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Cosmology : a short introduction

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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…)

(COBE data, 1996)

First

detection

1965

at 7.35 cm

Penzias & Wilson

Nobel Prize 1978

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

The Milky Way

Cosmological interpretation:

Dicke, Peebles, Roll, Wilkinson (1965)

(COBE data, 1996)

COBE, 1991-1996

First detection of anisotropies

(Nobel prize 2006: Smoot & Mather)

-200 µK < ΔT < 200 µK

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

WMAP: 2003, 2006, 2008

(Launched June 2001)

From temperature maps…

…to power spectra…

…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)

(2MASS, XSC & PSC)

Notice : isotropy & homogeneity!

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

Our understanding of the universe…

1. How do we understand what we see?

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

Friedmann-Lemaître-Robertson-Walker metric

equivalent to

where

Coordinates :

Scale factor a(t):

Redshift & Expansion :

Hubble’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 :

scatter in Hubble’s law

for nearby galaxies

Einstein equations : geometry energy content

Friedmann equations : dynamics of the Universe

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

and today:

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

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 wi constant,

* integrate

Rem : C.C. wΛ= -1

Matter-radiation equality

Expansion history wrt. dominant fluid

(from WMAP)

for zzeq : Universe dominated by radiation

Acceleration wrt. fluid equation of state of dominant fluid

Deceleration

Acceleration

Matter and radiation OK

Observed accelerationrequires exotic fluid withnegative pressure!

time, age

density, z, T

radiation & matter

in thermal equilibrium

radiation & matter

live separate lives

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

The CMB : a snapshot of the Baby Universe