Naoshi Sugiyama- Cosmic Microwave Background Basic Physical Process: Why so important for cosmology

Cosmic Microwave Background Cosmic Microwave Background Basic Physical Process:

Why so Important for Cosmology

Naoshi SugiyamaNaoshi SugiyamaDepartment of Physics, Nagoya University

Institute for Physics and Mathematics of the Universe, Univ. Tokyo

Before Start!GCOE @ Nagoya U.

• 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:

[email protected]

or visit

http://www.gcoe.phys.nagoya-u.ac.jp/

Institute for Physics and Mathematics of the Universe

• 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.

Basic Equations and Notations• Friedmann Equation

• redshift

2

K4r

3m2

22

0

aaaH

a

aH

energydark :

curvature: radiation,: matter,:

1

present denotes 0 factor, scale: Hubble,:

Krm

0

0

a

aH

aaaz /1/1 0

Basic Equations and Notations

• Metric: Friedmann-Robertson-Walker

• Horizon Scale

PhysicalH

comovingH

PhysicalH

daad

aHctadttaad

)/(

)(/)(/)()(

0

22

2

2222

1dr

Kr

dracdtds

§1. Introduction• What’s Cosmic Microwave Background 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

What happened at t=380,000yr

• 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!The universe became transparent!

TemperatureTemperature 　　 1GK1GK 　　　　　　　　　 　　　　　　　　　 30003000 Ｋ　　Ｋ　　　　　　　　　　 2.725K2.725K 　　　　　　　　　　

Multiple Scattering

photonphoton

Big BangBig Bang

１３ . ７ Gyr.Time3min 380Kyr.

helium

Big B

ang

Nucleo -

Synthesis

Recom

bination

Hydrogen atom

Photon transfer

transparent

Cosmic Microwave Background

• If the Universe was in the thermal equilibrium, photon distribution must be Planck distribution (Black Body)

• Energy Density of Photons is

4)1( z

Why Information beyond Horizon?

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

Horizon Size at recombination

• 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

Mpc)(6000

Mpc)1100()(180)(2/12

2/12/120

h

htd

M

MH

Horizon Size at present

• Angular size of the Horizon at z=1100 on the Sky can be written as

degree7.1rad030.0)(/)( 0 tdtd Hrecc

HC.f. angular size of the moon is 0.5 degree

dHc(z=1100)

dH(z=0)

1.7degree

There must not have any causal contact beyond HorizonSame CMB temperature

Univ. should expand faster than speed of light

Angular Size of the Horizon at z=1100

Horizon Problem

Inflation

§2. Anisotropies

• 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

2cm

kTndly

e

eTe

1exp

8 3

3

kThc

hf

Extremely Good Black Body Shape in average

Observation by COBE/FIRAS

2-1. Spectral Distortion

y-distortion y < 1.5x10y < 1.5x10-5-5

-distortion ||| < 9x10| < 9x10-5-5

Sunyaev-Zeldovich Effecty-distortion

• Caused by: Thermal electrons scatter off photons

• Photon distribution function: move low energy photons to higher energy

frequency

Distribution function

• distort Black Body low freq: lower temp high freq: higher temp no change: 220GHz

higher higher lower lower

SZ Effectf: photon distribution function

Energy Transfer: Kompaneets Equation

y-parameter:

k: Boltzmann Const, Te: electron temperature, me: electron mass, ne: electron number density, T: Thomson Scattering Cross-section , : Optication depth

Solution of the equation

low freq. limit: x<<1high freq. limit: x>>1

fPL: Planck distribution

yff 2/ 2/ yxff

decrementincrement

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

CMBPhoton

Hot ionized gas in a

cluster of galaxies

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

200 sigma error-bars

COBE/FIRAS

wavelength[mm]

frequency[GHz]

inte

nsit

y[M

Jy/s

tr]

2.725K Planck distribution

Cosmic Microwave Background

• 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

2-2. Spatial Anisotropies 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

Primordial Temperature Fluctuations of Cosmic Microwave Background• 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 (10-36s) 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

Temperature Anisotropies:Origin and Evolution

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

Temperature Anisotropies:Origin and Evolution

Evolution

• Density fluctuations within photon-proton-electron plasma, in the expanding Universe

• Dark matters control gravityPhoton:

Distribution function Boltzmann EquationProton-Electron

Fluid coupled with photons through Thomson Scattering Euler Equation

Dark MatterFluid coupled with others only through gravity Euler Eq.

