1. Early times
CMB

2. Today Galaxies and clusters of galaxies
NGC 1512

3. Structure formation : gravity at play
43 Mpc
N-body simulations (Kravtsov & Klypin)

4. Structure formation : a rapid primer
Basic ingredients
Matter conservation (continuity)
Momentum conservation (Euler)
Gravity (Poisson equation)
Expansion of the universe (H)
Density Contrast
Fourier Transform

5. Structure formation : gravity vs. pressure
“Cosmic” Oscillators
(comoving)
Damping due to expansion

6. Structure formation : gravity vs. pressure
“Cosmic” Oscillators
Competition between gravity and pressure
(comoving)
Damping due to expansion
cs = sound speed
Pressure > gravity  ωk2 > 0 : oscillations
Pressure < gravity  ωk2 < 0 : density grows
Depends on scale!
Depends on expansion!

7. Back to the CMB… : Temperature Fluctuations

8. Quick fluctuation analysis
Fourier Transform on the Celestial Sphere
Angular Power Spectrum Cl
Spherical
harmonics
Weight of
each mode 
multipole
where
 Cl : power in fluctuations of angular size θ

9. All modes l = 2 Multipoles l = 3 l = 4 l = 5 l = 6 l = 7 l = 8
(Hinshaw et al., 2007)
l = 7
l = 8

10. Harmonic multipole
decomposition
(Clem Pryke, Chicago)

11. CMB Power Spectrum
 how much the temperature varies from point to point on the sky vs. the angular frequency l

12. Basic physics of CMB anisotropies
Many contributions
Last Scattering
Intrinsic 
“primordial”
Super-imposed
“secondary”
Foregrounds
“contaminants”
Cosmological
Line-of-sight
Local
Sunyaev-Zel’dovich effect

13. Basic physics of CMB anisotropies
Many contributions
Last Scattering
Intrinsic 
“primordial”
Super-imposed
“secondary”
Foregrounds
“contaminants”
Cosmological
Line-of-sight
Local

14. Basic physics of CMB anisotropies
Many contributions
Primordial anisotropies
Last Scattering
Intrinsic 
“primordial”
Super-imposed
“secondary”
Foregrounds
“contaminants”
Cosmological
Line-of-sight
Local
Density
fluctuations
Doppler
effect
Gravitational
redshift

15. = comoving particle horizon
Acoustic peaks
“Equation of motion” for Θ = ΔT/T (comoving coord.)
Conformal time
Effective “mass”
Pulsation
= comoving particle horizon

16. Consider g = 0, and R << 1
Step by step…
Consider g = 0, and R << 1
= distance reached by a
sound wave at time η
where
Rem : CMB  s = scmb
On large scales, kscmb<< 1

17. Consider g = 0, and R << 1
Step by step…
Consider g = 0, and R << 1
distance reached by a
sound wave at time η
where
Rem : CMB  s = scmb
On smaller scales, kscmb>>1

18. (Wayne Hu, Chicago)
CMB

19. Searching for scales on the sky
Luminosity distance
Angular diameter distance
LS : intrinsic luminosity of a source at z
F : meas. flux = observed lumin./surface
(cf. Euclidean 1/d2 law)
FLRW space-time 
Reminder : fk geometry

20. Angular scales & Universe geometry
Spherical θ
Sound horizon scale must appear in Cl spectrum and probe geometry
 Position of the first peak!
Hyperbolic
Flat

22. The CMB & the geometry of the Universe
Actual data
(Boom., 1998)
Typical angular
scale : 1o
Simulated
maps
Spherical
Flat
Hyperbolic

23. Consider g = 0, and R << 1 (radiation dominates)
Step by step…
Consider g = 0, and R << 1 (radiation dominates)
= distance reached by a
sound wave at time η
where
Rem : CMB  s = scmb
Silk damping
On small scales : damping
Neutrino free streaming
Silk damping : photon mean free path
 viscosity, photon drag

24. Baryon loading, R ~ 1 at CMB
More effects…
Effect of gravity, g 0
 Shifts oscillation zero point :
photons have to climb out of potential wells
Baryon loading, R ~ 1 at CMB
 sound speed decreased, oscillation amplitude increased,
adds inertia to oscillations
Doppler term :
Velocity : π/2 out of phase modulation
Compression & rarefaction asymmetry
 Odd peaks higher, even peaks lower

27. Degeneracy in the CMB

28. Cosmological parameters & degeneracies
(WMAP team)

29. Curing the degeneracies?
Combining
independant
data !

31. CMB – The ultimate satellite : Planck
HFI : J.-L. Puget
Unequalled
resolution
(0.08 degrees)
Will measure
clearly the
polarisation
Launched
14 May 2009 !
LFI : N. Mandolesi

32. Kourou,
French Guiana
26 February 2009