Transcript sugiyama
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 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 r K a 2 m H H 0 3 4 2 a a a a 2 2 H 0 : Hubble, a : scale factor, 0 denotes present a0 1 m : matter, r : radiation, K : curvature : dark energy • redshift 1 z a0 / a 1 / a Basic Equations and Notations • Metric: Friedmann-Robertson-Walker 2 dr 2 2 2 2 2 ds cdt a r d 2 1 Kr • Horizon Scale (a) a(t ) dt / a(t ) c / H (a) dH Physical dH comoving (a0 / a)d H Physical §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 -5 Very Isotropic: T/T 10 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! 3min Temperature 1GK Multiple Scattering 380Kyr. transparent １３.７Gyr. Photon transfer Recombi nation Nucleo Synthesis Big Bang photon helium Time 3000Ｋ Big Bang Hydrogen atom 2.725K Cosmic Microwave Background • If the Universe was in the thermal equilibrium, photon distribution must be Planck distribution (Black Body) • Energy Density of Photons is (1 z ) 4 Why Information beyond Horizon? 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 (t0 ) 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 c dH (trec ) / dH (t0 ) 0.030rad 1.7degree C.f. angular size of the moon is 0.5 degree 1.7degree dHc(z=1100) dH(z=0) There must not have any causal contact beyond Horizon Same CMB temperature Univ. should expand faster than speed of light 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 2-1. Spectral Distortion Extremely Good Black Body Shape in average Observation by COBE/FIRAS y-distortion y < 1.5x10-5 y dlne T -distortion || < 9x10-5 8h f 3 c 3 h kTe me c 2 exp 1 kT Sunyaev-Zeldovich Effect y-distortion • Caused by: Thermal electrons scatter off photons • Photon distribution function: move low energy photons to higher energy Distribution function lower higher • distort Black Body low freq: lower temp high freq: higher temp no change: 220GHz frequency SZ Effect f: 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 fPL: Planck distribution low freq. limit: x<<1 f / f 2 y decrement high freq. limit: x>>1 f / f yx2 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] intensity[MJy/str] COBE/FIRAS 200 sigma error-bars 2.725K Planck distribution frequency[GHz] 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 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: Proton-electron dm dm dm dm Dark Matter Numerically Solve Photon, Proton-Electron and dark matter System in the Expanding Universe Boltzmann Code, e.g., CMBFAST, CAMB Fluctuations Long Wave Mode Scale Factor Fluctuations Short Wave Mode Scale Factor §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(l+1)Cl/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=110 180 Angular Scale 10 1 Horizon Scale at z=1100 (1.7degree) COBE 0.1 3-2. Physical Process 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 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 h h-mgh= h-(h /c2)gh = h(1-gh/c2) 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| 1 2 blue-shift 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 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 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 (b) Acoustic Oscillation: intermediate scales scales smaller than sound horizon Harmonic oscil. in grav. potential 2 analogy balls & springs in the well: balls’mass Bh 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 LSSfirst (second) peak Sound Horizon Long Wave Length diffusion Intermediate Wave Length Very Early Epoch All modes are outside the Horizon Short Wave Length Sound Horizon Long Wave Length diffusion 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 Acoustic Oscillation Long Wave Length Intermediate Wave Length Recombination Short Wave Length Diffusion Damping: Erase! Epoch Peak Locations -Projection of Sound Horizon• Sound Horizon: dsc (z=1100)= (cs/c)dHc (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. 180 Angular Scale 10 1 0.1 Sound Horizon z=1100 higher harmonics COBE Solution of the Boltzmann equation k (t ) A sin(cs k Physicalt ) B cos(cs k Physicalt ) A sin(cs k ) B cos(cs k ) dt / a(t ) d comoving H cs k 1 k (cs / c ) d comoving H comoving kd Sound 1 1 /c (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 ld 180(1degree/ ) 1700 2 2 h 0 . 02 , h 0.15 Here, assume B M 180 Angular Scale 10 1 0.1 Diffusion scale at z=1100 (l=1700) COBE Acoustic Oscillations Late ISW for dark energy COBE Gravitaional Redshift (Sachs-Wolfe) Large 10° Early ISW Diffusion damping 1° 10mi Small 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 (kcs) • Isocurvature corresponds to T/T(k, )=Asin(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). M large Bh2 large small small 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, H 2 H 2 M R 0 a 3 a 4 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 M small Mh2 Early ISW large 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 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 l large l smaller pushes peaks to smaller pushes peakes to 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! Define Optical Depth of Thomson Scattering as dt ne T Temperature Fluctuations are Damped as T / T T / TNoDamping 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 Big Bang Recombination Ionized Gas 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 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 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: [(t20bilion yr)- (t0)]/ (t0) = -0.72±0.1810-5 QSO absorption line = -0.72±0.1810-5 0.5 < z < 3.5 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 was smaller, recombination became later If =±5%, z~100 Flat, M=0.3, h=0.65, Bh2=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 G0/G If G was larger in the early universe, the horizon scale became smaller c/H = c(3/8G) Peaks shift to larger l larger G Nagata, Chiba, N.S. 