Early times CMB

Today Galaxies and clusters of galaxies NGC 1512

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

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

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

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!

Back to the CMB… : Temperature Fluctuations

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

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

Harmonic multipole decomposition (Clem Pryke, Chicago)

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

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

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

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

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

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

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

(Wayne Hu, Chicago) CMB

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

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

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

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

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

Degeneracy in the CMB

Cosmological parameters & degeneracies (WMAP team)

Curing the degeneracies? Combining independant data !

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

Kourou, French Guiana 26 February 2009