Boltzmann EquationC: Scattering Term

Perturbed FRW Space-Time

Temperature Fluctuations

Optical Depth Anisotropic Stress

C

Fluid Components:

Proton-electron

Dark Matterdm dm

dmdm

Numerically Solve Photon, Proton-Electron and dark matter System in the Expanding Universe

Boltzmann Code, e.g., CMBFAST, CAMB

Scale Factor

Flu

ctua

tion

s

Long Wave Mode

Scale Factor

Flu

ctua

tion

s

Short Wave Mode

§3. What can we learn from spatial anisotropies?

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)

3-1. Angular Power Spectrum• Cl

T/T(x)

Angular Power Spectrum• <|T/T(x)|2>=(2l+1)Cl/4dl (2l+1)Cl/4

= (dl/l) l(2l+1)Cl/4• Therefore, logarithmic interval of the temperature power in

l is l(2l+1)Cl/4 or often uses

• 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

l(l+1)Cl/2

COBE

180 10 1 0.1Angular Scale

Horizon Scale at z=1100(1.7degree)

Different Physical Processes had been working on different scalesDifferent Physical Processes had been working on different scales

3-2. Physical Process

• 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 RedshiftGravitational Redshift: large scales

What is the gravitational redshift?

• 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

Surface of the earth

h

h-mgh= h-(h /c2)gh = h(1-gh/c2) h’h

1)Lose energy when escape from gravitational potential : Sachs-Wolfe redshift

grav. potential at Last Scattering Surface

12

2)Get (lose) energy when grav. potential decays (grows)

: Integrated Sachs-Wolfe, Rees-Sciama

E=|1-2| blue-shift

Individual Process

(a) Gravitational RedshiftGravitational Redshift: large scales

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 Cl on very small l’s

•However, when the universe became matter domination from radiation domination, potential decayed! This epoch is near recombination

contribution on l ~ 100-200 Early ISWEarly ISW

Late ISWLate ISW

Late ISW(dark energy/curv)

No ISW, pure SW for flat no dark energy

Early ISW (low matter density)

(b) Acoustic Oscillation:(b) Acoustic Oscillation: intermediate scales

scales smaller than sound horizonsound horizon

Harmonic oscillation in gravitaional Potential Harmonic oscillation in gravitaional Potential

Why Acoustic Oscillation?

• 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 SymphonyCosmic Symphony

3) at Last Scatt. Surface (LSSLSS), climb up potential well

2) oscillate after sound horizon crossing

long wave length > sound horizon stay at initial location until LSS Pure Sachs-Wolfe

First Compress.(depress.) at LSSfirst (second) peak

(b) Acoustic Oscillation:(b) Acoustic Oscillation: intermediate scales

scales smaller than sound horizonsound horizon

Harmonic oscil. in grav. potential Harmonic oscil. in grav. potential

analogy balls & springs in the well: balls’mass Bh2

1) set at initial location = initial cond. hold them until sound horizon cross

Long Wave Length

Intermediate Wave Length

Short Wave Length

Sound Horizon

diffusion

All modes are outside the HorizonAll modes are outside the Horizon

Very Early Epoch

Long Wave Length

Intermediate Wave Length

Short Wave Length

diffusion

Start Acoustic OscillationStart Acoustic Oscillation

Sound Horizon

Long Wave Length

Intermediate Wave Length

Short Wave LengthDiffusion Damping: Erase!Diffusion Damping: Erase!

