1. Cosmic Microwave Background 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

2. 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: naoshi@a.phys.nagoya-u.ac.jp or visit http://www.gcoe.phys.nagoya-u.ac.jp/

3. 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.

4. Basic Equations and Notations Friedmann Equation redshift

5. Basic Equations and Notations Metric: Friedmann-Robertson-Walker Horizon Scale

6. §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

7. 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!

8. Temperature 1GK 3000 Ｋ 2.725K Temperature 1GK 3000 Ｋ 2.725K Multiple Scattering photon Big Bang １３. ７ Gyr. Time 3min380Kyr. helium Big Bang Nucleo - Synthesis Recombi nation Hydrogen atom Photon transfer transparent

9. Cosmic Microwave Background If the Universe was in the thermal equilibrium, photon distribution must be Planck distribution (Black Body) Energy Density of Photons is

10. Why Information beyond Horizon? Here we assume matter dominant, a is the scale factor, H is the Hubble parameter. Horizon Size at recombination

11. 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 Horizon Size at present

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

13. Horizon Problem Inflation

14. §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

15. Extremely Good Black Body Shape in average Observation by COBE/FIRAS 2-1. Spectral Distortion y < 1.5x10 -5 y-distortion y < 1.5x10 -5 |  | < 9x10 -5  -distortion |  | < 9x10 -5

16. Sunyaev-Zeldovich Effect y-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 lower

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

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

19. SZ Effect Provides Information of –Thermal History of the Universe –Thermal Plasma in the cluster of galaxies CMB Photon 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?

20. 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

21. 200 sigma error-bars COBE/FIRAS wavelength[mm] frequency[GHz] intensity[MJy/str] 2.725K Planck distribution

22. 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 MatherArno Allan Penzias Robert Woodrow Wilson

23. 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

24. 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 -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

25. COBE 4yr data

26. COBE & WMAP George Smoot

27. 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

28. Temperature Anisotropies: Origin and Evolution 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.

29. Boltzmann Equation C: Scattering Term Perturbed FRW Space-Time Temperature Fluctuations Optical DepthAnisotropic Stress C

30. Fluid Components: Proton-electron Dark Matter dm

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

32. Scale Factor Fluctuations Long Wave Mode

33. Scale Factor Fluctuations Short Wave Mode

34. §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)

35. 3-1. Angular Power Spectrum C l  T/T(x) 

36. Angular Power Spectrum =  (2l+1)C l /4  dl (2l+1)C l /4  =  (dl/l) l(2l+1)C l /4  Therefore, logarithmic interval of the temperature power in l is l(2l+1)C l /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)C l /2 

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

38. Different 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

39. Individual Process Gravitational Redshift (a) Gravitational Redshift: large scales

40. 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 /c 2 )gh = h (1-gh/c 2 )  h ’ h

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

42. 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 However, when the universe became matter domination from radiation domination, potential decayed! This epoch is near recombination contribution on l ~ 100-200 Early ISW Late ISW

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

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

45. 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 Symphony

46. LSS 3) at Last Scatt. Surface (LSS), 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 LSS  first (second) peak (b) Acoustic Oscillation: (b) Acoustic Oscillation: intermediate scales sound horizon  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

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

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

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

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

51. Peak Locations -Projection of Sound Horizon- Sound Horizon: d s c (z=1100)= (c s /c)d H c (z=1100) Distance: Horizon Scale d H dsds dHdH

52. Sound velocity at recombination 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

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

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

55. Solution of the Boltzmann equation

56. (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

57. Comoving diffusion scale (physical  (1+z)) At recombination The corresponding angular scale and l are Here, assume

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

59. 10°1°10mi n LargeSmall Gravitaional Redshift (Sachs-Wolfe) Acoustic Oscillations Diffusion damping COBE Early ISW Late ISW for dark energy

60. 3-3. What control Angular Spectrum 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

61. 3-3. What control Angular Spectrum 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

