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…). - PowerPoint PPT PresentationTRANSCRIPT
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