Basic Physical Process:
Why so Important for Cosmology
Naoshi Sugiyama
Department of Physics, Nagoya University
Institute for Physics and Mathematics of the Universe, Univ.
Tokyo

• We have a program of Japanese government, Global
Center of Excellence Program (GCOE). This Global COE recruits graduate students. For those who are interested in doing their PhD work on particle physics, cosmology, astrophysics, please contact me! We are also planning to have a winter school in Feb. for dark matter and dark energy.
If you are interested, please contact me: naoshi@a.phys.nagoya-u.ac.jp
or visit http://www.gcoe.phys.nagoya-u.ac.jp/

• IPMU is a new truly international institute established in 2008.
• There are a number of post doc positions available every year.
• We are hiring faculties too.
• At least 30% of members have to be non-Japanese.
• Official language of this institute is English.

• Friedmann Equation
H
2 


 a  a 

 2

H
0
2


  m a
3

 r a
4


K a
2
 




H
0
: Hubble, a : scale factor, 0 denotes present a
0



 m
: matter,
 r
:
1 dark energy
: radiation,

K
: curvature
• redshift
1
 z
 a
0
/ a

1 / a

• Metric: Friedmann-Robertson-Walker ds
2   cdt
2  a
2


1
 dr
2
Kr
2
 r
2 d
 2


• Horizon Scale d
H
Physical
( a )
 a ( t )
 dt / a ( t )
 c / H ( a ) d
H comoving 
( a
0
/ a ) d
H
Physical

§
• What’s
C osmic M icrowave B ackground radiation?

Directly Brings Information at t=380,000, T=3000K
Fossil of the early Universe

Almost perfect Black Body
Evidence of Big Bang

Very Isotropic:

T/T

10
-5
Evidence of the Friedmann Universe

Information beyond Horizon
Evidence of Inflation

• Recombination
: almost of all free electrons were captured by protons, and formed hydrogen atoms
• Hereafter, photons could be freely traveled.
Before recombination, photons frequently scattered off electrons.
The universe became transparent!

photon helium
3min
Time
Multiple
Scattering
380Kyr.
transparent
１３ .
７ Gyr.
Photon transfer
Hydrogen atom
Temperature 1GK
Big Bang
3000 Ｋ 2.725K

• If the Universe was in the thermal equilibrium, photon distribution must be Planck distribution
(Black Body)
• Energy Density of Photons is
( 1
 z )
4

Horizon Size at recombination
• Here we assume matter dominant, a is the scale factor, H is the Hubble parameter.

Horizon Size at present
• Using the same formula in the previous page, but insert z=0, instead z=1100. Here we ignore a dark energy contribution in the Hubble parameter d
H
( t
0
)

180 (

M h
2
)

1 / 2
( 1100 )
1 / 2
Mpc

6000 (

M h
2
)

1 / 2
Mpc

Angular Size of the Horizon at z=1100
• Angular size of the Horizon at z=1100 on the Sky can be written as
  d
H c
( t rec
) / d
H
( t
0
)

0 .
030 rad

1 .
7 degree
C.f. angular size of the moon is 0.5 degree
1.7degree
d
H c (z=1100) d
H
(z=0)
There must not have any causal contact beyond Horizon
Same CMB temperature
Univ. should expand faster than speed of light

Horizon Problem

§
• As a first approximation, CMB is almost perfect
Black Body, and same temperature in any direction
(Isotropic)
• It turns out, deviation from isotropy, i.e., anisotropy contains rich information
• Two anisotropies
– Spectral Distortion
– Spatial Anisotropy

Extremely Good Black Body Shape in average
Observation by COBE/FIRAS y-distortion y < 1.5x10
-5 y
  dl n e

T kT e m e c
2
 -distortion |  | < 9x10 -5 f


8
 h c
3 exp
 h

3
 kT
 
1

• Caused by: Thermal electrons scatter off photons
• Photon distribution function: move low energy photons to higher energy lower higher
• distort Black Body low freq: lower temp high freq: higher temp no change: 220GHz frequency

f: photon distribution function
Energy Transfer: Kompaneets Equation y-parameter: k : Boltzmann Const, T e mass, n e
: electron temperature, m e
: electron number density,

