cosmology : a short introduction

Cosmology : a Cosmology : a shortshort introduction introduction

Mathieu Langer

Institut d’Astrophysique SpatialeUniversité 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 ?0. What do we see ?0. What do we see ?

(depends on wavelength…)

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

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

(CO

BE

dat

a,

1996

)

Penzias & WilsonNobel Prize 1978

Firstdetection

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

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

(CO

BE

dat

a,

1996

)

The Cosmic Microwave Background : a “perfect” black bodyThe Cosmic Microwave Background : a “perfect” black bodyThe Cosmic Microwave Background : a “perfect” black bodyThe Cosmic Microwave Background : a “perfect” black body

The Cosmic Microwave Background : a “perfect” black bodyThe Cosmic Microwave Background : a “perfect” black bodyThe Cosmic Microwave Background : a “perfect” black bodyThe Cosmic Microwave Background : a “perfect” black body

CMB : tiny anisotropiesCMB : tiny anisotropiesCMB : tiny anisotropiesCMB : tiny anisotropies

COBE, 1991-1996 First detection of anisotropies

(Nobel prize 2006: Smoot & Mather)

CMB : tiny anisotropies, huge informationCMB : tiny anisotropies, huge informationCMB : tiny anisotropies, huge informationCMB : 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

CMB anisotropies : angular power spectrumCMB anisotropies : angular power spectrumCMB anisotropies : angular power spectrumCMB 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 scalesDistribution of structure on large scalesDistribution of structure on large scalesDistribution of structure on large scales

Panoramic view of the entire near-infrared skyBlue : nearest galaxiesRed : most distant (up to ~ 410 Mpc)

(2MA

SS, X

SC &

PS

C)

Notice : isotropy & homogeneity!

Hubble’s law, expansion of the universeHubble’s law, expansion of the universeHubble’s law, expansion of the universeHubble’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

Ambitious cosmology…Ambitious cosmology…Ambitious cosmology…Ambitious cosmology…

Our understanding of the universe…Our understanding of the universe…

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

Fundamental principlesFundamental principlesFundamental principlesFundamental 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-timeMaximally symmetric space-timeMaximally symmetric space-timeMaximally symmetric space-time

• Friedmann-Lemaître-Robertson-Walker metric

2

2 2 2 2 2 2 22

( ) sin 1

dxds dt a t x d d

kx

2 2 2 2 2 2 2 2( ) ( ) sin kds dt a t d f d d

sin 1 spherical

( ) 0 flat

sinh 1 hyperbolick

k

f k

k

equivalent to

where

Scale factor, expansion, Hubble’s lawScale factor, expansion, Hubble’s lawScale factor, expansion, Hubble’s lawScale factor, expansion, Hubble’s law

• Coordinates :

• Scale factor a(t):

• Redshift & Expansion :

2 2 2 2 2 2 2( ) vs.ds dt a t dx ds dt dr

( )dr a t dx

: physical coordinate (distance, scale), changes in timer

: constant in time, comoving coordinatex

22 1 1

1

( ) ( )a t

r t t r ta t

0obs 0

em em

11

1

a t aVz

V a t a t

Scale factor, expansion, Hubble’s lawScale factor, expansion, Hubble’s lawScale factor, expansion, Hubble’s lawScale factor, expansion, Hubble’s law

• 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 :

12 1 2( ) ( )( )r t a t x x

12 1 2 12

0today

( )( )

Hubble constant :

ar a t x x r

aa

Ha

Hubble proper

( )r Hr a t x

V V

scatter in Hubble’s law

for nearby galaxies

Dynamics : Einstein, Friedmann, etc.Dynamics : Einstein, Friedmann, etc.Dynamics : Einstein, Friedmann, etc.Dynamics : Einstein, Friedmann, etc.

• Einstein equations : geometry energy content

• Friedmann equations : dynamics of the Universe

1( 2 ) 8

2 NR g R G T

diag( , , , ) (perfect fluid)T p p p Stress-energy tensor:

22

8

3NG k

Ha

24 ( )N

kH G p

a

Expansion rate

Variation of H

Dynamics and cosmological parametersDynamics and cosmological parametersDynamics and cosmological parametersDynamics and cosmological parameters

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

• Density parameters :

• Equation of state :

for each fluid i : pi = wi ρi

0

0

22

38

3 8N

c cN

HGH

G

( )( ) i

ic

tt

0,0

( )ii

c

t

and today:

• Photons : p = ρ/3 wr=1/3

• Matter : ρ = m n, p = nkT ρ wm = 0

Dynamics of the UniverseDynamics of the UniverseDynamics of the UniverseDynamics of the Universe

• Friedmann equations– expansion

– variation

– acceleration

• Matter-Energy conservation :

2 20 Total ( )H H t

20

3( )(1 )

2H H t w

0Total 0( ) ( ) 1ii

t t so clearly

20

4 1 3( 3 ) ( )

3 2NGa w

p H ta

0T

3 (1 ) 0H w

(Rem: only 2 independent equations)

• Evolution of a given fluid :Conservation equation gives

• Summary :

3 (1 )i i i

aw

a

3(1 ),0

iwi i a

* assume wi constant,* integrate

Matter : Ωm = Ωm,0a-3 = Ωm,0(1+z)3

Radiation : Ωr = Ωr,0a-4 = Ωr,0(1+z)4

Cosm. Const.: ΩΛ = ΩΛ,0

Rem : C.C. wΛ= -1

Universe Expansion HistoryUniverse Expansion HistoryUniverse Expansion HistoryUniverse Expansion History

• Matter-radiation equality

• Expansion history wrt. dominant fluid3

(1 )2

0 ,0

iw

i

aH H a

a

Radiation dom. : a(t) t1/2

Matter dom.: a(t) t2/3

C.C. dom.: a(t) exp (H0t)

2

3(1 )( ) iwa t t

m,0r eq m eq eq

r,0

( ) ( ) 1 5825z z z

for z zeq : Universe dominated by radiation

(from WMAP)

Universe Expansion HistoryUniverse Expansion HistoryUniverse Expansion HistoryUniverse Expansion History

• Acceleration wrt. fluid equation of state of dominant fluid

• Deceleration

• Acceleration

Observed accelerationObserved acceleration requires exotic fluid with negative pressurenegative pressure!

3(1 )20 ,0

1 3

2iw i

i

waH a

a

10

3ia w

Matter and radiation OK

10

3ia w

Back to the CMB…Back to the CMB…Back to the CMB…Back to the CMB…

time, age

radiation & matter in thermal equilibrium

radiation & matter live separate lives

density, z, T

CMB : Primordial Photons’ Last ScatteringCMB : Primordial Photons’ Last ScatteringCMB : Primordial Photons’ Last ScatteringCMB : Primordial Photons’ Last Scattering

time, age

radiation & matter in equilibrium

via tight coupling

radiation & matter are decoupled,no interaction

density, z, T

CMBz =1100

380 000 years

(Planck)

The CMB : a snapshot of the Baby UniverseThe CMB : a snapshot of the Baby Universe