Start Acoustic OscillationStart Acoustic Oscillation

Long Wave Length

Intermediate Wave Length

Short Wave LengthDiffusion Damping: Erase!Diffusion Damping: Erase!

Acoustic OscillationAcoustic Oscillation

RecombinationEpoch

Conserve Initial FluctuationsConserve Initial Fluctuations

Peak Locations-Projection of Sound Horizon-

• Sound Horizon: dsc (z=1100)= (cs/c)dH

c (z=1100)

• Distance: Horizon Scale dH

ds

dH

Sound velocity at recombination

• baryon density

b=(1+z)3Bc=1.88h210-29(1+z)3B g/cm3

• Photon density

=4.6310-34(1+z)4g/cm3

Sound Horizon Size at recombination

• Here we take Bh2=0.02

Question: Calculate angular size of the sound horizon at recombination, and corresponding l.

COBE

180 10 1 0.1Angular Scale

Sound Horizon z=1100 higher harmonics

Solution of the Boltzmann equation

cdtadt

kcBkcA

tkcBtkcAt

comovingH

ss

Physicals

Physicalsk

/)(/

)cos()sin(

)cos()sin()(

1

1)/(

1

comovingSound

comovingHs

s

kd

dcck

kc

(c) Diffusion damping:(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

1700)degree/1(180 dl

15.0,02.0 22 hh MBHere, assume

COBE

180 10 1 0.1Angular Scale

Diffusion scale at z=1100 (l=1700)

10° 1° 10min

Large Small

Gravitaional Redshift (Sachs-Wolfe)

Acoustic Oscillations

Diffusion damping

COBE

Early ISW

Late ISW for dark energy

3-3. What control Angular Spectrum• Initial Condition of Fluctuations

– If Power law, its index n (P(k)kn)– Adiabatic vs Isocurvature

• Sound Velocity at Recombination– Baryon Density: Bh2

• Radiation component at recombination

modifies Horizon Size and generates early ISW– Matter Density: Mh2

• Radiative Transfer between Recombination and Present– Space Curvature: K

3-3. What control Angular Spectrum• Initial Condition of Fluctuations

– If Power law, its index n (P(k)kn)– Adiabatic vs Isocurvature

• Sound Velocity at Recombination– Baryon Density: Bh2

• Radiation component at recombination

modifies Horizon Size and generates early ISW– Matter Density: Mh2

• Radiative Transfer between Recombination and Present– Space Curvature: K

Initial Condition

Adiabatic vs Isocurvature

• Adiabatic corresponds to

T/T(k, )=Bcos cos (kcs)

• Isocurvature corresponds to

T/T(k, )=Asinsin(kcs)

3-3. What control Angular Spectrum• Initial Condition of Fluctuations

– If Power law, its index n (P(k)kn)– Adiabatic vs Isocurvature

• Sound Velocity at Recombination– Baryon Density: Bh2

• Radiation component at recombination

modifies Horizon Size and generates early ISW– Matter Density: Mh2

• Radiative Transfer between Recombination and Present– Space Curvature: K

Sound velocity at recombination

• If Cs becomes smaller, i.e., bBh2 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).

BBhh22

small

large

large

small

M

3-3. What control Angular Spectrum• Initial Condition of Fluctuations

– If Power law, its index n (P(k)kn)– Adiabatic vs Isocurvature

• Sound Velocity at Recombination– Baryon Density: Bh2

• Radiation component at recombination

modifies Horizon Size and generates early ISW– Matter Density: Mh2

• Radiative Transfer between Recombination and Present– Space Curvature: K

Horizon Size at recombination

• Here we assume matter dominant.

