Redshift of neutrino and photon thermal distributions so that today we have for massless neutrinos

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**Cosmological Limit on Neutrino Masses**

Cosmic neutrino “sea” ~ 112 cm-3 neutrinos + anti-neutrinos per flavor mn ≲ 40 eV For all stable flavors A classic paper: Gershtein & Zeldovich JETP Lett. 4 (1966) 120

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**Weakly Interacting Particles as Dark Matter**

More than 30 years ago, beginnings of the idea of weakly interacting particles (neutrinos) as dark matter Massive neutrinos are no longer a good candidate (hot dark matter) However, the idea of weakly interacting massive particles as dark matter is now standard

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**What is wrong with neutrino dark matter?**

Galactic Phase Space (“Tremaine-Gunn-Limit”) mn > eV Maximum mass density of a degenerate Fermi gas mn > eV Spiral galaxies Dwarf Nus are “Hot Dark Matter” Ruled out by structure formation Neutrino Free Streaming (Collisionless Phase Mixing) At T < 1 MeV neutrino scattering in early universe ineffective Stream freely until non-relativistic Wash out density contrasts on small scales Neutrinos Over-density

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**Sky Distribution of Galaxies (XMASS XSC)**

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**Galaxy distribution from the CfA redshift survey**

A Slice of the Universe Cosmic “Stick Man” ~ 185 Mpc Galaxy distribution from the CfA redshift survey [ApJ 302 (1986) L1]

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**2dF Galaxy Redshift Survey (2002)**

~ 1300 Mpc

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SDSS Survey

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**Generating the Primordial Density Fluctuations**

Early phase of exponential expansion (Inflationary epoch) Zero-point fluctuations of quantum fields are stretched and frozen Cosmic density fluctuations are frozen quantum fluctuations

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**Gravitational Growth of Density Perturbations**

The dynamical evolution of small perturbations is independent for each Fourier mode dk For pressureless, nonrelativistic matter (cold dark matter) naively expect exponential growth Only power-law growth in expanding universe Matter dominates a t2/3 Sub-horizon l ≪ H-1 Super-horizon l ≫ H-1 dk const dk a2 t dk a t2/3 Radiation dominates a t1/2

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**Structure Formation by Gravitational Instability**

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**Redshift Surveys vs. Millenium Simulation**

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**Power Spectrum of Density Fluctuations**

Field of density fluctuations Fourier transform Power spectrum essentially square of Fourier transformation Power spectrum is Fourier transform of two-point correlation function (x=x2-x1) with the d-function Gaussian random field (phases of Fourier modes dk uncorrelated) is fully characterized by the power spectrum or equivalently by

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**Processed Power Spectrum in Cold Dark Matter Scenario**

Primordial spectrum Suppressed by stagnation during radiation phase Primordial spectrum usually assumed to be of power-law form Harrison-Zeldovich (“flat”) spectrum n = 1 expected from inflation (actually slightly less than 1, as confirmed by precision data)

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**Power Spectrum of Cosmic Density Fluctuations**

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**Cosmic Microwave Background Radiation**

Robert W. Wilson Born 1936 Arno A. Penzias Born 1933 Discovery of 2.7 Kelvin Cosmic microwave background radiation by Penzias and Wilson in 1965 (Nobel Prize 1978) Beginning of “big-bang cosmology”

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**Last Scattering Surface**

Big Bang Singularity Recombination Last Scattering Surface Galaxies Here & Now 1 3 Q 20 Horizon 1000 1500 Redshift z

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**COBE Temperature Map of the Cosmic Microwave Background**

Dynamical range DT = 18 mK (DT/ T 10-5) Primordial temperature fluctuations T = K (uniform on the sky) Dynamical range DT = mK (DT/ T 10-3) Dipole temperature distribution from Doppler effect caused by our motion relative to the cosmic frame

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**COBE Satellite Nobel Prize 2006 John C. Mather Born 1946**

