CMB Early times. Galaxies and clusters of galaxies Today NGC 1512.

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


Many contributions




Cosmological

LocalLine-of-sight

Last Scattering


Many contributions

Primordial anisotropies




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


• Consider g = 0, and R << 12 2

s eq0 ( ) cosk c ks

~3

ss c dwhere distance reached by a


• 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


• Consider g = 0, and R << 1 (radiation dominates)2 2

s eq0 ( ) cosk c ks

~3

ss c dwhere = distance reached by a


• 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

CMB Early times. Galaxies and clusters of galaxies Today NGC 1512.

Documents

chicago cmb power spectrum

effectseffect of gravity

cmb sound speed

stepconsider g

sound speedpressure

r step

angular frequency

expansion cs