In reality,

43

20

2

aaHH RM

Larger Rh2 or smaller Bh2 makes the horizon size smaller

Shift the peak to smaller scale i.e., larger l

Early ISW effect

• Larger Rh2 or smaller Bh2 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

MMhh22small

large

M

Early ISW

3-3. What control Angular Spectrum• Initial Condition of Fluctuations

– If Power law, its index n (P(k)kn)– Adiabatic vs Isocurvature

• Sound Velocity at Recombination– Baryon Density: Bh2

• Radiation component at recombination

modifies Horizon Size and generates early ISW– Matter Density: Mh2

• Radiative Transfer between Recombination and Present– Space Curvature: K

Observer

Radiative Transfer:

depend on the curvature

Flat

Horizon DistanceObserve Apparent SizeObserve Apparent Size

Observer

Radiative Transfer:

depend on the curvature

Flat, 0 Curvature

Space Curvature=LensSpace Curvature=Lens

Observer

Positive Curvature

Magnify!

Radiative Transfer:

depend on the curvature

Space Curvature=LensSpace Curvature=Lens

Observer

Negative Curvature

Shrink!

Radiative Transfer:

depend on the curvature

Space Curvature=LensSpace Curvature=Lens

Projection from LSS to l

[iii] open <1: Geodesic effect

smaller pushes peakes to

large l

[ii] & <1: Further LSS

smaller pushes peaks to

large l

[i] flat =1

More Negatively Curved

Optical Depth • 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!

Tendt Define Optical Depth of Thomson Scattering as

Temperature Fluctuations are Damped as

e // NoDampingTTTT

can be a probe of the epoch of reionization (first star formation).

(Polarization is very important clue for reionization)

Recombination400,000yr

Big Bang 13.7Byr.

Ionized gas

Scattering at recombination Scattering at recombination

Recombination

Big Bang

Star Formation

Ionized Gas Ionized gas

Some photons last scattered at the late epoch Some photons last scattered at the late epoch

Temperature Fluctuations Damped away on the Temperature Fluctuations Damped away on the scale smaller than the horizon at reionizatoionscale smaller than the horizon at reionizatoion

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

What else can CMB anisotropies be sensitive?

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 FamilyNumber 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

• Peak heights become higher

• Peak locations shift to smaller scales, i.e., larger l

More Early Integrated ISWMore Early Integrated ISW

Measure the family number at z=1000

Varying Varying and CMB anisotropies and CMB anisotropies Battye et al. PRD 63 (2001) 043505

QSO absorption lines:

[[(t(t20bilion yr20bilion yr)- )- (t(t00)]/ )]/ (t(t00) = -0.72±0.18) = -0.72±0.181010-5-5

Time Variation of Fundamental ConstantsTime Variation of Fundamental Constants

= -0.72±0.1810-5

0.5 < z < 3.5

QSO absorption line

Webb et al.

Influence on CMB

Thomson Scattering:

d/dtxeneT

: optical depth, xe: ionization fraction

ne: total electron density, T: cross section

If is changed

1) T2 is changed

2) Temperature dependence of xe i.e., temperature

dependence of recombination preocess is modified

For example, 13.6eV = 2mec2/2 is changed!

If If was smaller, recombination became later was smaller, recombination became later

If If =±5%, =±5%, z~100z~100

=0.05

=-0.05

Flat, M=0.3, h=0.65, Bh2=0.019

Ionization fraction

Temperature Fluctuation

Peaks shift to smaller l for smaller since the Universe was larger at recombination

=0.05

=-0.05

Varying Varying G G and CMB anisotropiesand CMB anisotropies

• Brans-Dicke / Scalar-Tensor Theory

G 1/ (scalar filed)

: G may be smaller in the early epoch

BUT, it’s not necessarily the case

in the early universe

• Stringent Constraint from Solar-system

: must be very close to General Relativity

GG00/G/G

If G was larger in the early universe,

the horizon scale became smaller

c/H = c(3/8G)

Peaks shift to larger Peaks shift to larger ll

Nagata, Chiba, N.S.