T
Cross-section ,

: Optication depth
: electron
: Thomson Scattering

Solution of the equation f
PL
: Planck distribution low freq. limit: x<<1 high freq. limit: x>>1
 f / f
 
2 y
 f / f
 yx
2 decrement increment
 f / f =

T/T in low frequency limit (depend on the definition of the temperature)

• SZ Effect Provides Information of
– Thermal History of the Universe
– Thermal Plasma in the cluster of galaxies
Hot ionized gas in a cluster of galaxies
CMB
Photon
Q: typically, gas within a big cluster of galaxies is 100 million
K, and optical depth is 0.01. What are the values of y and temperature fluctuations (low frequency) we expect to have?

http://astro.uchicago.edu/sza/overview.html
•
Clusters provide SZ signal.
•
However, in total, the Universe is filled by CMB with almost perfect Planck distribution

wavelength[mm]
COBE/FIRAS
2.725K Planck distribution frequency[GHz]

• Direct Evidence of Big Bang
– Found in 1964 by Penzias & Wilson
– Very Precise Black Body by COBE in 1989 (J.Mather)
John Mather Arno Allan
Penzias
Robert
Woodrow
Wilson


1976: Dipole Anisotropy was discovered
3mK
 peculiar motion of the Solar System to the CMB rest frame
Annual motion of the earth is detected by COBE: the Final proof of heliocentrism

• Found by COBE/DMR in 1992 (G.Smoot), measured in detail by WMAP in 2003
• Structure at 380,000 yrs (z=1100)
– Recombination epoch of Hydrogen atoms
• Missing Link between Inflation (10 -36 s) and
Present (13.7 Billion yrs)
• Ideal Probe of Cosmological Parameters
– Typical Sizes of Fluctuation Patters are
Theoretically Known as Functions of Various
Cosmological Parameters

COBE 4yr data

COBE &
WMAP
George Smoot

Origin: Hector de Vega’s Lecture
• Quantum Fluctuations during the Inflation Era
10 -36 [s]
• 0-point vibrations of the vacuum generate inhomogeneity of the expansion rate, H
• Inhomogeneity of H translates into density fluctuations

Evolution
• Density fluctuations within photon-proton-electron plasma, in the expanding Universe
• Dark matters control gravity
 Photon :
Distribution function

Boltzmann Equation
 Proton-Electron
Fluid coupled with photons through Thomson Scattering

Euler Equation
 Dark Matter
Fluid coupled with others only through gravity

Euler Eq.

C
Boltzmann Equation
C: Scattering Term
Perturbed FRW Space-Time
Temperature Fluctuations
Optical Depth Anisotropic Stress

Fluid Components: dm dm dm dm
Proton-electron
Dark Matter

Numerically Solve Photon, Proton-Electron and dark matter System in the Expanding Universe
Boltzmann Code, e.g., CMBFAST, CAMB

Long Wave Mode
Scale Factor

Short Wave Mode
Scale Factor

§
Observables
1. Angular Power spectrum
– If fluctuations are Gaussian, Power spectrum (r.m.s.) contain all information
2. Phase Information
– Non-Gaussianity
– Global Topology of the Universe
3. Polarization
– Tensor (gravitational wave) mode
– Reionization (first star formation)

• C l

T/T(x)


• <| 
T/T(x)| 2 >=

(2 l +1)C l
/4
 d l (2 l +1)C l
/4

=

(d l/l ) l (2 l +1)C l
/4

• Therefore, logarithmic interval of the temperature power in l is l (2 l +1)C l
/4
 or often uses l ( l +1)C l
/2

• l corresponds to the angular size
 l =

/

=180

[(1 degree)/

]
C.f. COBE’s angular resolution is 7 degree, l<16
Horizon Size (1.7 degree) corresponds to l=110

