COSMIC MICROWAVE BACKGROUND Lecture I

Transcription

1 COSMIC MICROWAVE BACKGROUND Lecture I Isabella Masina Univ. & INFN Ferrara, Italy CP3-Origins SDU, Denmark 18/10/2010 CP3-Origins

2 SUGGESTED BIBLIOGRAPHY 1. W. Hu Lectures and animations 2. W.Hu and S.Dodelson Cosmic Microwave Background Anisotropies, astro-ph/ A. Challinor and H. Peiris Lecture notes on the physics of cosmic microwave background anisotropies arxiv: PDG review on Big Bang Cosmology by K.A. Olive and J.A. Peacock (2009) review on CMB by D. Scott and G.F. Smoot (2009) 5. S.Dodelson Modern Cosmology, Academic Press, Elsevier, 2003

3 INTRODUCTION The energy content in radiation from beyond our Galaxy is dominated by the Cosmic Microwave Background (CMB)

4 Experimental Milestones 1965: Discovery of CMB by Penzias and Wilson The spectrum of the CMB is well described by a blackbodody with T = 2.725K, i.e. 2mm wavelength (microwaves) This spectral form is a major pillar of the hot Big Bang (BB) model for the early Universe

5

6 Another observable quantity inherent in the CMB is the variation in temperature from one part of the microwave sky to another, first observed by the Cosmic Microwave Background Explorer (COBE) satellite 1992: COBE detection of large scale (7 ) anisotropies (l=20)

7 for their discovery of the blackbody form and anisotropy of the cosmic microwave background radiation Mather coordinator and project leader Smoot responsible for measurements Their Majesties Queen Silvia and King Carl XVI Gustaf of Sweden (middle) posing with John C. Mather and his wife, Jane Mather (left), and George F. Smoot and Christina Skube (right) at the Nobel Banquet.

8 Since then there has been intense activity to map the sky at increasing levels of sensitivity and angular resolution by ground-based and balloon-borne measurements These were joined by the NASA s Wilkinson Microwave Anisotropy Probe (WMAP) 2003: WMAP detection of anisotropies up to 0.2 (l=800); detection of CMB polarization These observations have led to a robust confirmation of the Standard Model of Cosmology

9 CMB anisotropy measurements (together with other astrophysical data) place quite precise constraints on a number of cosmological parameters. We are in the era of precision cosmology This is expected to continue with the Planck satellite 2009: PLANCK satellite launched Goal: detect small scale anisotropies up to 0.1 (l=1900) and better study CMB polarization

10 The Energy Pie Chart The energy content in radiation is dominated by the CMB, but it constitutes a TINY fraction of the total energy Radiation % According to the theory of the Big Bang, the universe started hot and dense and then expanded and cooled

11 The Energy Pie Chart The energy content in radiation is dominated by the CMB, but it constitutes a TINY fraction of the total energy Radiation % radiation density scales as a -4, matter density as a -3, dark energy density stays constant

12 The Energy Pie Chart The energy content in radiation is dominated by the CMB, but it constitutes a TINY fraction of the total energy Radiation % So, there has been a time when radiation and matter densities were comparable and cosmological constant was negligibe.

13 The Energy Pie Chart The energy content in radiation is dominated by the CMB, but it constitutes a TINY fraction of the total energy Radiation % So, there has been a time when radiation and matter densities were comparable and cosmological constant was negligibe. According to BB theory, the CMB gives a snapshot of the universe at that time

14 Universe s snapshot More precisely, a snaphot of the universe when T dropped enough to allow e and p to RECOMBINE forming H atoms, thus making the universe transparent to radiation, since then in thermal equilibrium with matter, including the dark one Fiat lux Sistine Chapel, Vatican Separation of Light and Darkness

15 This recombination or last scattering time happened 380,000 yrs after BB when the universe was about 1000 times smaller (z=1100) and had T about 4000 K, i.e ev or 2 mm wavelength It took place over roughly 115,000 yrs. When it was complete, the universe was roughly 487,000 yrs old. From: W.Hu and M.White, The cosmic Symphony,2004 NOW, 10 billion yrs after the BB, the CMB is a cold sea of photons with an average T of 2.7K (-270C ).

