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The Standard Model
of Cosmology
Avishai Dekel, HUJI, PANIC08
Lick Survey
1M galaxies
isotropy→homogeneity
North Galactic
Hemisphere
Microwave Anisotropy Probe
February 2003, 2004
Science breakthrough of the year
WMAP
δT/T~10-5
isotropy→homogeneity
Homogeneity & Isotropy - Robertson-Walker Metric
ds  dt  a (t ) [du  S k (u ) d ]
2
2
2
expansion factor
2
comoving radius
Sk (u)  sin u
k  1
S k (u )  sinh u
k  1
S k (u )  u
k 0
r  a (t ) u
2
angular area
d 2  d 2  sin 2 d 2
Friedman Equation
Homogeneity + Gravity (G   g   8 GT ) 
2
2
2

a
8

G

(
a
)
kc

c
8 G
H 2 (t )  2 
 2 

i (t )

a
3
a
3
3
kinetic potential curvature vacuum
  m  r
 m   m0 a 3  r   r 0 a 4
1   m (t )   k (t )   (t )
i
i 
3H 2 8 G
 crit ~ 10 29 g cm 3
Two basic free parameters
tot   m     1   k
closed/open
a 1
a
q   2  m  
a
2
decelerate/accelerate
Solutions of Friedman
eq.
matter era, Λ=0
*
2a
2
a 
 k
4 G
a

 const .
a
3
*
k  0 : a  t 2/3
a small : a  t
2/3
a 2 8 G m0 kc2 c 2

 2 
2
3
3
a
3a
a
H 
2
1  m  k  
m0
a(t )
any k
acceleration
  0
expansion
forever
a large, k  1 : a  t  m  1
k  1 d  dt / a(t )
a  a*[1  cos( )]
conformal
time
m  1
t  a*[  sin(  )]
2
2

a

c
H2  2 
a
3
 a  e Ht
m  1
m  1
collapse
big bang here & now
t
Dark Matter and Dark Energy
vacuum –
repulsion?
1

unbound
0
bound
EdS
0
m
1
2
mass - attraction
Luminous Matter
3
Spiral galaxy M74
Elliptical Galaxy
‫שביל החלב בצבעים‬
Luminous mass
all sources, all wavelengths
luminous  0.01
With Λ=0, Universe unbound and infinite?
Dark Matter
4
Measuring Dark Matter
Disk galaxies: rotation curves
Clusters and Elliptical galaxies: virial theorem
All scales: gravitational Lensing
Clusters: X-ray
Clusters: scattering of CMB by gas
Large-Scale: cosmic flows
Large-Scale: power-spectrum of density fluctuations
Cluster abundance at early times
Dark-Matter Halos in Galaxies
dark halo
flat rotation curve
v
v
R
R
GM ( R)
V 
RR
 M ( R)  R
2
3,000 light years
30,0000 ly
Flat Rotation Curves: Extended Massive
Dark-Matter Halos in Disk Galaxies
Milky Way
Sofue & Rubin 2001
The Cosmic Web of Dark Matter
dark-matter halo
the millenium cosmological simulation
Virial Equilibrium in Clusters of Galaxies
GM
V 
R
2
V~1500 km/s
R~1.5 Mpc
 M~7x1014 M
Gravitational Lensing: Dark Matter in Galaxy Clusters
HST
Gravitational Lensing
Observed Radial Peculiar Velocities
Mark III
POTENT: Cosmic Flows
Observe radial peculiar velocities:
Potential flow:
 
 
v (r )   (r )
cz  H 0 r  vr
 
(  v  0)
Smooth the radial velocity field.
Integrate from the origin along radial trajectories
to obtain the potential at any point in space.


r
 (r )    vr dr
0
Differentiate to obtain the 3-dimensional velocity
field.
Compute density-fluctuation field by another
differentiation:
 

1

 V

H 0 f ( m )

1 v
  I
 1
Hf x
Large-Scale Cosmic Flows - POTENT
Great
Attractor
Dark-Matter Density
us
Mass
Density
in 3D
3D
dark-matter
density
Great
Attractor
Perseus
Pisces
Great Void
Matter Density from Void Outflows
high Ωm
Dekel & Rees 1993
low Ωm
ρ=0 δ=-1
 
