cmb early times. galaxies and clusters of galaxies today ngc 1512
TRANSCRIPT
CMB
Early timesEarly times
Galaxies and clusters of galaxies
TodayToday
NGC 1512
Structure formation : gravity at playStructure formation : gravity at playStructure formation : gravity at playStructure formation : gravity at play
N-body simulations (Kravtsov & Klypin)
43 M
pc
Structure formation : a rapid primerStructure formation : a rapid primerStructure formation : a rapid primerStructure formation : a rapid primer
• Basic ingredients– Matter conservation (continuity)
– Momentum conservation (Euler)
– Gravity (Poisson equation)
– Expansion of the universe (H)
• Density Contrast
• Fourier Transform
( ) FT[ ( , )]k t r t
( , ) ( )( , ) 1
( )
r t tr t
t
Structure formation : gravity vs. pressureStructure formation : gravity vs. pressureStructure formation : gravity vs. pressureStructure formation : gravity vs. pressure
• “Cosmic” Oscillators
22 0k k k kH
Damping due to expansion
(comoving)
Structure formation : gravity vs. pressureStructure formation : gravity vs. pressureStructure formation : gravity vs. pressureStructure formation : gravity vs. pressure
• “Cosmic” Oscillators
• Competition between gravity and pressure
22 0k k k kH
2 22
24s
k N
c kG
a
Damping due to expansion
cs = sound speed
Pressure > gravity ωk2 > 0 : oscillations
Pressure < gravity ωk2 < 0 : density grows
Depends on scale!
(comoving)
Depends on expansion!
Back to the CMB… : Temperature FluctuationsBack to the CMB… : Temperature FluctuationsBack to the CMB… : Temperature FluctuationsBack to the CMB… : Temperature Fluctuations
cmb cmb
( )( ) ~ ( , )
T n Tn r t
T
2.725 KT
Quick fluctuation analysisQuick fluctuation analysisQuick fluctuation analysisQuick fluctuation analysis
• Fourier Transform on the Celestial Sphere
• Angular Power Spectrum Cl
0
( , ) ( , )l
mlm l
l m l
Ta Y
T
* ( , ) ( , )mlm l
Ta d Y
T
2
l lmC a
180~l
Sphericalharmonics
Cl : power in fluctuations of angular size θ
= FT ( ) ( ')l
T TC n n
T T
Weight ofeach mode
multipole where , 'n n
180~l
Multipoles
All modes
l = 2
l = 4
l = 6
l = 8
l = 3
l = 5
l = 7
(Hin
shaw
et a
l.,
2007
)
Harmonic multipole decomposition
(Clem Pryke, Chicago)
CMB Power SpectrumCMB Power SpectrumCMB Power SpectrumCMB Power Spectrum
how much the temperature varies from point to point on the sky vs. the angular frequency l
Basic physics of CMB anisotropiesBasic physics of CMB anisotropiesBasic physics of CMB anisotropiesBasic physics of CMB anisotropies
Many contributions
Intrinsic “primordial”
Super-imposed “secondary”
Foregrounds “contaminants”
Cosmological
Local
Sunyaev-Zel’dovich effect
Last Scattering
Line-of-sight
Basic physics of CMB anisotropiesBasic physics of CMB anisotropiesBasic physics of CMB anisotropiesBasic physics of CMB anisotropies
Many contributions
Intrinsic “primordial”
Super-imposed “secondary”
Foregrounds “contaminants”
Cosmological
LocalLine-of-sight
Last Scattering
Basic physics of CMB anisotropiesBasic physics of CMB anisotropiesBasic physics of CMB anisotropiesBasic physics of CMB anisotropies
Many contributions
Primordial anisotropies
Intrinsic “primordial”
Super-imposed “secondary”
Foregrounds “contaminants”
Cosmological
LocalLine-of-sight
Last Scattering
LS
1( ) ( ) ( ) . ( )
3 r r
Tn n n n v n
T
Densityfluctuations
Dopplereffect
Gravitationalredshift
Acoustic peaksAcoustic peaksAcoustic peaksAcoustic peaks
• “Equation of motion” for Θ = ΔT/T (comoving coord.)
• Conformal time
• Effective “mass”
• Pulsation
22
eff eff3
cm k m g
where dt
a
= comoving particle horizon
eff
31 where
4bm R R
sound
eff3
kckc
m
Step by step…Step by step…Step by step…Step by step…
• Consider g = 0, and R << 12 2
s eq0 ( ) cosk c ks
~3
ss c dwhere = distance reached by a
sound wave at time η
Rem : CMB s = scmb
• On large scales, kscmb<< 1
eq ( ) ~ plateau
Step by step…Step by step…Step by step…Step by step…
• Consider g = 0, and R << 12 2
s eq0 ( ) cosk c ks
~3
ss c dwhere distance reached by a
sound wave at time η
• On smaller scales, kscmb>>1
cmb oscillationsnk s n
Rem : CMB s = scmb
CMB CMB
(Wayne Hu, Chicago)
Searching for scales on the skySearching for scales on the skySearching for scales on the skySearching for scales on the sky
• Luminosity distance
• Angular diameter distance
2 S
4L
Ld
F
(cf. Euclidean 1/d2 law)
LS : intrinsic luminosity of a source at z
F : meas. flux = observed lumin./surface
0 S S1L kd a f z FLRW space-time
phys
2 SS A A k
dSd d a f
d
Reminder : fk geometry
Angular scales & Universe geometryAngular scales & Universe geometryAngular scales & Universe geometryAngular scales & Universe geometry
Spherical
Flat
Hyperbolic
θ
180~l
Sound horizon scale must appear in Cl
spectrum and probe geometry
Position of the Position of the first peak!first peak!
The CMB & the geometry of the UniverseThe CMB & the geometry of the Universe
Actual data(Boom., 1998)
Simulatedmaps
Spherical Flat Hyperbolic
Typical angularscale : 1o
Step by step…Step by step…Step by step…Step by step…
• Consider g = 0, and R << 1 (radiation dominates)2 2
s eq0 ( ) cosk c ks
~3
ss c dwhere = distance reached by a
sound wave at time η
• On small scales : damping
Silk dampingRem : CMB s = scmb
• Neutrino free streaming
• Silk damping : photon mean free path viscosity, photon drag
More effects…More effects…More effects…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
11 3 cos
3
TR ks R
T
Compression & rarefaction asymmetry
Odd peaks higher, even peaks lower
Degeneracy in the CMBDegeneracy in the CMB
Cosmological parameters & degeneraciesCosmological parameters & degeneraciesCosmological parameters & degeneraciesCosmological parameters & degeneracies(W
MA
P team
)
Curing the degeneracies?
Combining independant
data !
CMB – The ultimate satellite : PlanckCMB – The ultimate satellite : Planck
Unequalledresolution
(0.08 degrees)
Will measureclearly the
polarisationpolarisation
Launched14 May 2009 !
HFI : J.-L. PugetHFI : J.-L. Puget
LFI : N. Mandolesi
Kourou, French Guiana
26 February 2009
