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CMB

Early times. CMB. Today. Galaxies and clusters of galaxies. NGC 1512. Structure formation : gravity at play. 43 Mpc. N-body simulations (Kravtsov & Klypin). Basic ingredients Matter conservation (continuity) Momentum conservation (Euler) Gravity (Poisson equation)

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CMB

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

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

  6. “Cosmic” Oscillators Competition between gravity and pressure Structure formation : gravity vs. 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. Fourier Transform on the Celestial Sphere Angular Power Spectrum Cl Quick fluctuation analysis 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 (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. Many contributions Basic physics of CMB anisotropies Last Scattering Cosmological Line-of-sight Local Sunyaev-Zel’dovich effect

  13. Many contributions Basic physics of CMB anisotropies Last Scattering Cosmological Line-of-sight Local

  14. Many contributions Primordial anisotropies Basic physics of CMB anisotropies Last Scattering Cosmological Line-of-sight Local Density fluctuations Doppler effect Gravitational redshift

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

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

  18. CMB CMB (Wayne Hu, Chicago)

  19. Luminosity distance Angular diameter distance Searching for scales on the sky 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

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

  22. Consider g = 0, and R << 1 (radiation dominates) Step by step… = 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

  23. 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 More effects… Compression & rarefaction asymmetry  Odd peaks higher, even peaks lower

  24. Degeneracy in the CMB

  25. Cosmological parameters & degeneracies (WMAP team)

  26. Curing the degeneracies? Combining independant data !

  27. 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

  28. Kourou, French Guiana 26 February 2009

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