larger G

We have hope to determine We have hope to determine

cosmological parameters together with cosmological parameters together with

the values of fundamental quantities, the values of fundamental quantities,

i.e., i.e., , , G G

and the nature of elementary particles and the nature of elementary particles

at the recombination epoch at the recombination epoch

by measuring CMB anisotropies by measuring CMB anisotropies

Angular Power Spectrum is sensitive to

• Values of the Cosmological Parameters Mh2

Bh2

– h

– Curvature K

– Initial Power Spectral Index n

• Amount of massless and massive particles

• Fundamental Physical Parameters

Comparison with Observations and set constraints

Bayesian analysisMarkov chain Monte Carlo (MCMC)

Question

• increase Bh2 higher peak, decrease Mh2 higher peak. How do you distinguish these two effects?

For that, calculate l(l+1)Cl /2 for Bh2=0.02 and Mh2 =0.15 (fiducial model). Then increase Bh2 to 0.03, and find the value of Mh2 which provides the same first peak height as the fiducial model. And compare the resultant l(l+1)Cl /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

3-4. Beyond Power Spectrum: Phase

Non-GaussianityNon-Gaussianity

Fluctuations generated during the inflation Fluctuations generated during the inflation epochepoch Quantum OriginQuantum Origin Gaussian as a first approximationGaussian as a first approximation

(x)(x)(((x)-(x)-)/)/

(x)0

How to quantify non-Gaussianity

• In real space– Skewness

– Kurtosis

How to quantify non-Gaussianity• In Fourier Space

– Bispectrum

Fourier Transfer of 3 point

correlation function

In case of the temperature angular spectrum,

– Trispectrum

Wigner 3-j symbol

Bispectrum• 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

Global Topology of the Universe

CMB sky in a flat three torus universe

Cornish & Spergel PRD62 (2000)087304

Angular Power Spectrum is sensitive to

• Values of the Cosmological Parameters Mh2

Bh2

– h

– Curvature K

– Initial Power Spectral Index n

• Amount of massless and massive particles

• Fundamental Physical Parameters

Comparison with Observations and set constraints

Bayesian analysisMarkov chain Monte Carlo (MCMC)

ONE NOTE!ONE NOTE!

m= 1- K-

= 0

Degenerate contour

flat

Efstathiou and Bond

close to the close to the flat geometryflat geometryBUT not quite!BUT not quite!

Geometrical Degeneracy

Identical baryon and CDM density: Bh2, Mh2

Identical primordial

fluctuation spectra Identical Angular

Diameter R(, K)

Should Give IdenticalPower SpectrumShould Give IdenticalPower Spectrum

Projection from LSS to l

[iii] open <1: Geodesic effect

smaller pushes peakes to

large l

[ii] & <1: Further LSS

smaller pushes peaks to

large l

[i] flat =1

Almost degenerate models

For same value of R

Degenerate line

h=0.5

What we can determine from CMB power spectrum is

BBhh22, , mmhh22, ,

degenerate line (nearly curvature)degenerate line (nearly curvature)

Difficult to measure

curvature itself and , , mm, , B B directlydirectly

Question: Generate Cl’s on this degenerate line for M=0.3, 0.5, 0.6 and make sure they are degenerate.

§3. §3. Observations and ConstraintsObservations and Constraints

COBECOBE Clearly see large scale (low Clearly see large scale (low ll ) tail ) tail angular resolution was too bad to resolve peaksangular resolution was too bad to resolve peaks

Balloon borne/Grand Base experimentsBalloon borne/Grand Base experiments Boomerang, MAXMA, CBI, Saskatoon, Python, OVRO, Boomerang, MAXMA, CBI, Saskatoon, Python, OVRO,

etc etc See some evidence of the first peak, even in Last See some evidence of the first peak, even in Last