62. Initial Condition Adiabatic vs Isocurvature Adiabatic corresponds to cos  T/T(k,  )=Bcos (kc s  ) Isocurvature corresponds to sin  T/T(k,  )=Asin(kc s  )

64. 3-3. What control Angular Spectrum 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

65. Sound velocity at recombination 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).

66. Bh2Bh2Bh2Bh2 small large small M

67. 3-3. What control Angular Spectrum 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

68. Horizon Size at recombination Here we assume matter dominant. In reality, Larger  R h 2 or smaller  B h 2 makes the horizon size smaller Shift the peak to smaller scale i.e., larger l

69. Early ISW effect 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

70. Mh2Mh2Mh2Mh2 small large M Early ISW

71. 3-3. What control Angular Spectrum 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

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

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

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

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

76. 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

77. Open: Concave lens space Image becomes small Shifts to larger l

78. More Negatively Curved

80. 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!

81. Define Optical Depth of Thomson Scattering as Temperature Fluctuations are Damped as  can be a probe of the epoch of reionization (first star formation). (Polarization is very important clue for reionization)

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

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

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

85. 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)

86. 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 Peak heights become higher Peak locations shift to smaller scales, i.e., larger l More Early Integrated ISW

87. Measure the family number at z=1000

88. 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 Time Variation of Fundamental Constants

89.  = -0.72±0.18  10 -5 0.5 < z < 3.5 QSO absorption line Webb et al.

90. 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

91. 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

92.  =0.05  =-0.05 Flat,  M =0.3, h=0.65,  B h 2 =0.019 Ionization fraction

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

94. Varying G and 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

95. G 0 /G

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

97. Nagata, Chiba, N.S. larger G

98. 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

99. Angular Power Spectrum is sensitive to 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 Comparison with Observations and set constraints Bayesian analysis Markov chain Monte Carlo (MCMC)

100. Question 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  for  B h 2 =0.02 and  M h 2 =0.15 (fiducial model). Then increase  B h 2 to 0.03, and find the value of  M 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

101. 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

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

103. How to quantify non-Gaussianity In real space –Skewness –Kurtosis

104. 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

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

106. Three torus universe Circle in the sky Global Topology of the Universe

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

108. Angular Power Spectrum is sensitive to 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 Comparison with Observations and set constraints Bayesian analysis Markov chain Monte Carlo (MCMC) ONE NOTE!

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

110. 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

111. Almost degenerate models For same value of R

112. Degenerate line h=0.5

113. What we can determine from CMB power spectrum is  B h 2,  m h 2, degenerate line (nearly curvature) Difficult to measure  ,  m,  B directly 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.

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

115. CMB observations by 1999

116. COBE & WMAP

117. 1 st yr 3 yr WMAPObservation

118. 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 Inflation and Cold Dark Matter Paradigm One Puzzle: Unexpectedly low Quadrupole (l=2)

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

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

121. Finally Cosmologists Have the “Standard Model!” But… But… 72% of total energy/density is unknown: Dark Energy 72% of total energy/density is unknown: Dark Energy 23% of total energy/density is unknown: Dark Matter 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 Dark Energy is perhaps a final piece of the puzzle for cosmology equivalent to Higgs for particle physics

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

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

124. CMB as Dark Energy Probe Integrated Sachs-Wolfe Effect (ISW) Integrated Sachs-Wolfe Effect (ISW) Induced by large scale structure formation Induced by large scale structure formation Unique Probe of dark energy: dark energy slows down the growth of 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 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)

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

128. Cross-Correlation between CMB and weak lensing Weak lensing Weak lensing Distortion of shapes of galaxies due to the gravitational field of structure Distortion of shapes of galaxies due to the gravitational field of structure Can extend to small scales 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

129. Nonlinear Integrated Sachs-Wolfe Effect Rees-Siama Effect Nonlinear Integrated Sachs-Wolfe Effect Rees-Siama Effect 11 22 Photon redshifted 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 Large Scale: Blue-Shift  Correlated with Lens Small Scale: Red-Shift  Anti-Correlated

