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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…).

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Cosmology a short introduction

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

0. What do we see ?

(depends on wavelength…)


Cosmic microwave background detected 1965 penzias wilson nobel prize 1978
Cosmic Microwave Background (detected 1965, Penzias & Wilson, Nobel prize 1978)

(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)


Cosmic microwave background detected 1965 penzias wilson nobel prize 19781
Cosmic Microwave Background full sky(detected 1965, Penzias & Wilson, Nobel prize 1978)

(COBE data, 1996)




Cmb tiny anisotropies
CMB : tiny anisotropies full sky

COBE, 1991-1996

First detection of anisotropies

(Nobel prize 2006: Smoot & Mather)


Cmb tiny anisotropies huge information
CMB : tiny anisotropies, huge information full sky

-200 µK < ΔT < 200 µK

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

WMAP: 2003, 2006, 2008

(Launched June 2001)


Cmb anisotropies angular power spectrum
CMB anisotropies : angular power spectrum full sky

From temperature maps…

…to power spectra…


…to cosmological parameters and cosmic pies : full sky

Age : 13.7 billion years


Distribution of structure on large scales

Panoramic view of the entire near-infrared sky full sky

Blue : nearest galaxies

Red : most distant (up to ~ 410 Mpc)

Distribution of structure on large scales

(2MASS, XSC & PSC)


Notice : full skyisotropy & homogeneity!


Hubble s law expansion of the universe
Hubble’s law, expansion of the universe full sky

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





Fundamental principles

Cosmological principle full sky

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 principles


Maximally symmetric space time

Friedmann-Lemaître-Robertson-Walker metric full sky

Maximally symmetric space-time

equivalent to

where


Scale factor expansion hubble s law

Coordinates : full sky

Scale factor a(t):

Redshift & Expansion :

Scale factor, expansion, Hubble’s law


Scale factor expansion hubble s law1

Hubble’s flow : full sky

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


Dynamics einstein friedmann etc

Einstein equations : full skygeometry  energy content

Friedmann equations : dynamics of the Universe

Dynamics : Einstein, Friedmann, etc.

Stress-energy tensor:

Expansion rate

Variation of H


Dynamics and cosmological parameters

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

Density parameters :

Equation of state :

for each fluid i : pi = wiρi

Dynamics and cosmological parameters

and today:

  • Photons : p = ρ/3  wr=1/3

  • Matter : ρ = mn, p = nkTρ wm = 0


Dynamics of the universe

Friedmann equations full sky

expansion

variation

acceleration

Matter-Energy conservation :

Dynamics of the Universe

so clearly

(Rem: only 2 independent equations)


Evolution of a given fluid : full sky

Conservation equation gives

Summary :

* assume wi constant,

* integrate

Rem : C.C.  wΛ= -1


Universe expansion history

Matter-radiation equality full sky

Expansion history wrt. dominant fluid

Universe Expansion History

(from WMAP)

 for zzeq : Universe dominated by radiation


Universe expansion history1

Acceleration wrt. fluid equation of state of dominant fluid full sky

Deceleration

Acceleration

Universe Expansion History

Matter and radiation OK

Observed accelerationrequires exotic fluid withnegative pressure!


Back to the cmb
Back to the CMB… full sky

time, age

density, z, T

radiation & matter

in thermal equilibrium

radiation & matter

live separate lives


Cmb primordial photons last scattering
CMB : Primordial Photons’ Last Scattering full sky

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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