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Geheimnis der dunklen Materie

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

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Geheimnis der dunklen Materie

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  1. 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

  2. ThomasWright(1750),AnOriginalTheoryoftheUniverse

  3. Title Dark Energy 73% (Cosmological Constant) Neutrinos 0.1-2% Ordinary Matter 4% (of this only about 10% luminous) Dark Matter 23%

  4. Dark Matter in Galaxy Clusters A gravitationally bound system of many particles obeys the virial theorem Velocity dispersion from Doppler shifts and geometric size Total Mass Coma Cluster

  5. 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.

  6. Structure of Spiral Galaxies Spiral Galaxy NGC 2997 Spiral Galaxy NGC 891

  7. 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]

  8. Structure of a Spiral Galaxy Dark Halo

  9. 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 1 Mpc = 3.26  106lyr = 3.08  1024cm Expansion age of the universe t0 H0-1 14  109 years

  10. Big Bang

  11. 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

  12. 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 Yakov Borisovich Zeldovich 1914-1987 Cosmological constant L (new constant of nature) allows for a static universe by “global anti-gravitation” • 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 rvacis equivalent to L

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

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

  15. Hubble Diagram Supernova Ia as cosmological standard candles Accelerated expansion (WM=0.3, WL=0.7) Decelerated expansion (WM=1)

  16. Latest Supernova Data Kowalski et al., Improved cosmological constraints from new, old and combined supernova datasets, arXiv:0804.4142

  17. Expansion of Different Cosmological Models M = 0.3 L = 0.7 M = 0 Cosmic scale factor a M = 1 M > 1 Time (billion years) -9 -14 -7 today Adapted from Bruno Leibundgut

  18. Title Dark Energy 73% (Cosmological Constant) Neutrinos 0.1-2% Ordinary Matter 4% (of this only about 10% luminous) Dark Matter 23%

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

  20. 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 = 0.511 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

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

  22. 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

  23. What is wrong with neutrino dark matter? Galactic Phase Space (“Tremaine-Gunn-Limit”) Maximum mass density of a degenerate Fermi gas mn> 20 - 40 eV Spiral galaxies mn> 100 - 200 eV Dwarf galaxies Neutrino Free Streaming (Collisionless Phase Mixing) • AtT<1MeVneutrinoscatteringinearlyuniverseineffective • Stream freely until non-relativistic • Wash out density contrasts on small scales • Nus are “Hot Dark Matter” • Ruled out • by structure formation Neutrinos Neutrinos Over-density

  24. Sky Distribution of Galaxies (XMASS XSC) http://spider.ipac.caltech.edu/staff/jarrett/2mass/XSC/jarrett_allsky.html

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

  26. 2dF Galaxy Redshift Survey (2002) ~ 1300 Mpc

  27. SDSS Survey

  28. 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

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

  30. Structure Formation by Gravitational Instability

  31. Redshift Surveys vs. Millenium Simulation www.mpa-garching.mpg.de/millennium

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

  33. 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)

  34. Power Spectrum of Cosmic Density Fluctuations

  35. 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”

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

  37. COBE Temperature Map of the Cosmic Microwave Background T = 2.725 K (uniform on the sky) Dynamical range DT = 3.353 mK (DT/T  10-3) Dipole temperature distribution from Doppler effect caused by our motion relative to the cosmic frame Dynamical range DT = 18 mK (DT/T  10-5) Primordial temperature fluctuations

  38. COBE Satellite Nobel Prize 2006 John C. Mather Born 1946 George F. Smoot Born 1945

  39. Power Spectrum of CMBR Temperature Fluctuations Sky map of CMBR temperature fluctuations Multipole expansion Acoustic Peaks Angular power spectrum

  40. Flat Universe from CMBR Angular Fluctuations Spergel et al. (WMAP Collaboration) astro-ph/0302209 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

  41. Latest CMB Results (WMAP-5 and Others) Komatsu et al., arXiv:0803.0547

  42. Best-Fit Universe Kowalski et al. arXiv:0804.4142 Perlmutter Physics Today (Apr. 2003)

  43. 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

  44. 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

  45. 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, http://whome.phys.au.dk/~haugboel

  46. 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/0404239

  47. Power Spectrum of Cosmic Density Fluctuations

  48. Some Recent Cosmological Limits on Neutrino Masses Smn/eV (limit 95%CL) Data / Priors Hannestad 2003 [astro-ph/0303076] 1.01 WMAP-1, CMB, 2dF, HST Spergel et al. (WMAP) 2003 [astro-ph/0302209] 0.69 WMAP-1, 2dF, HST, s8 Crotty et al. 2004 [hep-ph/0402049] 1.0 0.6 WMAP-1, CMB, 2dF, SDSS & HST, SN Hannestad 2004 [hep-ph/0409108] 0.65 WMAP-1, SDSS, SN Ia gold sample, Ly-a data from Keck sample Seljak et al. 2004 [astro-ph/0407372] 0.42 WMAP-1, SDSS, Bias, Ly-a data from SDSS sample Hannestad et al. 2006 [hep-ph/0409108] 0.30 WMAP-1, CMB-small, SDSS, 2dF, SN Ia, BAO (SDSS), Ly-a (SDSS) Spergel et al. 2006 [hep-ph/0409108] 0.68 WMAP-3, SDSS, 2dF, SN Ia, s8 Seljak et al. 2006 [astro-ph/0604335] 0.14 WMAP-3, CMB-small, SDSS, 2dF, SN Ia, BAO (SDSS), Ly-a (SDSS)

  49. Lyman-alpha Forest • Hydrogen clouds absorb from QSO • continuum emission spectrum • Absorption dips at Ly-a wavelengh • corresponding to redshift • www.astro.ucla.edu/~wright/Lyman-alpha-forest.html Examples for Lyman-a forest in low- and high-redshift quasars http://www.astr.ua.edu/keel/agn/forest.gif

  50. Weak Lensing - A Powerful Probe for the Future Distortion of background images by foreground matter Unlensed Lensed

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