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Observational Cosmology: 1. Observational Parameters

Observational Cosmology: 1. Observational Parameters. “The Universe is not made of Atoms it is made of Stories” —  Muriel Rukeyser (1913-1980) poet. 1.1: A Brief History of Observational Cosmology. The state of play at the beginning of the 20th Century - Kapetyn universe .

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Observational Cosmology: 1. Observational Parameters

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  1. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 Observational Cosmology: 1.Observational Parameters “The Universe is not made of Atoms it is made of Stories” —  Muriel Rukeyser (1913-1980) poet.

  2. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 1.1: A Brief History of Observational Cosmology • The state of play at the beginning of the 20th Century - Kapetyn universe. • The Heliocentric model of the Solar System well established • The Milky Way, is an isolated disk shaped island of stars • Other Galaxies e.g. M31 “Spiral Nebulae” observed but are they inside or outside the Milky Way? Modern Observational Cosmology Timeline • 1912年: Slipher - Measures a doppler shift (redshift) in the spectra of the nebulae (36/41 receding) • c.1912年: Leavitt - Discovers Period-Luminosity relation for Cepheid variable stars • c.1918年: Shapley - Measures distance to LMC using Cepheid variable stars • c.1926年: Hubble - Measures distance to M31, M33 discovers the proportionality between velocity and distance  Hubbles law and the expanding Universe • c.1964年: Penzias & Wilson - Discover the 2.73K microwave background radiation Confirms Theoretical Big Bang model • c.1983年: IRAS - Maps the entire infrared sky • c.1985年: Geller, Huchra, de Lapparent, Maddox, Efstathiou et al. CfA/APM Redshift Surveys map large Scale Structures on order of 20-100Mpc • c.1987-91年: Gregory, Condon - Greenbank Radio Surveys emphasis Isotropy of the Universe • c.1992年: COBE - Discovery of the 1/105 anisotropy in the Cosmic Microwave Background • c.1995-2000年: HST - HST Key Project  value of the Hubble Constant • c.2003年: WMAP - Dark Energy is the major constituant of the Universe

  3. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 /R(to) H = The Hubble Parameter q = The Deceleration Parameter 1.2: Cosmological Parameters The Search for 2 (or more) numbers : Allan Sandage 1970 Evolution of the Universe is described by the Friedmann Equations We would like to know the Scale FactorR Expand Scale factor R(t) as Taylor Series around the present time to Ho and qo are observable mathematical parameters (no physics!!)

  4. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 Hubble Constant Hubble Parameter Linear Relationv = cz = HodHUBBLE’s LAW Hubble Time Hubble Distance • Recession velocity • Distance to Galaxy Measuring The Hubble Constant 1.2: Cosmological Parameters The Hubble Parameter, H

  5. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 Universe is decelerating (relative velocity between 2 points is decreasing) Universe is accelerating (relative velocity between 2 points is increasing) 1.2: Cosmological Parameters The Deceleration Parameter, q • for L = 0  W = 2q • for k = 0 3W = 2(q+1)

  6. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 L=0, W=2q Sandage 1961, ApJ, 133, 355 ~mJy Measuring Numbers of Galaxies to faint fluxes The Deceleration Parameter qo 1.2: Cosmological Parameters The Deceleration Parameter, q

  7. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 General Friedmann Equation ~ 5x10-27kg m-3 To flatten the Universe (k=0) can define a critical density • W>1  k>0 • W<1  k<0 • W=1 k=0 THE DENSITY PARAMETER Rewrite as 1.2: Cosmological Parameters The Density Parameter, W(a close relation of qo)

  8. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 DARK ENERGY DARK MASS • Galaxy Rotation Curves • Galaxy Cluster Velocities • Satellite Galaxy Motions The Density Parameter Wo Measuring Dynamics 1.2: Cosmological Parameters The Density Parameter, W(a close relation of qo) Light baryons (~0.5%) Dark baryons (~3.5%) Radiation (<0.005)

