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

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

4. 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

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

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
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

13. 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

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

17. 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

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

19. 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

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 = 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-3 neutrinos + 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”)
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

24. Sky Distribution of Galaxies (XMASS XSC)

25. 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]

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
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

30. Structure Formation by Gravitational Instability

31. Redshift Surveys vs. Millenium Simulation

32. 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

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
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

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
Angular power spectrum
Acoustic Peaks

40. 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

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

42. Best-Fit Universe Perlmutter Kowalski et al. Physics Today
arXiv:
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,

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/

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/ ]
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)

49. 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

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

51. 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

52. 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

53. “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

54. “KATRIN Approaching” (25 Nov 2006)

55. 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

56. 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)

57. 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)

58. 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: ]

59. 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)

60. Title
Inner space and
outer space
are closely related