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
0. What do we see ? (depends on wavelength…)
Cosmic Microwave Background (detected 1965, Penzias & Wilson, Nobel prize 1978) (COBE data, 1996)
Penzias & Wilson Nobel Prize 1978 First detection 1965 at 7.35 cm
What Penzias & Wilson would have seen, had they observed the full sky Cosmological interpretation : Dicke, Peebles, Roll, Wilkinson (1965) The Milky Way
Cosmic Microwave Background (detected 1965, Penzias & Wilson, Nobel prize 1978) (COBE data, 1996)
The Cosmic Microwave Background : a “perfect” black body
CMB : tiny anisotropies COBE, First detection of anisotropies (Nobel prize 2006: Smoot & Mather)
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
The CMB and the geometry of the Universe Actual data (Boom., 1998) Simulated maps SphericalFlatHyperbolic Typical size : 1 o
CMB anisotropies : angular power spectrum From temperature maps… …to power spectra…
…to cosmological parameters and cosmic pies : Age : 13.7 billion years
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)
Notice : isotropy & homogeneity!
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 ~ light years ~ 3.1×10 13 km
Ambitious cosmology…
Our understanding of the universe…
1. How do we understand what we see?
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
Maximally symmetric space-time Friedmann-Lemaître-Robertson-Walker metric equivalent to where
Scale factor, expansion, Hubble’s law Coordinates : Scale factor a(t): Redshift & Expansion :
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
Dynamics : Einstein, Friedmann, etc. Einstein equations : geometry energy content Friedmann equations : dynamics of the Universe Stress-energy tensor: Expansion rate Variation of H
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
Dynamics of the Universe Friedmann equations –expansion –variation –acceleration Matter-Energy conservation : so clearly (Rem: only 2 independent equations)
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
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)
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
Back to the CMB… time, age radiation & matter in thermal equilibrium radiation & matter live separate lives density, z, T
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 = years (Planck)
The CMB : a snapshot of the Baby Universe