  9. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 General Friedmann Equation 1.2: Cosmological Parameters Dark Energy (a Cosmological Constant), L The Energy Density of the Universe is dominated by a dark energy - but what is it ?? • Vacuum Energy ? • Particle/antiparticle pairs continually created and annihilated  Vacuum Energy Density CONSTANT • Pervades all of space at a constant value for all time • Prediction from Quantum Mechanics = rL~1095kg m-3 120 orders of magnitude too high ! • “Quintessence” - The Fifth Element ? • Rolling homogeneous scalar field behaving like a decaying cosmological constant (i.e. NOT CONSTANT ) • Tracker Fields  Quintessence Field will attain the same present value independent of initial conditions • (like a marble spiraling down the plughole) • Eventually attain the true vacuum energy (energy zero point) It is somewhat strange that at this epoch this dark energy is small but >0 such thatWL Wm

  10. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 Dark Energy Dominated here and now Scale Factor (Size) Matter Dominated Cosmological Constant Quintessence t0 Normal Matter w < -1/3Repulsion  cosmic acceleration time • Supernovae Brightness • Angular Scales on CMB • Number of Gravitational Lenses Dark Energy L Measuring 1.2: Cosmological Parameters Dark Energy (a Cosmological Constant), L • Cosmological : w =-1 , Stiff Fluid, • Pervades all of space at a constant value for all time - our fate already decided • Quintessence : w < -1/3 , Soft Fluid, • Depends on properties of quintessence field (which can change with time)

  11. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 Observables in the Universe are fn(H, q, W, L) 1.2: Cosmological Parameters The Cosmological Parameters From Acceleration Equation (from Friedmann & Fluid eqns)

  12. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 Flux from star of Luminosity, L, at distance, r is Intensity, I, from a shell of stars of thickness dr r dr Intensity from shell is independent of distance. Integrating over all shells  Total Intensity, I 1.3: The Age of the Universe WHY IS THE SKY SO DARK ? Heinrich Olbers 1826 (Thomas Digges 1576) Olbers’ Paradox Consider an infinitely large and old Universe populated by stars of number density, n, average luminosity, L The Sky should be infinitely bright !!!

  13. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 1.3: The Age of the Universe WHY IS THE SKY SO DARK ? Heinrich Olbers 1826 (Thomas Digges 1576) Olbers’ Paradox The Sky should be infinitely bright !!! Possible Solutions to Olbers’ Paradox ????? • Absorption by dust ? -Dust would be heated until it emitted at the same temperature as the stars  • Not all lines of sight intersect a star ? - Finite angular size of stars may block a line of sight  Intensity = surface brightness of stars  • Number density and Luminosity not constant (nLconstant) ? - would require nL to decline faster than 1/r, r • Universe is not infinitely large ? - For a finite universe, the average stellar background intensity, I ~ (nL/4p)rmax • Universe is not infinitely old ? - Not all light has reached us, the maximum intensity would be I ~ (nL/4p)cto Primary Resolution to Olbers’ Paradox - The Universe is NOT infinitely old The light outside our horizon has not yet had time to reach us (Thermodynamic interpretation: why is the Universe so cold ?- Stars have not had time to heat up Universe) Olbers’ Paradox - Evidence for a finite age of our Universe

  14. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 R decelerating universe Ro accelerating universe t to to 1.3: The Age of the Universe How old is our Universe ? - Evidence • For an expanding (decelerating) Universe, the age of the Universe ~ HUBBLE TIME= 1/Ho=to • Hubble Time to ~ age by assuming Universe has always been expanding at its current rate. • If Universe was expanding faster in the past - to overestimates the age of the universe (to). • If Universe is expanding faster today than in the past - to underestimates true age of Universe (to). Observational Constraints on to • Radioactive Dating • White Dwarf Cooling Age • Age of Globular Clusters

  15. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 CS22892-052 1.3: The Age of the Universe How old is our Universe ? - 1) Radioactive Dating • Dating from proportions of element isotopes • Oldest Rocks from Earth, Moon, Meteorites  t ~ 4.5±0.3 Gyr • Consistent with formation age of the Solar System (~5Gyr) Dating of radioactive isotopes in stellar atmospheres 232Th half life 14Gyr  too long (only changes by factor ~2 on timescale of Universe) Use Uranium 238U half life 4.5Gyr 385.957nm Cayrel et al. (2001) - First measurement of Stellar Uranium CS31082-0018 lg(U/H)=-13.7±0.14 t ~ 12.5 ± 3 Gyr (Principal uncertainty from production ratios) N.B. usually the lines are too weak but CS31082-0018 had unusually weak Fe line strengths