George F. Smoot Born 1945

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**Power Spectrum of CMBR Temperature Fluctuations**

Sky map of CMBR temperature fluctuations Multipole expansion Angular power spectrum Acoustic Peaks

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**Flat Universe from CMBR Angular Fluctuations**

Spergel et al. (WMAP Collaboration) astro-ph/ Triangulation with acoustic peak flat (Euclidean) negative curvature positive curvature Known physical size of acoustic peak at decoupling (z 1100) Measured angular size today (z = 0) Wtot = 1.02 0.02

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**Latest CMB Results (WMAP-5 and Others)**

Komatsu et al., arXiv:

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**Best-Fit Universe Perlmutter Kowalski et al. Physics Today**

arXiv: Perlmutter Physics Today (Apr. 2003)

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**Concordance Model of Cosmology**

A Friedmann-Lemaître-Robertson-Walker model with the following parameters perfectly describes the global properties of the universe Expansion rate Spatial curvature Age Vacuum energy Cold Dark Matter Baryonic matter The observed large-scale structure and CMBR temperature fluctuations are perfectly accounted for by the gravitational instability mechanism with the above ingredients and a power-law primordial spectrum of adiabatic density fluctuations (curvature fluctuations) P(k) kn Power-law index

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**Structure Formation in the Universe**

Smooth Structured Structure forms by gravitational instability of primordial density fluctuations A fraction of hot dark matter suppresses small-scale structure

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**Structure Formation with Hot Dark Matter**

Standard LCDM Model Neutrinos with Smn = 6.9 eV Structure fromation simulated with Gadget code Cube size 256 Mpc at zero redshift Troels Haugbølle,

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**Neutrino Free Streaming: Transfer Function**

Power suppression for lFS ≳ 100 Mpc/h Transfer function P(k) = T(k) P0(k) Effect of neutrino free streaming on small scales T(k) = 1 - 8Wn/WM valid for 8Wn/WM ≪ 1 mn = 0 mn = 0.3 eV mn = 1 eV Hannestad, Neutrinos in Cosmology, hep-ph/

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**Power Spectrum of Cosmic Density Fluctuations**

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**Some Recent Cosmological Limits on Neutrino Masses**

Smn/eV (limit 95%CL) Data / Priors Hannestad 2003 [astro-ph/ ] 1.01 WMAP-1, CMB, 2dF, HST Spergel et al. (WMAP) 2003 [astro-ph/ ] 0.69 WMAP-1, 2dF, HST, s8 Crotty et al. 2004 [hep-ph/ ] 1.0 0.6 WMAP-1, CMB, 2dF, SDSS & HST, SN Hannestad 2004 [hep-ph/ ] 0.65 WMAP-1, SDSS, SN Ia gold sample, Ly-a data from Keck sample Seljak et al. 2004 [astro-ph/ ] 0.42 WMAP-1, SDSS, Bias, Ly-a data from SDSS sample Hannestad et al. 2006 [hep-ph/ ] 0.30 WMAP-1, CMB-small, SDSS, 2dF, SN Ia, BAO (SDSS), Ly-a (SDSS) Spergel et al. 2006 [hep-ph/ ] 0.68 WMAP-3, SDSS, 2dF, SN Ia, s8 Seljak et al. 2006 [astro-ph/ ] 0.14 WMAP-3, CMB-small, SDSS, 2dF, SN Ia, BAO (SDSS), Ly-a (SDSS)

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**Lyman-alpha Forest Hydrogen clouds absorb from QSO**

continuum emission spectrum Absorption dips at Ly-a wavelengh corresponding to redshift Examples for Lyman-a forest in low- and high-redshift quasars

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**Weak Lensing - A Powerful Probe for the Future**

Distortion of background images by foreground matter Unlensed Lensed

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**Sensitivity Forecasts for Future LSS Observations**