1
1    
 V
H 0 f ( m )
f 
0.6
m
rees/void21.gif

0.6
m
 
  V
power spectrum
2dF Pk
2D correlation function
anisotropy in z-space
 k Pk
3
m h  0.2  m  0.3
m
0.6
Measuring m from
the 2dF Survey
redshift
 0.5  0.1  m  0.3
angular separation
Total Mass
exerting gravitational attraction
m  0.308  0.012
With Λ=0, Universe still unbound and infinite?
What is the dark matter made of?
Baryonic Mass
Baryonic dark matter:
planets, black holes, …
Big-Bang Nucleosynthesis:
 baryons  0.044  0.004
Big Bang Nucleosynthesis
mn  m p  n   p  e
only 12.5% n left after decaying to
p  75% H + 25% He (in mass)
At T~109K deuterium becomes
stable and nucleosynthesis starts:
p  n  d ( pn)  
p
n
3
4
d

He ( ppn) 

He
A minute later p becomes too cold
to penetrate the Coulomb barrier
by p in d and the process stops.
Rate  np2  abundances of d and
3He decrease with 
b
b=0.04  0.01
bh2=0.02
Non-Baryonic Dark-Matter Particles
Neutralinos, photinos,
axions, ... all those
damn super-symmetric
particles you can’t
see… that’s what drove
me to drink… but now I
can see them!
Dark Matter and Dark Energy
1

unbound
0
EdS
bound
LSS
0
m
1
2
Dark Energy
measure the expected deceleration
under gravitational attraction
8
The Telescope as a Time Machine
young
billions of
light-years
old
2
millions of
light-years
13.69
13.7
looking far → back in time
0
Hubble Deep
Field
Supernova: Crab
Bright Standard Candle: Supernovae Type Ia
observed luminosity

  4 d L 2 ( z; H 0 ,  m ,   )
intrinsic luminosity
L
Luminosity-distance to a standard candle
l ~ L/d2
magnitude = -2.5 log (luminosity) +const.
m( z )  M  5 log DL ( z; m ,  )  5 log H 0  25
Luminosity distance (DL=dLH0)
DL ( z;  m ,   )  c(1  z ) |  k |
1 / 2
z


1/ 2
S k  |  k |  [(1  z ' ) 2 (1   m z ' )  z ' (2  z ' )  ]1/ 2 dz ' 
0


z

cz
1
Observe a sample of z-m
Determine M and H0 at low z
Find Ωm and ΩΛ by best fit at high z
Deceleration?
Today’s expansion rate V=H0R
distance
R
nearby
supernovae
velocity
‫רחוק‬
V V
‫היקום מאיץ‬
Past expansion rate V=H(t) R
distance
R
Acceleration!
nearby
far away
Saul
Brian
Perlmutter Schmidt
velocity
V
‫היקום מאיץ‬
Acceleration by a cosmological constant
H2 
a 2 8 G m0 kc2 c 2

 2 
2
3
3
a
3a
a
a(t)
aa 1
q   2  m  
2
a
ae
Ht
m  1
m  1
  0
  0
m  1
Big Bang
here & now
time
Acceleration
1
  m  0
2
Vacuum Energy
  0.72  0.02
25
Dark Matter and Dark Energy
1

unbound
0
EdS
bound
LSS
0
m
1
2
Curvature
11
Use a Standard Ruler
known intrinsic length
flat
curved
observed angle
intrinsic length
x
  d A ( z; H 0 ,  m ,   )
observed angle 
Cosmic Microwave
Background
time
Origin of Cosmic Microwave Background
horizon big-bang
t=0
last-scattering surface
trec~380 kyr
T~4000K
T
1 
~
~ 10 5
T 10 
Thomson
scattering
 T  m 2
T~2.7K
here & now
t0~14 Gyr
transparent
neutral H
ionized p+eopaque
horizon at trec
~100 comoving Mpc
~1o
Characteristic Scale
time
here & now
space
z=0
t=13.7 Gyr
past light cone
neutral H
transparent
ionized
opaque
last scattering
horizon
big bang singularity
z~1090
t=380 kyr
z=∞ t=0
Horizon at last scattering ~ 100 comoving Mpc ~
Acoustic Peaks
In the early hot ionized universe, photons and baryons
are coupled via Thomson scattering off free electrons.
Initial fluctuations in density and curvature (quantum,
Inflation) drive acoustic waves, showing as temperature
fluctuations, with a characteristic scale - the sound
horizon cst.
 T  1/ 4  A(k ) cos( k c t )
s
At z~1,090, T~4,000K, H recombination, decoupling of
photons from baryons. The CMB is a snapshot of the
fluctuations at the last scattering surface.
Primary acoustic peak at rls ~ ctls ~ 100 co-Mpc
or θ~1˚ (~200) – the “standard ruler”.
Secondary oscillations at fractional wavelengths.
Curvature
closed
flat
open
Curvature
closed
flat
open
CMB Temperature Maps
isotropy T2.725K
T/T~10-3
COBE
1992
resolution ~10o
dipole
WMAP
T/T~10-5
2003
resolution ~ 10’
WMAP: Wilkinson Microwave Anisotropy Probe
WMAP-5 2008
δT/T~10-5 10 arcmin
Charles
Bennett
Angular Power Spectrum
 angle
=2/
T ( ,  )  l
   almYlm ( ,  )
T
l 0 m   l
Cl  | alm |2
l (l  1)
 T 

