Download - Cosmology : a short introduction
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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
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0. What do we see ?0. What do we see ?0. What do we see ?0. What do we see ?
(depends on wavelength…)
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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
)
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Penzias & WilsonNobel Prize 1978
Firstdetection
1965at 7.35 cm
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What Penzias & Wilson would have seen, had they observed the full sky
Cosmological interpretation :Dicke, Peebles, Roll, Wilkinson (1965)
The Milky Way
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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
)
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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
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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
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CMB : tiny anisotropiesCMB : tiny anisotropiesCMB : tiny anisotropiesCMB : tiny anisotropies
COBE, 1991-1996 First detection of anisotropies
(Nobel prize 2006: Smoot & Mather)
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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
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CMB anisotropies : angular power spectrumCMB anisotropies : angular power spectrumCMB anisotropies : angular power spectrumCMB anisotropies : angular power spectrum
From temperature maps…
…to power spectra…
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…to cosmological parameters and cosmic pies :
Age : 13.7 billion years
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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)
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Notice : isotropy & homogeneity!
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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
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Ambitious cosmology…Ambitious cosmology…Ambitious cosmology…Ambitious cosmology…
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Our understanding of the universe…Our understanding of the universe…
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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?
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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
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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
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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
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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
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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
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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
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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)
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• 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
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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)
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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
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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
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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)
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The CMB : a snapshot of the Baby UniverseThe CMB : a snapshot of the Baby Universe