Century!Century! WMAPWMAP

CMB observations

by 1999

COBE & WMAP

1st yr

3 yr

WMAP WMAP ObservationObservation

WMAP Temperature Power Spectrum

• Clear existence of large scale Plateau

• Clear existence of Acoustic Peaks (up to 2nd or 3rd )

• 3rd Peak has been seen by 3 yr data

Consistent with Consistent with

Inflation and Cold Dark Matter ParadigmInflation and Cold Dark Matter Paradigm

One Puzzle:

Unexpectedly low Quadrupole (l=2)

Measurements of Cosmological Measurements of Cosmological Parameters by WMAPParameters by WMAP

BBhh2 2 =0.02229=0.022290.00073 (3% error!)0.00073 (3% error!)

MMhh2 2 =0.128 =0.128 0.0080.008

KK=0.014=0.0140.017 (with H=720.017 (with H=728km/s/Mpc)8km/s/Mpc) n=0.958 n=0.958 0.016 0.016

Baryon 4%

Dark Matter20%

Dark Energy76%

Spergel et al.WMAP 3yr alone

Measurements of Cosmological Measurements of Cosmological Parameters by WMAPParameters by WMAP

BBhh2 2 =0.02273=0.022730.00062 0.00062

MMhh2 2 =0.1326 =0.1326 0.00630.0063

=0.742=0.7420.030 (with BAO+SN, 0.72)0.030 (with BAO+SN, 0.72) n=0.963 n=0.963 0.015 0.015

Baryon 4.6%

Dark Matter23%

Dark Energy72%

Komatsu et al.WMAP 5yr alone

Finally Cosmologists Have the Finally Cosmologists Have the “Standard Model!”“Standard Model!”

But…But… 72% of total energy/density is unknown: Dark 72% of total energy/density is unknown: Dark

EnergyEnergy 23% of total energy/density is unknown: Dark 23% of total energy/density is unknown: Dark

MatterMatter

Dark Energy is perhaps a final piece of the puzzle for cosmology

equivalent to Higgs for particle physics

Dark EnergyDark Energy

How do we determine How do we determine =0.76 or 0.72? =0.76 or 0.72?

Subtraction!: Subtraction!: = 1- = 1- MM - - KK

Q: Can CMB provide a direct probe of Dark Energy?Q: Can CMB provide a direct probe of Dark Energy?

Dark EnergyDark Energy CMB can be a unique probe of dark energyCMB can be a unique probe of dark energy

Temperature Fluctuations are generated by the Temperature Fluctuations are generated by the growth (decay) of the Large Scale Structure (z~1)growth (decay) of the Large Scale Structure (z~1)

Integrated Sachs-Wolfe Effect

1

2

Photon gets blue Shift due to decayE=|1-2|

Gravitational Potential of Structure decays due to Dark Energy

CMB as Dark Energy ProbeCMB as Dark Energy Probe

Integrated Sachs-Wolfe Effect (ISW)Integrated Sachs-Wolfe Effect (ISW) Induced by large scale structure formationInduced by large scale structure formation Unique Probe of dark energy: dark energy slows down the Unique Probe of dark energy: dark energy slows down the

growth of structure formationgrowth of structure formation Not dominant, hidden within primordial fluctuations Not dominant, hidden within primordial fluctuations

generated during the inflation epochgenerated during the inflation epoch

Cross-Correlation between CMB and Large Scale Cross-Correlation between CMB and Large Scale StructureStructure

Only pick up ISW (induced by structure formation)Only pick up ISW (induced by structure formation)

Various Samples of CMB-LSS Cross-Correlation as a function of redshift

Measure w!w=-0.5w=-1w=-2

LessThan 10min

Cross-Correlation between CMB Cross-Correlation between CMB and weak lensingand weak lensing

Weak lensingWeak lensing Distortion of shapes of galaxies due to the Distortion of shapes of galaxies due to the

gravitational field of structuregravitational field of structure Can extend to small scalesCan 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

