Cosmic Microwave Background

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. Time transparent 3min 380Kyr. １３.７Gyr. Multiple Scattering Photon transfer photon helium Hydrogen atom Recombination Nucleo -Synthesis Big Bang Temperature1GK3000Ｋ　　　　　　2.725K Big Bang

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

11. 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

12. Angular Size of the Horizon at z=1100 • 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 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

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

16. Sunyaev-Zeldovich Effecty-distortion • Caused by: Thermal electrons scatter off photons • Photon distribution function: move low energy photons to higher energy lower higher • distort Black Body • low freq: lower temp • high freq: higher temp • no change: 220GHz Distribution function frequency

17. 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

18. Solution of the equation fPL: Planck distribution low freq. limit: x<<1 high freq. limit: x>>1 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 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?

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

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)

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 (10-36s) 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

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 C Perturbed FRW Space-Time Temperature Fluctuations Optical Depth Anisotropic Stress

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

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

32. Long Wave Mode Fluctuations Scale Factor

33. Short Wave Mode Fluctuations Scale Factor

34. §3. What can we learn from spatial anisotropies? Observables • Angular Power spectrum • If fluctuations are Gaussian, Power spectrum (r.m.s.) contain all information • Phase Information • Non-Gaussianity • Global Topology of the Universe • Polarization • Tensor (gravitational wave) mode • Reionization (first star formation)

35. 3-1. Angular Power Spectrum • Cl T/T(x)

36. Angular Power Spectrum • <|T/T(x)|2>=(2l+1)Cl/4dl (2l+1)Cl/4 = (dl/l) l(2l+1)Cl/4 • Therefore, logarithmic interval of the temperature power in l isl(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

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

38. 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

39. Individual Process (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 h-mgh= h-(h /c2)gh = h(1-gh/c2)  h’ h h Surface of the earth

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

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 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 Late ISW Early ISW

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

44. (b) Acoustic Oscillation:intermediate scales  scales smaller thansound 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. 1) set at initial location = initial cond. hold them until sound horizon cross 2) oscillate after sound horizon crossing (b) Acoustic Oscillation:intermediate scales  scales smaller thansound horizon Harmonic oscil. in grav. potential analogyballs & springs in the well:balls’mass Bh2 3) at Last Scatt. Surface (LSS), climb up potential well  long wave length > sound horizon stay at initial location until LSS Pure Sachs-Wolfe  First Compress.(depress.) at LSSfirst(second)peak

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

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

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

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