Cl
 
2
T 
2
Curvature
1st peak
open
closed
flat
Curvature
The Universe is nearly flat:
1  k  m    1.005  0.006
Open? Closed?
Surely much larger than our horizon!
Dark Matter and Dark Energy
1
*

unbound
0
EdS
bound
LSS
0
40
m
1
2
Other Parameters:
Baryons, Fluctuations
CMB Acoustic Oscillations explore all parameters
compression kctls=π
curvature
velocity max
dark matter
initial conditions
rarefaction
kcstls=2π
baryons
The ΛCDM model is very successful
Accurate parameter determination
curvature
initial
fluctuations
dark matter
baryons
Polarization by scattering off electrons;
re-ionization by stars & quasars at z~10
Cosmic History
dark ages
galaxy formation
big bang
last scattering
reionization
t=380 kyr
t=430 Myr
today
t=13.7
Gyr
Baryonic Acoustic Oscillations observed in the
galaxy-galaxy correlation function (SDSS, z=0.35)
The Sloan Digital Sky Survey
Redshifts to 1M galaxies
Success of the Standard Model:
Fluctuation Power Spectrum
Success of the LCDM Power Spectum
Standard ΛCDM Model Parameters
2015: Planck (+BAO+SN)
Hubble constant
H0=67.8  0.9 km s-1 Mpc-1
Total density
Ωm+λ = 1.000  0.005
Dark energy density
ΩΛ=0.692  0.012
Mass density
Ωm=0.308  0.012
Baryon density
Ωb=0.0478  0.0004
Fluctuation spectral index
ns=0.968  0.006
Fluctuation amplitude
σ8=0.830  0.015
Optical depth
=0.066  0.016
Age of universe
t0=13.80  0.02 Gyr
Beyond the Standard Model
20
What is the Dark Energy?
“ ‘Most embarrassing observation in physics’ –
that’s the only quick thing I can say about dark
energy that’s also true.”
……………………………………..Edward Witten
G  g   8 G T
or
G  8 G (T   vacuum g  )
- Cosmological constant in GR?
- Failure of GR? Quintessence? Novel property of matter?
- Why so small? in cosmology 10-48 Gev4
…
…vs QFT: 108 Gev4 (ElectroWeak) or 1072 Gev4 (Planck)
- Why becoming dominant now? (Anthropic principle?)
Generalized Dark Energy
Cosmological constant
tot    const.
Energy conservation during
expansion
d (  c 2 a 3 )   p d (a 3 )
Equation of state
Generalized eq. of state
e.g. Quintessence
p   c2
p  w  c2
w( x, t ) ?
a  0  w  1 / 3
  w  1
Friedman eq. and the fluctuation growth-rate eq. probe
different parts of the theory and can constrain w(t)
Equation of State and its Time Variation
Very close to standard GR
with a cosmological constant
Beyond the Standard ΛCDM
Model
2015: Planck (+BAO+SN)
Total density
Ωtot = 1-Ωk = 1.001  0.004
Equation of state
w = -1.006  0.045
Tensor/scaler fluctuations
r < 0.11 (95% CL)
Running of spectral index
dn/dlnk = -0.03  0.02
Neutrino mass
∑ mν < 0.23 eV (95% CL)
# of light neutrino families Neff=3.15  0.23
Neutrino Mass and # of Families
Open Questions
- The Big Bang? Inflation?
- What is the dark energy?
- What is the dark matter particle?
- How do galaxies form from the cosmic web?
- How do stars form in galaxies
Conclusions
- Cosmology has a Standard Model: ΛCDM
- The basic parameters are accurately measured
….using multiple techniques
- Mysteries: dark matter, dark energy, big-bang,
….inflation
- Next step: probe physics beyond the standard
….model
- Current effort: galaxy formation
‫הרכב היקום‬
‫חומר אפל‬
‫חומר רגיל‬
‫אנרגיה אפלה‬
Age of the oldest globular star clusters
Age of an old star cluster
12
16
The Age of the Universe