Nonlinear Integrated Sachs-Wolfe EffectRees-Siama Effect

1

2

Photon redshifted due to growthE=|1-2|

Gravitational Potential of Structure evolves due to non-linear effect

Large Scale: Blue-ShiftLarge Scale: Blue-Shift Correlated with Lens Correlated with Lens Small Scale: Red-Shift Small Scale: Red-Shift Anti-Correlated Anti-Correlated

Cross-Correlation between CMB & Lensing

l10 100 1000 10000

=0.95, 0.8, 0.74, 0.65, 0.5, 0.35, 0.2, 0.05,

Nishizawa, Komatsu, Yoshida, Takahashi, NS 08

positive

negative

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

What else can we learn about What else can we learn about fundamental physics from fundamental physics from

WMAP or future Experiments?WMAP or future Experiments? Properties of NeutrinosProperties of Neutrinos

Numbers of NeutrinosNumbers of Neutrinos Masses of NeutrinosMasses of Neutrinos

Fundamental Physical ConstantsFundamental Physical Constants Fine Structure ConstantFine Structure Constant Gravitational ConstantGravitational Constant

Constraints on Neutrino PropertiesConstraints on Neutrino Properties

Change NChange Neffeff or m or m modifies the peak heights modifies the peak heights

and locations of CMB spectrum.and locations of CMB spectrum.

Neutrino Numbers Neutrino Numbers Neff and mass m

Measure the family number at z=1000

CMB Angular Power SpectrumTheoretical Prediction

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

Constraints on mConstraints on m and N and Neffeff

WMAP 3yr Data paper by Spergel et al.WMAP 3yr Data paper by Spergel et al.

WMAP 5yr Data paper by Komatsu et al.WMAP 5yr Data paper by Komatsu et al.

CL)%68(5.14.4N

CL)0.66eV(95%

eV(95%CL)5.1

m WMAP aloneWMAP+SDSS(BAO)+SNWMAP+BAO+SN+HST

Constraints on Fundamental Constraints on Fundamental Physical ConstantsPhysical Constants

There are debates whether one has seen variation There are debates whether one has seen variation of of in QSO absorption lines in QSO absorption lines

Time variation of Time variation of affects on recombination affects on recombination process and scattering between CMB photons and process and scattering between CMB photons and electronselectrons

WMAP 3yr data set:WMAP 3yr data set:

-0.039<-0.039<//<0.010 (by P.Stefanescu 2007)<0.010 (by P.Stefanescu 2007)

Fine Structure Constant Fine Structure Constant

GG can couple with Scalar Field (c.f. Super can couple with Scalar Field (c.f. Super String motivated theory)String motivated theory)

Alternative Gravity theory: Brans-Dicke Alternative Gravity theory: Brans-Dicke /Scalar-Tensor Theory/Scalar-Tensor Theory G G 1/1/ (scalar filed)(scalar filed) G G may be smaller in the early epochmay be smaller in the early epoch

WMAP data set constrain: |WMAP data set constrain: |G/G|<0.05 (2G/G|<0.05 (2) ) ((Nagata, Chiba, N.S.)Nagata, Chiba, N.S.)

Gravitational Constant Gravitational Constant GG

Phase is the IssuePhase is the Issue

Power Spectrum is OKPower Spectrum is OK How about more detailed structureHow about more detailed structure

Alignment of low multipolesAlignment of low multipoles Non-GaussianityNon-Gaussianity Cold SpotCold Spot Axis of Evil 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?

Recent Hot Topics: Non-Recent Hot Topics: Non-GaussianityGaussianity

Fluctuations generated during the inflation Fluctuations generated during the inflation epochepoch Quantum OriginQuantum Origin Gaussian as a first approximationGaussian as a first approximation

(x)(x)(((x)-(x)-)/)/

(x)0

Non Gaussianity from Second Non Gaussianity from Second Order Perturbations of the Order Perturbations of the

inflationary induced fluctuations inflationary induced fluctuations

==LinearLinear+ f+ fNLNL((LinearLinear))22

LinearLinear=O(10=O(10-5-5), non-Gaussianity is tiny!), non-Gaussianity is tiny!