Angular Scale
180 10 1 0.1
Horizon Scale at z=1100
(1.7degree)
COBE

Different Physical Processes had been working on different scales
• Gravitational Redshift on Large Scale
– Sachs-Wolfe Effect
• Acoustic Oscillations on Intermediate Scale
– Acoustic Peaks
• Diffusion Damping on Small Scale
– Silk Damping

Individual Process
(a) Gravitational Redshift : large scales

• Photon loses its energy when it climbs up the potential well : becomes redder
• Photon gets energy when it goes down the potential well : becomes bluer h h

-mgh= h

-(h

/c 2 )gh
= h

(1-gh/c 2 ) h
  h
 ’
Surface of the earth

Individual Process
(a) Gravitational Redshift : large scales
1)Lose energy when escape from gravitational potential
: Sachs-Wolfe redshift
 grav. potential at Last Scattering Surface
2)Get (lose) energy when grav. potential decays (grows)
: Integrated Sachs-Wolfe, Rees-Sciama

E=|

1
-

2
| blue-shift
2

1

Comments on Integrated Sachs-Wolfe Effect (ISW)
•
If the Universe is flat without dark energy
(Einstein-de Sitter Univ.), potential stays constant for linear fluctuations: No ISW effect
ISW probes curvature / dark energy
•
Curvature or dark energy can be only important in very late time for evolution of the Universe
Since late time=larger horizon size , ISW affects C l on very small l
’s
Late ISW
•
However, when the universe became matter domination from radiation domination, potential decayed! This epoch is near recombination contribution on l ~ 100-200 Early ISW

Early ISW (low matter density)
Late ISW(dark energy/curv)
No ISW, pure SW for flat no dark energy

(b) Acoustic Oscillation: intermediate scales
 scales smaller than sound horizon
Harmonic oscillation in gravitaional Potential

• Before Recombination, the Universe contained electrons, protons and photons (plasma) which are compressive fluid.
• The density fluctuations of compressive fluid are sound wave, i.e., Acoustic Oscillation .
Before Recombination, the Universe was filled be a sound of ionized.
Cosmic Symphony

(b) Acoustic Oscillation: intermediate scales
 scales smaller than sound horizon
Harmonic oscil. in grav. potential analogy balls & springs in the well: balls’mass 
B h
2
1) set at initial location = initial cond.
hold them until sound horizon cross
2) oscillate after sound horizon crossing
3) at Last Scatt. Surface ( LSS ), climb up potential well
 long wave length > sound horizon stay at initial location until LSS

Pure Sachs-Wolfe

First Compress.
(depress.) at LSS
 first (second) peak

Sound Horizon diffusion
Long Wave Length
Intermediate Wave Length
Very Early Epoch
All modes are outside the Horizon
Short Wave Length

Sound Horizon diffusion
Long Wave Length
Intermediate Wave Length
Start Acoustic Oscillation
Short Wave Length

Long Wave Length
Start Acoustic Oscillation
Intermediate Wave Length
Diffusion Damping: Erase!
Short Wave Length

Conserve Initial
Fluctuations
Long Wave Length
Acoustic Oscillation
Intermediate Wave Length
Recombination
Epoch Diffusion Damping: Erase!
Short Wave Length

• Sound Horizon: d s c (z=1100)= (c s
/c)d
H c (z=1100)
• Distance: Horizon Scale d
H d s d
H

• baryon density
 b
=(1+z) 3

B
 c
=1.88h
2

10 -29 (1+z) 3

B g/cm 3
• Photon density


=4.63

10 -34 (1+z) 4 g/cm 3

• Here we take 
B h 2 =0.02
Question: Calculate angular size of the sound horizon at recombination, and corresponding l .

