1. The Standard Model of Cosmology
Avishai Dekel, HUJI, PANIC08

2. North Galactic Hemisphere
Lick Survey
1M galaxies
isotropy→homogeneity
North Galactic Hemisphere

3. Microwave Anisotropy Probe
February 2003, 2004
WMAP
Science breakthrough of the year
δT/T~10-5
isotropy→homogeneity

4. Homogeneity & Isotropy - Robertson-Walker Metric
comoving radius
angular area
expansion factor

5. kinetic potential curvature vacuum
Friedman Equation
Homogeneity + Gravity ( ) 
kinetic potential curvature vacuum
Two basic free parameters
closed/open
decelerate/accelerate

6. Solutions of Friedman eq.
matter era, Λ=0
acceleration
expansion
forever
conformal time
collapse
big bang
here & now

7. Dark Matter and Dark Energy
vacuum – repulsion? 1
decelerate
accelerate
m /2 - =0
open
closed
flat
m + =1 
bound
unbound
=0
EdS 1 2 m
mass - attraction

8. Luminous Matter 3

9. Spiral galaxy M74

10. Elliptical Galaxy

11. שביל החלב בצבעים

12. Luminous mass all sources, all wavelengths
With Λ=0, Universe unbound and infinite?

13. Dark Matter 4

14. Measuring Dark Matter Disk galaxies: rotation curves
Clusters and Elliptical galaxies: virial theorem
All scales: gravitational Lensing
Clusters: X-ray
Clusters: scattering of CMB by gas
Large-Scale: cosmic flows
Large-Scale: power-spectrum of density fluctuations
Cluster abundance at early times

15. Dark-Matter Halos in Galaxies
30,0000 ly
dark halo v R
flat rotation curve v R
3,000light years

16. Flat Rotation Curves: Extended Massive Dark-Matter Halos in Disk Galaxies
Milky Way
Sofue & Rubin 2001

17. dark-matter halo The Cosmic Web of Dark Matter
the millenium cosmological simulation

18. Virial Equilibrium in Clusters of Galaxies
 M~7x1014 M
V~1500 km/s
R~1.5 Mpc

19. Gravitational Lensing: Dark Matter in Galaxy Clusters
HST

20. Gravitational Lensing

21. Observed Radial Peculiar Velocities
Mark III

22. POTENT: Cosmic Flows Observe radial peculiar velocities:
Potential flow:
Smooth the radial velocity field.
Integrate from the origin along radial trajectories to obtain the potential at any point in space.
Differentiate to obtain the 3-dimensional velocity field.
Compute density-fluctuation field by another differentiation:

23. Large-Scale Cosmic Flows - POTENT
Great Attractor

24. Dark-Matter Density us
200 Mpc
Supergalactic Plane

25. Mass Density in 3D 3D dark-matter density Great Attractor
Perseus Pisces
Great Void

26. Matter Density from Void Outflows
Dekel & Rees 1993
ρ=0 δ=-1
high Ωm
low Ωm
rees/void21.gif

27. 2dF Pk Measuring m from the 2dF Survey
power spectrum
2dF Pk Measuring m from the 2dF Survey
2D correlation function
angular separation
redshift
anisotropy in z-space

28. Total Mass What is the dark matter made of?
exerting gravitational attraction
With Λ=0, Universe still unbound and infinite?
What is the dark matter made of?

29. Baryonic dark matter: planets, black holes, …
Baryonic Mass
Baryonic dark matter: planets, black holes, …
Big-Bang Nucleosynthesis:

30. Big Bang Nucleosynthesis
only 12.5% n left after decaying to p  75% H + 25% He (in mass)
At T~109K deuterium becomes stable and nucleosynthesis starts:
A minute later p becomes too cold to penetrate the Coulomb barrier by p in d and the process stops.
Rate  np2  abundances of d and 3He decrease with b
b=0.04  0.01
bh2=0.02

31. Non-Baryonic Dark-Matter Particles
Neutralinos, photinos, axions, ... all those damn super-symmetric particles you can’t see… that’s what drove me to drink… but now I can see them!

32. Dark Matter and Dark Energy1
accelerate
decelerate 
unbound
bound
EdS
LSS
closed
open
flat 1 2 m

33. measure the expected deceleration under gravitational attraction
Dark Energy
measure the expected deceleration under gravitational attraction 8

34. The Telescope as a Time Machine
young
billions of light-years
old 2
millions of light-years
 age of universe (Gyr)

13.69
13.7
looking far → back in time

35. Hubble Deep Field

36. Supernova: Crab

37. Bright Standard Candle: Supernovae Type Ia

38. Luminosity-distance to a standard candle
magnitude = -2.5 log (luminosity) +const.
Luminosity distance (DL=dLH0)
Observe a sample of z-m Determine M and H0 at low z Find Ωm and ΩΛ by best fit at high z

39. Today’s expansion rate V=H0R
Deceleration?
distance R
nearby supernovae
רחוק V
velocity V
היקום מאיץ

40. Acceleration! Past expansion rate V=H(t) R R V distance nearby
far away
Saul Brian Perlmutter Schmidt
velocity V
היקום מאיץ