16 MICROWAVE VISIBLE 2 mm 2mm 3 K 3000K NOW RECOMBINATION

17 HERE IS THE SNAPSHOT with contrast at 1 part in 10^6 ignore the pattern around the equator as that is our own galaxy

18 HERE IS THE SNAPSHOT with contrast at 1 part in 10^6 ignore the pattern around the equator as that is our own galaxy Well, it looks noisy... But that s exactly what it is! It is the random quantum noise of the early universe

19 These ripples reflect tiny density fluctuations in the primordial soup of particles. We think that inflation (a rapid period of expansion) took these random seed fluctuations in the density of matter and brought them to cosmic scales. The small seed fluctuations photographed here are of exactly the right order of magnitude for all of large-scale structure in the universe (stars, galaxies, and clusters of galaxies) to have grown from them by gravitational attraction If what we are dealing with is actually noise, what do we do with it? To determine its spectral properties: Is the noise white or monocromatic or does it have some features?

20 END OF INTRODUCTION To better understand T fluctuations we NOW have to be more quantitave and tell how the snapshot was taken

21 Interpreting the snapshot 1. Spherical harmonic expansion 2. Monopole 3. Moving in the CMB 4. A first look at the power spectrum

22 Let introduce a spherical harmonic expansion of the CMB sky Multipoles at l encode angular information with characteristic angular scale (i.e. angular period) q 2p/l q

23 Let introduce a spherical harmonic expansion of the CMB sky Multipoles at l encode angular information with characteristic angular scale (i.e. angular period) q 2p/l q l=0 l=1 l=2 l=3 l=4 l=5 l=6 etc monopole dipole quadrupole octupole etc

24 Graphic from WMAP website CMB snapshot with constrast smaller than 1/1000 It is just a monopole, l=0

25 THE MONOPOLE The CMB radiation has a blackbody thermal spectrum, with very nearly the same temperature T CMB in all directions on the sky The CMB is thus nearly isotropic in its rest frame and has a Lorentz-invariant distribution function where E CMB and T CMB is the photon energy in the CMB frame is the isotropic temperature.

26 Measurements of the spectrum can only be made with absolute temperature devices, such as FIRAS (Far-Infrared Absolute Spectrophotometer) on COBE: consistent with a blackbody distribution over more than 3 decades in frequency! CMB spectrum measured by FIRAS Intensity, 10-4 ergs/cm 2 sr sec cm -1 data points are obscured by the theoretical curve! waves/cm

27 Measurements of the spectrum can only be made with absolute temperature devices, such as FIRAS (Far-Infrared Absolute Spectrophotometer) on COBE: consistent with a blackbody distribution over more than 3 decades in frequency! CMB spectrum measured by FIRAS Intensity, 10-4 ergs/cm 2 sr sec cm -1 mean 5 waves/cm 2 mm 150 GHz 0.6 mev T=4K

28 More precisely T CMB = (2.726 ± 1σ COBE residuals (Mather et al 1994)

29 A blackbody of the measured temperature corresponds to

30 A blackbody of the measured temperature corresponds to while HENCE W g = r g /r c 0.2 h %

31 Graphic from WMAP website contamination from Milky Way along the equator snapshot of CMB with contrast at 1/1000 It is nearly a dipole, l=1

32 Graphic from WMAP website snapshot of CMB with contrast at 1/1000 (264,48 ) It is nearly a dipole, l=1 towards galactic coordinates

33 MOVING IN THE CMB If we see a photon with energy E and direction e, the relativistic Doppler shift gives where v is our velocity relative to the CMB. In our reference frame then the CMB has distribution function Still a blackbody if we let the observed temperature to vary over the sky as

34 Define q the angle between v and e. Expand in b =v/c dipole quadrupole etc due to the Doppler shift caused by solar system motion relative to the nearly isotropic CMB rest frame (the frame where the dipole would be zero) The observed dipole (first detected in the 1980s) has amplitude DT=(3.355±0.008) mk, HENCE the velocity of the solar system barycenter relative to the CMB is v = (369.0 ± 0.9) km/s, i.e. b 1.23 x 10-3