Angular Scale
180 10 1 0.1
COBE
Sound Horizon z=1100 higher harmonics

Solution of the Boltzmann equation
 k
( t )


 
A sin(
A sin( c s k c s k
Physical t )

)

B

B cos( c s k cos( c s k

)
Physical t )
 dt / a ( t )
 d
H comoving
/ c c s k
 
1 k ( c s
/ c ) d
H comoving comoving kd
Sound

1

1

(c) Diffusion damping: small scales
(Silk Damping) caused by photon’s random walk
Number of photon scattering per unit time
Mean Free Path
N is the number of scattering during cosmic time.
Cosmic time is 2/H for matter dominated universe
Diffusion of random walk

Comoving diffusion scale (physical

(1+z))
At recombination
The corresponding angular scale and l are l d

180 ( 1 degree/

)

1700
Here, assume

B h
2 
0 .
02 ,

M h
2 
0 .
15

Angular Scale
180 10 1 0.1
Diffusion scale at z=1100 (l=1700)
COBE

Acoustic Oscillations
Late ISW for dark energy
COBE
Gravitaional Redshift
(Sachs-Wolfe)
Early ISW
Diffusion damping
Large 10 ° 1 ° 10mi n
Small

• Initial Condition of Fluctuations
– If Power law, its index n (P(k)  k n )
– Adiabatic vs Isocurvature
• Sound Velocity at Recombination
– Baryon Density: 
B h 2
• Radiation component at recombination modifies Horizon Size and generates early ISW
– Matter Density: 
M h 2
• Radiative Transfer between Recombination and
Present
– Space Curvature: 
K

• Initial Condition of Fluctuations
– If Power law, its index n (P(k)  k n )
– Adiabatic vs Isocurvature
• Sound Velocity at Recombination
– Baryon Density: 
B h 2
• Radiation component at recombination modifies Horizon Size and generates early ISW
– Matter Density: 
M h 2
• Radiative Transfer between Recombination and
Present
– Space Curvature: 
K

Adiabatic vs Isocurvature
• Adiabatic corresponds to

T/T(k,

)=B cos (kc s

)
• Isocurvature corresponds to

T/T(k,

)=A sin (kc s

)

• Initial Condition of Fluctuations
– If Power law, its index n (P(k)  k n )
– Adiabatic vs Isocurvature
• Sound Velocity at Recombination
– Baryon Density: 
B h 2
• Radiation component at recombination modifies Horizon Size and generates early ISW
– Matter Density: 
M h 2
• Radiative Transfer between Recombination and
Present
– Space Curvature: 
K

• If
C s becomes smaller, i.e.,
 b

B h 2 becomes larger, balls are heavier (or spring becomes weaker) in our analogy of acoustic oscillation.
• Heavier balls lead to larger oscillation amplitude for compressive modes (but not rarefaction modes).

M

B h 2 large large small small

• Initial Condition of Fluctuations
– If Power law, its index n (P(k)  k n )
– Adiabatic vs Isocurvature
• Sound Velocity at Recombination
– Baryon Density: 
B h 2
• Radiation component at recombination modifies Horizon Size and generates early ISW
– Matter Density: 
M h 2
• Radiative Transfer between Recombination and
Present
– Space Curvature: 
K

• Here we assume matter dominant.
In reality,
H
2 
H
0
2



M a
3


R a
4


Larger

R h 2 or smaller

B h 2 makes the horizon size smaller
Shift the peak to smaller scale i.e., larger l

• Larger 
R h 2 or smaller

B h 2 shifts the matter domination to the later epoch
• Early ISW: decay of gravitational potential when matter and radiation densities are equal
More Early ISW on larger scale i.e., smaller l

M
Early ISW small

M h 2 large

• Initial Condition of Fluctuations
– If Power law, its index n (P(k)  k n )
– Adiabatic vs Isocurvature
• Sound Velocity at Recombination
– Baryon Density: 
B h 2
• Radiation component at recombination modifies Horizon Size and generates early ISW
– Matter Density: 
M h 2
• Radiative Transfer between Recombination and
Present
– Space Curvature: 
K

Radiative Transfer: depend on the curvature
Flat
Observer
Horizon Distance
Observe Apparent Size

Space Curvature=Lens
Radiative Transfer: depend on the curvature
Flat, 0 Curvature
Observer

Space Curvature=Lens
Radiative Transfer: depend on the curvature
Positive Curvature
Observer
Magnify!