  16. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 AGB Red Giant Branch M4 Globular Cluster Turn off Main sequence WHITE DWARF 1.3: The Age of the Universe How old is our Universe ? - 2) White Dwarf Cooling Age • Stars <8Mo White Dwarfs • Passively cool and dim after formation • Fainter White Dwarfs  Older White Dwarfs • Search for the faintest White Dwarfs Richer et al. (2002) - HST 8 days exposure 30th mag. White dwarfs (109 fainter than faintest stars with the naked eye) Sharp edge in White Dwarf LF corresponding to age ~11Gyr t ~ 12 - 13 Gyr (uncertainty from White Dwarf core crystallization)

  17. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 AGB Red Giant Branch Turn off Main sequence WHITE DWARF 1.3: The Age of the Universe How old is our Universe ? - 3) Age of Globular Clusters • Globular Clusters  Stars form ~ same time • These stars evolve  Main Sequence of HR diagram • Massive stars evolve to giant branch • Main Sequence Turn off • at MSTO LM4 • Main Sequence Lifetime tM3 L-3/4 • Most massive stars evolve fastest • Turn off Main Sequence faster • Less luminous = Older Cluster • MSTO point occurs at lower To • Use RR Lyrae Stars to calculate distance to Cluster  From the distance, can calculate the luminosity Chaboyer (2001) -t ~ 13.5 ± 2 Gyr (Principal uncertainty from distance scale)

  18. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 Friedmann Equation (matter dominated universe) 1 1 writing 1.3: The Age of the Universe The Age of the Universe (L = 0 World Models)

  19. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 R Ro to t • For an empty Universe: the age is the Hubble Time • This will be the maximum age for any L = 0 universe • i.e. any universe where to 1.3: The Age of the Universe Age of the Universe (L = 0, W=0 World Model)

  20. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 R Ro to t to 1.3: The Age of the Universe Age of the Universe (L = 0, W=1 World Model) • The L = 0, W=1 World Model is the classical Einstein De Sitter (EdeS) universe • For Ho=72  already inconsistent with age estimates • For Ho=50  already still O.K.

  21. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 • Age of L = 0, W>1 World Models is always • For W>>1 1.3: The Age of the Universe Age of the Universe (L = 0, W>1 World Models)

  22. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 • Age of L = 0, W<1 World Models can be • For W<<1 1.3: The Age of the Universe Age of the Universe (L = 0, W<1 World Models)

  23. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 Friedmann Equation (matter + lambda universe) 1 writing 1.3: The Age of the Universe Age of the Universe (L  0World Models)

  24. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 c.f. Einstein De Sitter (k=0, L=0 ) universe 1.3: The Age of the Universe Age of the Universe (L  0) (Wm+ WL=1 flat case)

  25. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 to(Ho=72) = 16.6Gyr 12.5Gyr 10.4Gyr 8.3Gyr 6.7Gyr • Decrease Ho • Decrease Wo • Increase L To increase the age of the Universe: 1.3: The Age of the Universe An Age Crisis ? Age Problem ! Ho=72 EdeS ruled out !

  26. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 le lo Frequency increasing Wavelength decreasing Wave crests get closer together Colour gets BLUER = BLUESHIFT Frequency decreasing Wavelength increasing Wave crests get further apart Colour gets REDDER = REDSHIFT Doppler redshift: (between observed and emitted frames ) 1.4: The Redshift The Redshift

  27. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 • Doppler Redshift • Special Relativistic Redshift • Gravitational Redshift • Frequency of electromagnetic radiation is dependent on the strength of the gravitational field • Experimentally verified: Pound and Rebka in 1960 • Measured change in frequency (blueshift ~ 10-15) of emitted gamma ray as Fe Nucleus fell through ~18m • Observed in white dwarf stars (Sirrius B, Eridani B) on the order of 10-5 • Cosmological Redshift Hubble’s Law 1.4: The Redshift The Redshift • The correct interpretation of the cosmological Redshift of galaxies is NOT a Doppler shift. • Rather, the wave fronts expand with the expanding Universe, stretching the photon wavelength.

  28. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 R(to) lo le R(te) 1.4: The Redshift Cosmological Redshift Cosmological explanation: Redshift - natural consequence of assumption that R(t) is an increasing function of time The wavefronts expand with the expanding Universe, stretching the photon wavelength.