35 Define q the angle between v and e. Expand in b =v/c dipole quadrupole etc BUT contributions of the primordial perturbation to T anisotropies are at the level of 10-5 (18 mk) HENCE they dominate over the quadrupole and higher multipoles induced by solar system motion

36 Graphic from WMAP website HERE IS THE SNAPSHOT with contrast at the level of 1/100,000 AND DIPOLE REMOVED ignore the pattern around the equator as that is our own galaxy

37 Graphic from WMAP website HERE IS THE SNAPSHOT with contrast at the level of 1/100,000 AND DIPOLE & Milky Way REMOVED ignore the pattern around the equator as that is our own galaxy We can NOW investigate quantum noise spectral properties

38 We have then to consider the angular coherence of temperature fluctuations: multipole moment l

39 We have then to consider the angular coherence of temperature fluctuations: Since T=2.7K, fluctuations are 1 part in 10 5 multipole moment l No model other than the inflationary BB has yet explained the temperature fluctuations or ANISOTROPIES, which are about 10-5 (rms variation 18mK)

40 We have then to consider the angular coherence of temperature fluctuations: multipole moment l Correlations on the largest angular scales (so large that there has not been enough time for the universe to evolve). Measured by COBE, whose resolution was 7

41 We have then to consider the angular coherence of temperature fluctuations: 1 peak at twice full moon 300 multipole moment l

42 We have then to consider the angular coherence of temperature fluctuations: 1 Interesting structures below 1, called acoustic peaks 300 multipole moment l Acoustic oscillations arise because of a competition in the photon-baryon plasma in the early universe. The pressure of the photons tends to erase anisotropies, whereas the gravitational attraction of the baryons makes them tend to collapse to form dense haloes.

43 THERMAL HISTORY 1. Expansion 2. Recombination 3. Electron Glue 4. Acoustic Oscillations 5. Angular Peaks: Fist, Second and Higher Peaks 6. Diffusion Damping

44 Expansion There is evidence that galaxies receed The reason the night sky is dark is entirely due to the expansion, which cools the radiation temperature to 2.73 K The slope of the relation between the distance d and recession velocity v is defined to be the Hubble constant: H 0 =d/v = 100 h km s 1 Mpc 1 Numerically H 0 = (74±4) km s 1 Mpc 1 (h = ) Going back in time then

45 DEFINITIONS Comoving distance x AB between 2 points on the grid stays constant, A x AB B while the physical distance d AB evolves with time: d AB (t) = a(t) x AB scale factor whose present (t 0 ) value is set to 1 while a(t<t 0 )<1

46 It is convenient to define conformal time Since c = 1, η is also the maximum comoving distance a particle could have traveled since t = 0. It is often called the comoving horizon x H (t).. The physical horizon is a(t) times η:

47 Robertson-Walker Metric Observed homogeneity and isotropy of the universe allow to describe the overall geometry and evolution of the Universe in terms of 2 parameters accounting for the spatial curvature and the overall expansion where describes 3D space of constant curvature curvature constant k takes only the discrete values +1, 1, or 0 corresponding to closed, open, or spatially flat geometries

48 As the universe expands, everything that isn't bound by electromagnetic or other interactions expands with it, including physical distances and wavelengths of CMB photons z is called redshift today z(t 0 )=0 and hence the temperature of the Universe decrease

49 The physical size d O (t) of an object is related to its comoving size x O by d O (t) = x O a(t) If the object is now seen by us to subtend an angle q, we define its angular diameter distance d A (t) as d O (t) = q d A (t) It properly takes into account the expansion of the Universe between t and t 0. In a nonexpanding Universe, this would simply be the physical distance between us and the object.