Space Curvature=Lens
Radiative Transfer: depend on the curvature
Negative Curvature
Observer
Shrink!

Projection from LSS to l
[i] flat

=1
[ii]

&

<1: Further LSS
[iii] open

<1: Geodesic effect large large l l

 smaller
 pushes peaks to smaller
 pushes peakes to

More Negatively
Curved


• After recombination, the universe is really transparent?
• Answer: NO!
It is known z<6, the inter-galactic gases are ionized from observations

Free Electrons
• Stars and AGN (quasars) produced ionized photons, E>13.6eV
The Universe gets partially Clouded!

Define Optical Depth of Thomson Scattering as
   dt n e

T
Temperature Fluctuations are Damped as

T / T



T / T
NoDamping

 e
 
 can be a probe of the epoch of reionization
(first star formation).
(Polarization is very important clue for reionization)

Recombination
400,000yr
Big Bang
13.7Byr.
Ionized gas
Scattering at recombination

Recombination
Ionized Gas
Big Bang
Ionized gas
Star Formation
Some photons last scattered at the late epoch
Temperature Fluctuations Damped away on the scale smaller than the horizon at reionizatoion

N.S., Silk, Vittorio, ApJL (1993), 419, L1

For Example
• Number of Neutrino Species (light particle species)
• Time Variation of Fundamental Constants such as
G, c,

(Fine Structure Constant)

Number of Massless Neutrino Family
If neutrino masses < 0.1eV, neutrinos are massless until the recombination epoch
Let us increase the number of massless species
Shifts the matter-radiation equality epoch later
More Early Integrated ISW
• Peak heights become higher
• Peak locations shift to smaller scales, i.e., larger l

Measure the family number at z=1000

Time Variation of Fundamental Constants
Varying
 and CMB anisotropies
Battye et al. PRD 63 (2001) 043505
QSO absorption lines:
 
[

(t
20bilion yr
)-

(t
0
)]/

(t
0
) = -0.72
± 0.18

10 -5

QSO absorption line

= -0.72
± 0.18

10 -5
0.5 < z < 3.5
Webb et al.

Influence on CMB
Thomson Scattering: d

/dt
 x e n e

T

: optical depth, x e
: ionization fraction n e
: total electron density,

T
: cross section

If
 is changed
1)

T

2 is changed
2) Temperature dependence of x e i.e., temperature dependence of recombination preocess is modified
For example, 13.6eV =

2 m e c 2 /2 is changed!
If
 was smaller, recombination became later
If

= ± 5%,
 z~100

Flat,

M
=0.3, h=0.65,

B h 2 =0.019
Ionization fraction

=-0.05

=0.05


=0.05

=-0.05
Temperature Fluctuation
Peaks shift to smaller l for smaller
 since the Universe was larger at recombination

Varying G and CMB anisotropies
• Brans-Dicke / Scalar-Tensor Theory
G

1/

(scalar filed)
: G may be smaller in the early epoch
• Stringent Constraint from Solar-system
: must be very close to General Relativity
BUT, it’s not necessarily the case in the early universe

G
0
/G

If G was larger in the early universe, the horizon scale became smaller c/H = c

(3/8

G

)
Peaks shift to larger l

Nagata, Chiba, N.S.
larger G

We have hope to determine cosmological parameters together with the values of fundamental quantities, i.e.,

, G and the nature of elementary particles at the recombination epoch by measuring CMB anisotropies

• Values of the Cosmological Parameters
– 
M h 2
– 
B h 2
– h
– Curvature 
K
– Initial Power Spectral Index n
• Amount of massless and massive particles
• Fundamental Physical Parameters
Bayesian analysis
Markov chain Monte Carlo (MCMC)
Comparison with Observations and set constraints