Lesgourgues, Pastor & Perotto, hep-ph/ Planck & SDSS Smn > 0.21 eV detectable at 2s Smn > 0.13 eV detectable Ideal CMB & 40 x SDSS Abazajian & Dodelson astro-ph/ Future weak lensing survey 4000 deg2 σ(mν) ~ 0.1 eV Kaplinghat, Knox & Song, astro-ph/ σ(mν) ~ 0.15 eV (Planck) σ(mν) ~ eV (CMBpol) CMB lensing Wang, Haiman, Hu, Khoury & May, astro-ph/ Weak-lensing selected sample of > 105 clusters σ(mν) ~ 0.03 eV Hannestad, Tu & Wong astro-ph/ Weak-lensing tomography (LSST plus Planck) σ(mν) ~ 0.05 eV

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**Fermion Mass Spectrum 10 100 1 meV eV keV MeV GeV TeV d s b**

Quarks (Q = -1/3) u c t Quarks (Q = +2/3) Charged Leptons (Q = -1) e m t All flavors Neutrinos n3

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**“Weighing” Neutrinos with KATRIN**

Sensitive to common mass scale m for all flavors because of small mass differences from oscillations Best limit from Mainz und Troitsk m < 2.2 eV (95% CL) KATRIN can reach 0.2 eV Under construction Data taking foreseen to begin in 2009

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**“KATRIN Approaching” (25 Nov 2006)**

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**Lee-Weinberg Curve for Neutrinos and Axions**

log(Wa) log(ma) WM 10 eV 10 meV CDM HDM Axions Thermal Relics Non-Thermal Relics log(Wn) log(mn) WM 10 eV CDM HDM 10 GeV Neutrinos & WIMPs Thermal Relics

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**Axion Hot Dark Matter from Thermalization after LQCD**

Cosmic thermal degrees of freedom Freeze-out temperature 104 105 106 107 fa (GeV) Cosmic thermal degrees of freedom at axion freeze-out p a Chang & Choi, PLB 316 (1993) 51 Hannestad, Mirizzi & Raffelt, JCAP 07 (2005) 02 104 105 106 107 fa (GeV)

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**Low-Mass Particle Densities in the Universe**

Photons Cosmic microwave background radiation T = K 410 cm-3 Neutrinos Freeze out at T ~ 2-3 MeV before e-e+ annihilation 112 cm-3 ( in one flavor) Axions (QCD) For fa ~ 107 GeV (ma ~ 1 eV) Freeze out at T ~ 80 MeV (pppa interaction) ~ 50 cm-3 ALPs (two photon vertex) Primakoff freeze out (gagg ~ GeV-1) T ≫ TQCD ~ 200 MeV < 10 cm-3 No useful hot dark matter limit on ALPs in the CAST search range (too few of them today if they couple only by two-photon vertex) Axion mass limit comparable to limit on Smn (Axion number density comparable to one neutrino flavor)

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**Axion Hot Dark Matter Limits from Precision Data**

Credible regions for neutrino plus axion hot dark matter (WMAP-5, LSS, BAO, SNIa) Hannestad, Mirizzi, Raffelt & Wong [arXiv: ] Dashed (red) curves: Same with WMAP-3 From HMRW [arXiv: ] Marginalizing over unknown neutrino hot dark matter component ma < 1.0 eV (95% CL) WMAP-5, LSS, BAO, SNIa Hannestad, Mirizzi, Raffelt & Wong [arXiv: ] ma < 0.4 eV (95% CL) WMAP-3, small-scale CMB, HST, BBN, LSS, Ly-a Melchiorri, Mena & Slosar [arXiv: ]

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**Too much hot dark matter**

Axion Bounds 103 106 109 1012 [GeV] fa eV keV meV ma Experiments Tele scope CAST Direct search ADMX Too much hot dark matter Too much cold dark matter Globular clusters (a-g-coupling) Too many events Too much energy loss SN 1987A (a-N-coupling)

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