Amplitude fAmplitude fNL NL depends on inflation modeldepends on inflation model

[quadratic potential provides f[quadratic potential provides fNL NL =O(10=O(10-2-2)])]

First “Detection” in WMAP CMB map

Very Tiny Effect: Fancy analysis (Bispectrum etc) starts to reveal non-Gaussianity?

Komatsu et al. WMAP 5 yr.

Cold SpotCold Spot

Using Wavelet analysis for skewness and Using Wavelet analysis for skewness and kurtosis, Santander people found cold spotskurtosis, 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

Ongoing, Forthcoming Ongoing, Forthcoming ExperimentsExperiments

PLANCK is coming soon:PLANCK is coming soon: More Frequency Coverage More Frequency Coverage Better Angular ResolutionBetter Angular Resolution

Other ExperimentsOther 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 Bands

Microwave Band K Ka Q V W

Frequency (GHz) 22 30 40 60 90

Wavelength (mm) 13.6 10.0 7.5 5.0 3.3

Frequency 22 GHz 30 GHz 40 GHz 60 GHz 90 GHz

FWHM, degrees

0.93 0.68 0.53 0.35 <0.23

WMAP Frequency

WMAP Angular Resolution

PLANCK vs WMAPPLANCK vs WMAP

More Frequencies and better angular resolution

What We expect from PLANCKWhat We expect from PLANCK More Frequency CoverageMore Frequency Coverage

Better Estimation of Foreground Emission (Dust, Synchrotron Better Estimation of Foreground Emission (Dust, Synchrotron etc)etc)

Sensitivity to the SZ EffectSensitivity to the SZ Effect Better Angular ResolutionBetter Angular Resolution

Go beyond the third peak, and even reach Silk Damping: Go beyond the third peak, and even reach Silk Damping: Much Better Estimation of Cosmological Parameters, and Much Better Estimation of Cosmological Parameters, and sensitivity to the secondary effect. sensitivity to the secondary effect.

PolarizationPolarization Gravitational Wave: Probe InflationGravitational Wave: Probe Inflation Reionization: First Star FormationReionization: First Star Formation

Scattering & CMB quadrupolequadrupole anisotropies

produce linear polarization

• Information of last scattering

Thermal history of the universe, reionization

• Cosmological Parameters

• type of perturbations: scalar, vector, or tensor

PolarizationPolarization

Polarization must exist, because Big Bang existed!Polarization must exist, because Big Bang existed!

Scattering off photons by Ionized mediumScattering off photons by Ionized medium

velocity induce polarization: velocity induce polarization: phase is different from temperature phase is different from temperature

fluct. fluct.

SameFlux

Same Flux

Electron

No-Preferred DirectionUnPolarizeUnPolarizedd

Homogeneously Distributed Photons

Incoming Electro-MagneticField

scattering

StrongFlux

Weak Flux

Electron

Preferred DirectionPolarizePolarizedd

Photon Distributions with the Quadrupole Pattern

Incoming Electro-MagneticField

scattering

Wave number

Power spectrum

Hu & White

Velocity=polarization

Scalar Component

First Order EffectLiu et al. ApJ 561 (2001)

Reionization

2 independent

parity modes

E-mode

B-mode

Seljak

E-mode

SeljakScalar Perturbations only produce E-mode

B-mode

Tensor perturbations produce both E- and B- modes

Scalar Component

Hu & White

Tensor Component

Polarization is the ideal probe for Polarization is the ideal probe for the tensor (gravity wave ) modethe 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!You can prove the existence of Inflation!

STAY TUNE!

• PLANCK has been launched!

Higher Angular Resolution, Polarization

• More to Come from grand based and balloon borne Polarization Experiments