• increase 
B h 2
 higher peak, decrease

M h 2
 higher peak. How do you distinguish these two effects?
For that, calculate l ( l +1)C
 l
/2

M to 0.03, and find the value of
 for
M

B h 2 =0.02 and h 2 =0.15 (fiducial model). Then increase

B h 2 h 2 which provides the same first peak height as the fiducial model.
And compare the resultant l ( l +1)C l
/2
 with the fiducial model. h=0.7, n=1. flat, no dark energy

• Gaussian v.s. Non-Gaussian
– If Gaussian, angular power spectrum contains all information
– Inflation generally predicts only small non-Gaussianity due to the second order effect
• Rare Cold or Hot Spot?
• Global Topology of the Universe

 Fluctuations generated during the inflation epoch
 Quantum Origin
 Gaussian as a first approximation

(x)

(

(x)-

)/

0 
(x)

• In real space
– Skewness
– Kurtosis

• In Fourier Space
– Bispectrum
Fourier Transfer of 3 point correlation function
In case of the temperature angular spectrum,
Wigner 3-j symbol
– Trispectrum

• If Gaussian, Bispectrum must be zero
• Depending upon the shape of the triangle, it describes different nature
– Local
– Equilateral

Three torus universe
Circle in the sky

CMB sky in a flat three torus universe
Cornish & Spergel PRD62 (2000)087304

• Values of the Cosmological Parameters
– 
M h 2
– 
– h
B h 2
– Curvature
K
– Initial Power Spectral Index n
• Amount of massless and massive particles
• Fundamental Physical Parameters
Bayesian analysis
Markov chain Monte Carlo (MCMC)
Comparison with Observations and set constraints

Efstathiou and Bond
 Identical baryon and CDM density:

B h
2
,

M h
2
 Identical primordial
Degenerate contour fluctuation spectra
 Identical Angular
Diameter R (


,

K
)
 m
= 1-

K
-


= 0
Should Give Identical
Power Spectrum close to the flat geometry
BUT not quite!
flat

Projection from LSS to l
[i] flat

=1
[ii]

&

<1: Further LSS
[iii] open

<1: Geodesic effect large large l l

 smaller
 pushes peaks to smaller
 pushes peakes to

Almost degenerate models
For same value of R

Degenerate line h=0.5

What we can determine from CMB power spectrum is

B
2
 m
2
Difficult to measure curvature itself and


,
 m
,

B directly
Question: Generate C l
’s on this degenerate line for

M
=0.3, 0.5, 0.6 and make sure they are degenerate.

 COBE
 Clearly see large scale (low l ) tail
 angular resolution was too bad to resolve peaks
 Balloon borne/Grand Base experiments
 Boomerang, MAXMA, CBI, Saskatoon, Python,
OVRO, etc
 See some evidence of the first peak, even in Last
Century!
 WMAP

CMB observations by 1999

COBE &
WMAP

WMAP
Observation
3 yr
1 st yr

WMAP Temperature Power Spectrum
• Clear existence of large scale Plateau
• Clear existence of Acoustic Peaks (up to 2 nd or 3 rd )
• 3 rd Peak has been seen by 3 yr data
Consistent with
Inflation and Cold Dark Matter Paradigm
One Puzzle:
Unexpectedly low Quadrupole ( l =2)






B h 2 =0.02229

0.00073 (3% error!)

M h 2 =0.128

0.008

K
=0.014

0.017 (with H=72

8km/s/Mpc) n=0.958

0.016
Spergel et al.
WMAP 3yr alone
Dark Energy
76%
Dark Matter
20%
Baryon 4%






B h 2 =0.02273

0.00062

M h 2 =0.1326

0.0063


=0.742

0.030 (with BAO+SN, 0.72) n=0.963

0.015
Komatsu et al.
WMAP 5yr alone
Dark Energy
72%
Dark Matter
23%
Baryon 4.6%


But…
 72% of total energy/density is unknown: Dark
Energy
 23% of total energy/density is unknown: Dark
Matter
Dark Energy is perhaps a final piece of the puzzle for cosmology equivalent to Higgs for particle physics

 How do we determine


=0.76 or 0.72?
Subtraction!:


= 1-

M
-

K
Q: Can CMB provide a direct probe of
Dark Energy?