  29. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 space time For a single wave crest emitted at t=te observed at t=to l = cdt For the next wave crest (i.e. 1 wavelength later in time ) emitted at t=te+dte = te+le/c observed at t=to +dto = = to+lo/c 1.4: The Redshift Cosmological Redshift from General Relativity Start from The Robertson-Walker Metric ds = the interval t = time R = the scale factor r,q,f = co-moving coordinates k = the curvature For a photon (null geodesic dS=0) traveling radialy outward (df=0 dq=0)

  30. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 subtracting Cosmological Redshift integrating 1.4: The Redshift Cosmological Redshift from General Relativity Over single period of wave (blue light)t = l/c =1.5x10-15s  10-33 Ho-1 R(t) constant For an expanding Universe,R(to)> R(te)  z>0 redshift is observed Emission from more distant objects - traveling for greater time - more redshifted than nearer objectes At a redshift of 3  Universe was 1/4 present size Highest observable redshift at surface of last scattering, z= 1000  Universe was 1000th present size Note: 1+z is really more fundamental than z

  31. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 1.5 1.0 Flux 0.5 0 2000 4000 6000 8000 10,000 1.4: The Redshift Cosmological Redshift lobs(A) Cosmological explanation: Redshift - natural consequence of assumption that R(t) is an increasing function of time The wavefronts expand with the expanding Universe, stretching the photon wavelength.

  32. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 Look Back Time = tz Recall the age of the Universe where The Look Back Time 1.4: The Redshift Look Back Time Speed of light is finite  observations not instantaneous We cannot help but look back in time !! • Nearest star (4.3ly)  see as it was 4.3 years ago • Sun ~ 7mins • Andromeda Galaxy ~ 1.5 million years ago • For Distant galaxies at high redshift, z , • observe them at look back times of ~Gyr, • when Universe was a fraction of its present age

  33. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 WL=0 Milne Model Wm=WL=0 EdeS Wm=1, WL=0 Carroll and Press ARAA 1992 1.4: The Redshift Look Back Time

  34. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 HDF z~3 tz~ 11Gyr HDF z~0.1 tz~ 1.3Gyr HDF z~1 tz~ 7.5Gyr HDF z~2 tz~ 10Gyr 1.4: The Redshift Snapshots at different redshift sample different look back times Look Back Time

  35. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 Z = 1+ z= The Redshift The Scale Factor Ho= The Hubble Constant First derivative of the Scale Factor qo= The Deceleration Parameter Second derivative of the Scale Factor 1.4: The Redshift Observable Cosmological Parameters

  36. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 1.5: Our Universe Observations of the Cosmological Parameters • Supernova Project • (Observational Cosmology 2.1 “Observational Parameters” this seminar) • Hubble Key Project • (Observational Cosmology 2.4 “The Distance Scale”) • WMAP Results • (Observational Cosmology 2.2 “The Cosmic Background”)

  37. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 constant decelerating accelerating • For a population of objects of • standard proper size (standard ruler) • or • standard luminosity (standard candle) • and • high luminosity • can calculate • Distance • Measuring redshift cosmological parameters Ho, Wm,o, WL,o Scientific American 2002 1.5: Our Universe • Effect of Cosmological Constant: Changes relationship between Redshift - time - Distance Supernova Project Results • Can we find such a population ? • QSOs  • Supernova (Massive exploding stars)  • Supernova sub class - Type 1a o • Supernova sub class - Type 1a • After supernova occurs the light gradually fades. • Absolute magnitude at peak of supernovae depends on shape of their light decay curve. • Brighter Supernovae - slower climb and decay of light curve. • Measure absolute magnitude, observed flux  DISTANCE !!!

  38. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 Type Ib,c (H poor massive Star M>8Mo) Stellar wind or stolen by companion Type II (Hydrogen Lines) Type Ia (M~1.4Mo White Dwarf + companion) Type I (no Hydrogen lines) Supernova ! Massive star M>8Mo 1987 White dwarf begins to collapse against the weight of gravity, but rather than collapsing , material is ignited consuming the star in an an explosion 10-100 times brighter than a Type II supernova http://cfa-www.harvard.edu/cfa/oir/Research/supernova/ 1.5: Our Universe Supernova Project Results

  39. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 http://cfa-www.harvard.edu/cfa/oir/Research/supernova/ 1.5: Our Universe Supernova Project Results • Imagine yourself in your local TV store in front of a wall of TV's. • Let's say the average TV (monitor) is 500x500 pixels. Now, stack 4 rows of 8 TVs: that's 32 TVs which is the display size you need to display 1 entire image from 1 of our CCD chips. The Mosaic Camera on the CFHT telescope has 12 chips. • For 12 chips, you need to take your set of 4x8 TVs, place 6 of these sets side by side, & place another 6 sets more on top of them. That's 384 TV monitors. • 384 TVs = 1 entire exposure from our CCD camera. • In 1 night we take 42 exposures.... that's 8064 TVs worth of pixels. • We need to search 16128 TVs worth of data to find the handful of supernovae. • We get hungry doing this, and while in La Serena, Chile, we recommend getting your pizza delivered from Pizza Mania: Specialita in pasta e pizza, para servirse, llevar y domicilio.