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 Angular Power Spectrum is sensitive to • Values of the Cosmological Parameters – – – – – M h 2 Bh2 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 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 3-4. Beyond Power Spectrum: Phase • 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 Non-Gaussianity Fluctuations generated during the inflation epoch Quantum Origin Gaussian as a first approximation (x)((x)-)/ 0 (x) 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, Wigner 3-j symbol – Trispectrum Bispectrum • If Gaussian, Bispectrum must be zero • Depending upon the shape of the triangle, it describes different nature – Local – Equilateral Global Topology of the Universe Three torus universe Circle in the sky CMB sky in a flat three torus universe Cornish & Spergel PRD62 (2000)087304 Angular Power Spectrum is sensitive to • Values of the Cosmological Parameters – – – – – M h 2 Bh2 h Curvature K Initial Power Spectral Index n ONE NOTE! • Amount of massless and massive particles • Fundamental Physical Parameters Bayesian analysis Markov chain Monte Carlo (MCMC) Comparison with Observations and set constraints Geometrical Degeneracy Efstathiou and Bond baryon and CDM density: Bh , Mh Identical primordial Degenerate contour fluctuation spectra m= 1- K- Identical Angular Diameter R(, K) =0 2 Identical Should Give Identical Power Spectrum close to the flat geometry BUT not quite! flat 2 Projection from LSS to l [i] flat =1 [ii] & <1: Further LSS [iii] open <1: Geodesic effect large l large 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 Bh2, mh2, degenerate line (nearly curvature) Difficult to measure curvature itself and , m, B directly Question: Generate Cl’s on this degenerate line for M=0.3, 0.5, 0.6 and make sure they are degenerate. §3. Observations and Constraints 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 1st yr 3 yr 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 Inflation and Cold Dark Matter Paradigm One Puzzle: Unexpectedly low Quadrupole (l=2) Measurements of Cosmological Parameters by WMAP Bh2 =0.022290.00073 (3% error!) Mh2 =0.128 0.008 K=0.0140.017 (with H=728km/s/Mpc) n=0.958 0.016 Spergel et al. WMAP 3yr alone Dark Energy 76% Dark Matter 20% Baryon 4% Measurements of Cosmological Parameters by WMAP Bh2 =0.022730.00062 Mh2 =0.1326 0.0063 =0.7420.030 (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% Finally Cosmologists Have the “Standard Model!” 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 Dark Energy How do we determine =0.76 or 0.72? Subtraction!: = 1- M - K Q: Can CMB provide a direct probe of Dark Energy? Dark Energy CMB can be a unique probe of dark energy 1 Temperature Fluctuations are generated by the growth (decay) of the Large Scale Structure (z~1) Integrated Sachs-Wolfe Effect Photon gets blue Shift due to decay E=| - | 1 2 2 Gravitational Potential of Structure decays due to Dark Energy CMB as Dark Energy Probe 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) Various Samples of CMB-LSS Cross-Correlation as a function of redshift w=-0.5 w=-1 w=-2 Measure w! Less Than 10min Cross-Correlation between CMB and weak lensing 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 due to growth E=|1-2| 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 10 negative l 100 1000 10000 Future experiments (CMB & Large Scale Structure) will reveal the dark energy! What else can we learn about fundamental physics from WMAP or future Experiments? Properties of Neutrinos Numbers of Neutrinos Masses of Neutrinos Fundamental Physical Constants Fine Structure Constant Gravitational Constant Constraints on Neutrino Properties Neutrino Numbers Neff and mass m Change Neff 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 Constraints on m and Neff WMAP 3yr Data paper by Spergel et al. WMAP 5yr Data paper by Komatsu et al. m 1.5eV(95%CL) WMAP alone 0.66eV(95%CL) WMAP+SDSS(BAO)+SN N 4.4 1.5(68%CL) WMAP+BAO+SN+HST Constraints on Fundamental Physical Constants 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.) Phase is the Issue 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? Recent Hot Topics: NonGaussianity Fluctuations generated during the inflation epoch Quantum Origin Gaussian as a first approximation (x)((x)-)/ 0 (x) Non Gaussianity from Second Order Perturbations of the inflationary induced fluctuations =Linear+ fNL(Linear)2 Linear=O(10-5), non-Gaussianity is tiny! Amplitude fNL depends on inflation model [quadratic potential provides fNL =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. Cold Spot 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 Ongoing, Forthcoming Experiments PLANCK is coming soon: More Frequency Coverage Better Angular Resolution Other Experiments Ongoing Ground-based: Upcoming Ground-based: AMiBA, BICEP, PolarBear, QUEST, CLOVER Balloon: CAPMAP, CBI, DASI, KuPID, Polatron Archeops, BOOMERanG, MAXIPOL Space: Inflation Probe PLANCK vs WMAP WMAP Frequency 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 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 What We expect from PLANCK 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 Same Flux No-Preferred Direction UnPolarized Electron scattering Homogeneously Distributed Photons Incoming Electro-Magnetic Field Strong Flux Weak Flux Preferred Direction Polarized 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 B-mode Tensor perturbations produce both E- and B- modes 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! STAY TUNE! • PLANCK has been launched! Higher Angular Resolution, Polarization • More to Come from grand based and balloon borne Polarization Experiments