 CMB can be a unique probe of dark energy
 Temperature Fluctuations are generated by the growth (decay) of the Large Scale Structure (z~1)

1
Integrated Sachs-Wolfe Effect
Photon gets blue

2
Shift due to decay
E=|

1
-

2
|
Gravitational Potential of Structure decays due to Dark Energy

 Integrated Sachs-Wolfe Effect (ISW)
 Induced by large scale structure formation
 Unique Probe of dark energy: dark energy slows down the growth of structure formation
 Not dominant, hidden within primordial fluctuations generated during the inflation epoch
Cross-Correlation between CMB and Large Scale
Structure
Only pick up ISW (induced by structure formation)

w=-0.5
w=-1 w=-2
Various Samples of
CMB-LSS Cross-Correlation as a function of redshift
Measure w!
Less
Than
10min

 Weak lensing
 Distortion of shapes of galaxies due to the gravitational field of structure
 Can extend to small scales
Non-Linear evolution of structure formation on small scales
 evolution is more rapid than linear evolution
 rapid evolution makes potential well deeper
 deeper potential well: redshift of CMB


1
Nonlinear Integrated Sachs-Wolfe Effect
Rees-Siama Effect
Photon redshifted

2 due to growth
E=|

1
-

2
|
Gravitational Potential of Structure evolves due to non-linear effect
Large Scale: Blue-Shift

Correlated with Lens
Small Scale: Red-Shift

Anti-Correlated

Nishizawa, Komatsu, Yoshida, Takahashi, NS 08
Cross-Correlation between CMB & Lensing


=0 .95,
0.8,
0.74,
0.65,
0.5,
0.35,
0.2,
0.05,
 positive negative

10 100 1000 10000 l

Future experiments (CMB & Large Scale
Structure) will reveal the dark energy!

 Properties of Neutrinos
 Numbers of Neutrinos
 Masses of Neutrinos
 Fundamental Physical Constants
 Fine Structure Constant
 Gravitational Constant

Neutrino Numbers N eff and mass m

 Change N eff or m
 modifies the peak heights and locations of CMB spectrum.

CMB Angular Power Spectrum
Theoretical Prediction
Measure the family number at z=1000

For Neutrino Mass, CMB with Large Scale
Structure Data provide stringent limit since
Neutrino Components prevent galaxy scale structure to be formed due to their kinetic energy

Cold Dark Matter Neutrino as Dark Matter
(Hot Dark Matter)
Numerical Simulation


eff
WMAP 3yr Data paper by Spergel et al.
WMAP 5yr Data paper by Komatsu et al.
 m

N


1 .
5 eV(95%CL)

0.66eV(95% CL)

4 .
4

1 .
5 ( 68 % CL)
WMAP alone
WMAP+SDSS(BAO)+SN
WMAP+BAO+SN+HST

Fine Structure Constant



There are debates whether one has seen variation of
 in QSO absorption lines
Time variation of
 affects on recombination process and scattering between CMB photons and electrons
 WMAP 3yr data set:
-0.039<

/

<0.010 (by P.Stefanescu 2007)

Gravitational Constant G
 G can couple with Scalar Field (c.f. Super
String motivated theory)
 Alternative Gravity theory: Brans-Dicke
/Scalar-Tensor Theory
 G

1/

(scalar filed)

 G may be smaller in the early epoch
WMAP data set constrain: |

G/G|<0.05 (2

)
(
Nagata, Chiba, N.S.)