130. Cross-Correlation between CMB & Lensing l 10 100 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 

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

132. What else can we learn about fundamental physics from WMAP or future Experiments? Properties of Neutrinos Properties of Neutrinos Numbers of Neutrinos Numbers of Neutrinos Masses of Neutrinos Masses of Neutrinos Fundamental Physical Constants Fundamental Physical Constants Fine Structure Constant Fine Structure Constant Gravitational Constant Gravitational Constant

133. Constraints on Neutrino Properties Change N eff or m modifies the peak heights and locations of CMB spectrum. Change N eff or m modifies the peak heights and locations of CMB spectrum. Neutrino Numbers Neutrino Numbers N eff and mass m

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

135. P. Serpico et al., (2004) A. Cuoco et al., (2004) P. Crotty et al., (2003) S. Hannestad, (2003) V. Barger et al., (2003) R. Cyburt et al. (2005) E. Pierpaoli (2003) Unfortunately, difficult to set constraints on N eff by CMB alone: Need to combine with other data BBN: Big Bang Nucleothynthesis LSS: Large Scale Structure HST: Hubble constant from Hubble Space Telescope

136. 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

137. Cold Dark MatterNeutrino as Dark Matter (Hot Dark Matter) Numerical Simulation

139. Constraints on m and N eff WMAP 3yr Data paper by Spergel et al. WMAP 5yr Data paper by Komatsu et al. WMAP alone WMAP+SDSS(BAO)+SN WMAP+BAO+SN+HST

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

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

142. Phase is the Issue Power Spectrum is OK Power Spectrum is OK How about more detailed structure How about more detailed structure Alignment of low multipoles Alignment of low multipoles Non-Gaussianity Non-Gaussianity Cold Spot Cold Spot Axis of Evil Axis of Evil

143. 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?

145. Recent Hot Topics: Non- Gaussianity Fluctuations generated during the inflation epoch Fluctuations generated during the inflation epoch Quantum Origin Quantum Origin Gaussian as a first approximation Gaussian as a first approximation  (x)  (  (x)-  )/   (x)  (  (x)-  )/   (x) 0

146. Non Gaussianity from Second Order Perturbations of the inflationary induced fluctuations  =  Linear + f NL (  Linear ) 2  =  Linear + f NL (  Linear ) 2  Linear =O(10 -5 ), non-Gaussianity is tiny!  Linear =O(10 -5 ), non-Gaussianity is tiny! Amplitude f NL depends on inflation model Amplitude f NL depends on inflation model [quadratic potential provides f NL =O(10 -2 )] [quadratic potential provides f NL =O(10 -2 )]

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

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

151. 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

152. Ongoing, Forthcoming Experiments PLANCK is coming soon: PLANCK is coming soon: More Frequency Coverage More Frequency Coverage Better Angular Resolution Better Angular Resolution Other Experiments 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

153. WMAP Frequency Bands Microwave BandKKaQVW Frequency (GHz)2230406090 Wavelength (mm)13.610.07.55.03.3 Frequency22 GHz30 GHz40 GHz60 GHz90 GHz FWHM, degrees 0.930.680.530.35<0.23 WMAP Frequency WMAP Angular Resolution PLANCK vs WMAP

154. More Frequencies and better angular resolution

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

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

159. Same Flux Same Flux Electron No-Preferred DirectionUnPolarized Homogeneously Distributed Photons Incoming Electro-Magnetic Field scattering

160. Strong Flux Weak Flux Electron Preferred DirectionPolarized Photon Distributions with the Quadrupole Pattern Incoming Electro-Magnetic Field scattering

161. Wave number Power spectrum Hu & White Velocity= polarization

162. Scalar Component

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

164. 2 independent parity modes E-mode B-mode Seljak

165. E-mode Seljak Scalar Perturbations only produce E-mode

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

167. Scalar Component

168. Hu & White Tensor Component

169. 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!

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