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### Cosmology : a short introduction

### 0. What do we see ?

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

(depends on wavelength…)

Cosmic Microwave Background (detected 1965, Penzias & Wilson, Nobel prize 1978)

(COBE data, 1996)

What Penzias & Wilson would have seen, had they observed the full sky

The Milky Way

Cosmological interpretation:

Dicke, Peebles, Roll, Wilkinson (1965)

Cosmic Microwave Background (detected 1965, Penzias & Wilson, Nobel prize 1978)

(COBE data, 1996)

CMB : tiny anisotropies

COBE, 1991-1996

First detection of anisotropies

(Nobel prize 2006: Smoot & Mather)

CMB : tiny anisotropies, huge information

-200 µK < ΔT < 200 µK

First fine-resolution full-sky map (0.2 degrees)

WMAP: 2003, 2006, 2008

(Launched June 2001)

…to cosmological parameters and cosmic pies :

Age : 13.7 billion years

Panoramic view of the entire near-infrared sky

Blue : nearest galaxies

Red : most distant (up to ~ 410 Mpc)

Distribution of structure on large scales(2MASS, XSC & PSC)

Hubble’s law, expansion of the universe

V = H0 D

H0 = 71 ± 4 km/s/Mpc

(from WMAP + Structures)

(Hubble, 1929)

Rem : 1 parsec ~ 3.262 light years ~ 3.1×1013 km

Cosmological principle

Universe : spatially homogeneous & isotropiceverywhere

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

Fundamental principlesHubble’s flow :

2 observers at comoving coordinates x1 & x2

Physical distance :

Separation velocity :

Proper velocities

Galaxy moving relative to space fabric x not constant

Velocity :

Scale factor, expansion, Hubble’s law scatter in Hubble’s law

for nearby galaxies

Einstein equations : geometry energy content

Friedmann equations : dynamics of the Universe

Dynamics : Einstein, Friedmann, etc.Stress-energy tensor:

Expansion rate

Variation of H

Critical density : put k = 0 today (cf. measurements!)

Density parameters :

Equation of state :

for each fluid i : pi = wiρi

Dynamics and cosmological parametersand today:

- Photons : p = ρ/3 wr=1/3
- Matter : ρ = mn, p = nkTρ wm = 0

Friedmann equations

expansion

variation

acceleration

Matter-Energy conservation :

Dynamics of the Universeso clearly

(Rem: only 2 independent equations)

Evolution of a given fluid :

Conservation equation gives

Summary :

* assume wi constant,

* integrate

Rem : C.C. wΛ= -1

Matter-radiation equality

Expansion history wrt. dominant fluid

Universe Expansion History(from WMAP)

for zzeq : Universe dominated by radiation

Acceleration wrt. fluid equation of state of dominant fluid

Deceleration

Acceleration

Universe Expansion HistoryMatter and radiation OK

Observed accelerationrequires exotic fluid withnegative pressure!

Back to the CMB…

time, age

density, z, T

radiation & matter

in thermal equilibrium

radiation & matter

live separate lives

CMB : Primordial Photons’ Last Scattering

380 000 years

time, age

(Planck)

density, z, T

radiation & matter

in equilibrium

via tight coupling

radiation & matter

are decoupled,

no interaction

CMB

z =1100

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