  40. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 Flux, S, from star of Luminosity, L, at distance, DLis Luminosity Distance DISTANCEMODULUS Low z observations Ho Higher z observations qo 1.5: Our Universe Supernova Project Results  DL (z=0.1) = (Einstein De Sitter universe) ~ 95% (Concordance Cosmology Universe)  DL (z=1) = (Einstein De Sitter universe) ~ 75% (Concordance Cosmology Universe) qo<0Universe is accelerating standard candles of lower brightness qo>0 Universe is decelerating standard candles of higher brightness

  41. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 accelerating Wm,o=0.3 WL,o=0 decelerating 1.5: Our Universe A GOOD FIT Ho=72kms-1Mpc-1 Wm,o = 0.3 WL,o = 0.7 Supernova Project Results

  42. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 1.5: Our Universe SuperNova Acceleration Probe SNAP • The next generation of supernova detections • Dedicated dark energy probe • Discovery +12 years • Supernova Projects: Discovery ~ 80 Supernova • SNAP discovery rate 2,000 per year • 1.8- to 2.0-meter telescope, • 1-square-degree imager, • 1-square-arcminute near-IR imager, • 3-channel near-UV-to-near-IR spectrograph. • Observing strategy: monitor a twenty-square-degree region near NEP/SEP, • Discover and follow supernovae that explode in that region. • Every field visited frequently enough with sufficiently long exposures that every supernova up to z = 1.7 will be discovered within, on average, two restframe days of explosion.

  43. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 1.5: Our Universe SuperNova Acceleration Probe SNAP

  44. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 1.5: Our Universe The Hubble Key Project • Discovery of Cepheids with the HST • Comparison of many distance determination methods • Comparison of systematic errors • Determination of Ho±10% • Cepheids in nearby galaxies within 12 million light-years. • Not yet reached the Hubble flow • Need Cepheids in galaxies at least 30 million light-years away • Hubble Space Telescope observations of Cepheids in M100. • Calibrate the distance scale

  45. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 Mould et al. 2000; Freedman et al. 2000 H0 = 716 km s-1 Mpc-1 t0 = 1.3  1010 yr 1.5: Our Universe The Hubble Key Project

  46. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 1.5: Our Universe The WMAP Results Wilkinson Microwave Anisotropy Probe (2001 at L2) Detailed full-sky map of the oldest light in Universe. It is a "baby picture" of the 380,000yr old Universe • Temperature fluctuations imprinted on CMB at surface of last scattering • Open Universe - photons move on faster diverging pathes => angular scale is smaller for a given size • Temperature fluctuations over angular scales in CMB correspond to variations in matter/radiation density Scientific American 2002

  47. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 Closed Red - warm Blue - cool Flat Open 1.5: Our Universe The WMAP Results

  48. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 1.5: Our Universe • Supernovae Data •  Ho =72 •  Accelerating expansion • WL> 0 Putting it all together • Hubble Key Project Data • Ho =72 • CMB Data •  Flat universe •  WL> 0 • Combine SN, CMB, LSS •  Dark energy WL ~ 0.7

  49. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 Wb=0.02 H0=72 km s-1 Mpc-1 k=0,L>0 Wtot= 1.0 WL= 0.7 Wm=0.3 WL Wm Z = 1+ z= The Redshift The Scale Factor Ho= The Hubble Constant 1st derivative of the Scale Factor Lawrence Livermore Berkley qo= The Deceleration Parameter 2nd derivative of Scale Factor 1.6: Summary Summary

  50. Chris Pearson : Observational Cosmology 1: Observational Parameters - ISAS -2003 1.6: Summary Summary 終 Observational Cosmology 1. Observational Parameters Observational Cosmology 2. The Cosmic Background 次：

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