 Power Spectrum is OK
 How about more detailed structure
 Alignment of low multipoles
 Non-Gaussianity
 Cold Spot
 Axis of Evil

Tegmark et al.
• Cleaned Map (different treatment of foreground)
• Contribution from Galactic plane is significant
& obtain slightly larger quadrupole moment.
• alignment of quadrupole and octopole towards VIRGO?

 Fluctuations generated during the inflation epoch
 Quantum Origin
 Gaussian as a first approximation

(x)

(

(x)-

)/

0 
(x)



=

Linear
+ f
NL
(

Linear
) 2

Linear
=O(10 -5 ), non-Gaussianity is tiny!
Amplitude f
NL depends on inflation model
[quadratic potential provides f
NL
=O(10 -2 )]

Very Tiny Effect:
Fancy analysis (Bispectrum etc) starts to reveal non-Gaussianity?
First “Detection” in WMAP CMB map
Komatsu et al. WMAP 5 yr.

 Using Wavelet analysis for skewness and kurtosis, Santander people found cold spots
Kurtosis Coefficient Only 3-sigma away

This cold spot might be induced by a Super-Void due to ISW since Rudnick et al. claimed to find a dip in NVSS radio galaxy number counts in the Cold Spot.
Super Void: One Billion light yr size
Typical Void: *10 Million light yr size

 PLANCK is coming soon:
 More Frequency Coverage
 Better Angular Resolution
 Other Experiments
 Ongoing Ground-based:
 CAPMAP, CBI, DASI, KuPID, Polatron
 Upcoming Ground-based:
 AMiBA, BICEP, PolarBear, QUEST, CLOVER
 Balloon:
 Archeops, BOOMERanG, MAXIPOL
 Space:
 Inflation Probe

WMAP Frequency
WMAP Frequency Bands
Microwave Band
Frequency (GHz)
Wavelength (mm)
K Ka Q V W
22 30 40 60 90
13.6 10.0 7.5
5.0
3.3
WMAP Angular Resolution
Frequency 22 GHz 30 GHz 40 GHz 60 GHz 90 GHz
FWHM, degrees
0.93
0.68
0.53
0.35
<0.23

More Frequencies and better angular resolution

 More Frequency Coverage
 Better Estimation of Foreground Emission (Dust,
Synchrotron etc)
 Sensitivity to the SZ Effect
 Better Angular Resolution
 Go beyond the third peak, and even reach Silk
Damping: Much Better Estimation of Cosmological
Parameters, and sensitivity to the secondary effect.
 Polarization
 Gravitational Wave: Probe Inflation
 Reionization: First Star Formation

Polarization
Scattering & CMB quadrupole anisotropies produce linear polarization
Polarization must exist, because Big Bang existed!
Scattering off photons by Ionized medium velocity induce polarization: phase is different from temperature fluct.
• Information of last scattering
Thermal history of the universe, reionization
• Cosmological Parameters
• type of perturbations: scalar, vector, or tensor

Incoming
Electro-Magnetic
Field
Same Flux
No-Preferred
Direction
UnPolarized
Same
Flux
Electron scattering
Homogeneously Distributed Photons

Incoming
Electro-Magnetic
Field
Weak Flux
Preferred
Direction
Polarized
Strong
Flux
Electron scattering
Photon Distributions with the Quadrupole Pattern

Power spectrum
Velocity= polarization
Wave number
Hu &
White

Scalar
Component

Reionization
Liu et al. ApJ 561 (2001) First Order Effect

E-mode
2 independent parity modes
B-mode
Seljak

E-mode
Scalar Perturbations only produce E-mode
Seljak

Tensor perturbations produce both E- and B- modes
B-mode

Scalar
Component

Tensor
Component
Hu & White

Polarization is the ideal probe for the tensor (gravity wave ) mode
Tensor mode is expected from many inflation models
Consistency Relation
・ Tensor Amplitude/Scalar Amplitude
・ Tensor Spectral index
・ Scalar Spectral Index
You can prove the existence of Inflation!

• PLANCK has been launched!
Higher Angular Resolution, Polarization
• More to Come from grand based and balloon borne Polarization Experiments