1. Cosmology : a short introduction Mathieu Langer Institut d’Astrophysique Spatiale Université Paris-Sud XI Orsay, France Egyptian School on High Energy Physics CTP-BUE, Egypt 27 May – 4 June 2009

2. 0. What do we see ? (depends on wavelength…)

3. Cosmic Microwave Background (detected 1965, Penzias & Wilson, Nobel prize 1978) (COBE data, 1996)

4. Penzias & Wilson Nobel Prize 1978 First detection 1965 at 7.35 cm

5. What Penzias & Wilson would have seen, had they observed the full sky Cosmological interpretation : Dicke, Peebles, Roll, Wilkinson (1965) The Milky Way

6. Cosmic Microwave Background (detected 1965, Penzias & Wilson, Nobel prize 1978) (COBE data, 1996)

7. The Cosmic Microwave Background : a “perfect” black body

9. CMB : tiny anisotropies COBE, 1991-1996 First detection of anisotropies (Nobel prize 2006: Smoot & Mather)

10. CMB : tiny anisotropies, huge information WMAP: 2003, 2006, 2008 (Launched June 2001) First fine-resolution full-sky map (0.2 degrees) -200 µK < ΔT < 200 µK

11. The CMB and the geometry of the Universe Actual data (Boom., 1998) Simulated maps SphericalFlatHyperbolic Typical size : 1 o

12. CMB anisotropies : angular power spectrum From temperature maps… …to power spectra…

13. …to cosmological parameters and cosmic pies : Age : 13.7 billion years

14. Distribution of structure on large scales Panoramic view of the entire near-infrared sky Blue : nearest galaxies Red : most distant (up to ~ 410 Mpc) (2MASS, XSC & PSC)

15. Notice : isotropy & homogeneity!

16. Hubble’s law, expansion of the universe V = H 0 D H 0 = 71 ± 4 km/s/Mpc (from WMAP + Structures) (Hubble, 1929) Rem : 1 parsec ~ 3.262 light years ~ 3.1×10 13 km

17. Ambitious cosmology…

18. Our understanding of the universe…

19. 1. How do we understand what we see?

20. Fundamental principles Cosmological principle –Universe : spatially homogeneous & isotropic everywhere  Applies to regions unreachable by observation Copernican principle –Our place is not special  observations are the same for any observer –Isotropy + Copernicus  homogeneity  Applies to observable universe

21. Maximally symmetric space-time Friedmann-Lemaître-Robertson-Walker metric equivalent to where

22. Scale factor, expansion, Hubble’s law Coordinates : Scale factor a(t): Redshift & Expansion :

23. Scale factor, expansion, Hubble’s law Hubble’s flow : –2 observers at comoving coordinates x 1 & x 2 –Physical distance : –Separation velocity : Proper velocities –Galaxy moving relative to space fabric  x not constant –Velocity :  scatter in Hubble’s law for nearby galaxies

24. Dynamics : Einstein, Friedmann, etc. Einstein equations : geometry  energy content Friedmann equations : dynamics of the Universe Stress-energy tensor: Expansion rate Variation of H

25. Dynamics and cosmological parameters Critical density : put k = 0 today(cf. measurements!) Density parameters : Equation of state : for each fluid i : p i = w i ρ i and today: Photons : p = ρ/3  w r =1/3 Matter : ρ = m n, p = nkT  ρ  w m = 0

26. Dynamics of the Universe Friedmann equations –expansion –variation –acceleration Matter-Energy conservation : so clearly (Rem: only 2 independent equations)

27. Evolution of a given fluid : Conservation equation gives Summary : * assume w i constant, * integrate Matter :Ω m = Ω m,0 a -3 = Ω m,0 (1+z) 3 Radiation :Ω r = Ω r,0 a -4 = Ω r,0 (1+z) 4 Cosm. Const.:Ω Λ = Ω Λ,0 Rem : C.C.  w Λ = -1

28. Universe Expansion History Matter-radiation equality Expansion history wrt. dominant fluid Radiation dom. : a(t)  t 1/2 Matter dom.: a(t)  t 2/3 C.C. dom.: a(t)  exp (H 0 t)   for z  z eq : Universe dominated by radiation (from WMAP)

29. Universe Expansion History Acceleration wrt. fluid equation of state of dominant fluid Deceleration Acceleration Observed accelerationnegative pressure  Observed acceleration requires exotic fluid with negative pressure! Matter and radiation OK

30. Back to the CMB… time, age radiation & matter in thermal equilibrium radiation & matter live separate lives density, z, T

31. CMB : Primordial Photons’ Last Scattering time, age radiation & matter in equilibrium via tight coupling radiation & matter are decoupled, no interaction density, z, T CMB z =1100 380 000 years (Planck)

32. The CMB : a snapshot of the Baby Universe