42. Acceleration by a cosmological constant
Big Bang
here & now
time

43. Acceleration
Vacuum Energy 25

44. Dark Matter and Dark EnergySN 1
accelerate
decelerate 
unbound
bound
EdS
LSS
flat
closed
open 1 2 m

45. Curvature 11

46. Use a Standard Ruler
known intrinsic length
flat
curved
observed angle

47. Cosmic Microwave Background
time

48. Origin of Cosmic Microwave Background
horizon big-bang
t=0
last-scattering surface
Thomson scattering
trec~380 kyr
T~4000K
ct0
T~2.7K
c(t0-tdec)
here & now
t0~14 Gyr
horizon at trec ~100 comoving Mpc ~1o
transparent
neutral H
ionized p+e-
opaque

49. Horizon at last scattering ~ 100 comoving Mpc ~ 1˚
Characteristic Scale
time
here & now
z=0 t=13.7 Gyr
space
past light cone
neutral H transparent
last scattering
z~1090 t=380 kyr
ionized opaque
horizon
z=∞ t=0
big bang singularity
Horizon at last scattering ~ 100 comoving Mpc ~ 1˚

50. Acoustic Peaks
In the early hot ionized universe, photons and baryons are coupled via Thomson scattering off free electrons.
Initial fluctuations in density and curvature (quantum, Inflation) drive acoustic waves, showing as temperature fluctuations, with a characteristic scale - the sound horizon cst.
At z~1,090, T~4,000K, H recombination, decoupling of photons from baryons. The CMB is a snapshot of the fluctuations at the last scattering surface.
Primary acoustic peak at rls ~ ctls ~ 100 co-Mpc or θ~1˚ (~200) – the “standard ruler”.
Secondary oscillations at fractional wavelengths.

51. Curvature
closed
flat
open

52. Curvature
closed
flat
open

53. CMB Temperature Maps isotropy T2.725K T/T~10-3 dipole WMAP 2003
COBE
WMAP
resolution ~10o
resolution ~ 10’
T/T~10-5

54. WMAP: Wilkinson Microwave Anisotropy Probe
δT/T~ arcmin
Charles Bennett

55. Angular Power Spectrum
 angle =2/

56. Curvature
1st peak
closed
open
flat

57. Curvature The Universe is nearly flat: Open? Closed?
Surely much larger than our horizon!

58. Dark Matter and Dark EnergySN 1
open
closed
flat *
accelerate
decelerate 
CMB
unbound
bound
EdS
LSS 1 2 m 40

61. Other Parameters: Baryons, Fluctuations

62. CMB Acoustic Oscillations explore all parameters
compression kctls=π
curvature
velocity max
dark matter
initial conditions
dissipation
rarefaction kcstls=2π
baryons

63. The ΛCDM model is very successful Accurate parameter determination
curvature
dark matter
initial fluctuations
dissipation
baryons

64. Polarization by scattering off electrons; re-ionization by stars & quasars at z~10

65. Cosmic History galaxy formation dark ages big bang
last scattering t=380 kyr
reionization t=430 Myr
today t=13.7 Gyr

66. Baryonic Acoustic Oscillations observed in the galaxy-galaxy correlation function (SDSS, z=0.35)
D(z=0.35) is 10% of way to surface of last-scattering. Currently have a 4% measurement of s.

67. The Sloan Digital Sky Survey
Redshifts to 1M galaxies

68. Success of the Standard Model: Fluctuation Power Spectrum

69. Success of the LCDM Power Spectum

70. Standard ΛCDM Model Parameters
2015: Planck (+BAO+SN)
Hubble constant H0=67.8  0.9 km s-1 Mpc-1
Total density Ωm+λ =  0.005
Dark energy density ΩΛ=0.692  0.012
Mass density Ωm=0.308  0.012
Baryon density Ωb= 
Fluctuation spectral index ns=0.968  0.006
Fluctuation amplitude σ8=0.830  0.015
Optical depth =0.066  0.016
Age of universe t0=13.80  0.02 Gyr

71. Beyond the Standard Model20

72. What is the Dark Energy?
“ ‘Most embarrassing observation in physics’ – that’s the only quick thing I can say about dark energy that’s also true.” ……………………………………..Edward Witten or
- Cosmological constant in GR?
- Failure of GR? Quintessence? Novel property of matter?
- Why so small? in cosmology Gev … …vs QFT: 108 Gev4 (ElectroWeak) or Gev4 (Planck)
- Why becoming dominant now? (Anthropic principle?)

74. Generalized Dark Energy
Cosmological constant
Energy conservation during expansion
Equation of state
Generalized eq. of state
e.g. Quintessence
Friedman eq. and the fluctuation growth-rate eq. probe different parts of the theory and can constrain w(t)

75. Equation of State and its Time Variation
Very close to standard GR with a cosmological constant

76. Beyond the Standard ΛCDM Model
2015: Planck (+BAO+SN)
Total density Ωtot = 1-Ωk =  0.004
Equation of state w =  0.045
Tensor/scaler fluctuations r < 0.11 (95% CL)
Running of spectral index dn/dlnk =  0.02
Neutrino mass ∑ mν < 0.23 eV (95% CL)
# of light neutrino families Neff=3.15  0.23

77. Neutrino Mass and # of Families

78. Open Questions - The Big Bang? Inflation? - What is the dark energy?
- What is the dark matter particle?
- How do galaxies form from the cosmic web?
- How do stars form in galaxies

79. Conclusions - Cosmology has a Standard Model: ΛCDM
- The basic parameters are accurately measured ….using multiple techniques
- Mysteries: dark matter, dark energy, big-bang, ….inflation
- Next step: probe physics beyond the standard ….model
- Current effort: galaxy formation

80. Age of the oldest globular star clusters

81. Age of an old star cluster12 16

82. The Age of the Universe