50 The physical size d O (t) of an object is related to its comoving size x O by d O (t) = x O a(t) If the object is now seen by us to subtend an angle q, we define its angular diameter distance d A (t) as d O (t) = q d A (t) It properly takes into account the expansion of the Universe between t and t 0. In a nonexpanding Universe, this would simply be the physical distance between us and the object. The expression depends on the evolution of the content of the Universe. For a flat Universe, we have Usually: we suppose we know d O (t), we measure q we determine d A (t), i.e. how the universe has evolved

51 Recombination Going backwards in time, CMB photons have shorter wavelengths and temperature increase At 3000K, CMB photons ionize hydrogen Going forwards in time p and e combine to form H. This process is called recombination Before this time, the universe was a plasma of CMB photons, e, p (and a small amount of He and heavier elements), This mix is referred to a as photon-baryon plasma.

52 Derivation of z at recombination In the era preceding recombination, photons were primarily coupled to matter through the reaction requiring the photon to have an energy of at least 13.6 ev. As long as photons are coupled to matter, this reaction will be in statistical equilibrium, and the Saha eq. can be applied to determine the equilibrium values of the constituents where n stands for number density and Q is the binding energy of hydrogen Charge neutrality requires n e = n p. Defining the fractional ionization as the Saha equation can be rewritten as

53 The number density of photons is given by Put Saha eq. in terms of baryon-to-photon ratio η 10 9 (measured in BBN), i.e. the number density of baryons /number density of photons, Solving for a 50% ionization yields T rec 4,000 K Since T rec = (1 + z) K, this gives z 1,500 This T is roughly 0.3 ev, lower than Q. The reason is that photons greatly outnumber baryons η There will be some photons in the Wien region of the black body spectrum with E>13.6 ev. Their number does not drop below the number of H atoms until T is roughly 4000K or 0.3eV. A more careful treatment of the physics of recombination (here we assumed thermodynamic equilibrium and recombination directly to the H ground state) yields a value closer to z = 1,100

54 Electron Glue In the plasma before recombination, free electrons act to glue the CMB photons to the baryons. Thomson scattering couples photons to electrons E.m. Coulomb interactions couple electrons to baryons The plasma behaves as a nearly perfect fluid there are more CMB photons than baryons or electrons.

55 The photon-baryon fluid is sitting in the gravitational potential wells that are the seeds of structure in the universe Regions of high (low) density generate potential wells (hills). As gravity tries to compress the fluid, photon radiation pressure opposes the squeezing

56 The photon-baryon fluid is sitting in the gravitational potential wells that are the seeds of structure in the universe Regions of high (low) density generate potential wells (hills). As gravity tries to compress the fluid, photon radiation pressure opposes the squeezing The result is an oscillating sequence of compressions and rarefactions By analogy to the process in air, we call these oscillations in the photon-baryon fluid sound waves or acoustic oscillations.

57 Acoustic oscillations Compression in the wells corresponds to rarefaction in the hills wells hotter, hills colder in our color scheme red is cold and blue is hot Pattern of sound imprinted in the temperature of CMB

58 Inflation lays down potential fluctuations on all scales Take the T fluctuation in space and Fourier decompose it into plane waves of various wavelengths. Each mode oscillates independently: The frequency of the oscillation is w = kc s, where c s is speed of sound Assume negligible initial velocity perturbations, T distribution at recombination (*) is where is the sound horizon (the distance sound can travel by the conformal time) Oscillations are frozen in at recombination when the baryons release the photons

59 HENCE, for scales larger than sound horizon at recombination (ks * 1), the perturbation is frozen into its initial conditions WHILE modes that reach extrema of their oscillation (maximal compression or rarefaction ) at recombination will carry enhanced temperature fluctuations PEAKS (ks * = n 2p) The special modes for which the fluid just has enough time to etc compress once compress and rarify once The wavenumbers of the peaks are harmonically related to sound horizon

60 Recall what happens to sound in a cavity of a musical instrument: There are frequency harmonics of the fundamental tone For CMB, the cavity is the amount of time before recombination h(t rec ) = x H (t rec ) and thus there exists a fundamental frequency fundamental angular scale Because sound travels at a fixed speed we can also associate a fundamental scale to this, i.e. s(t rec ) the distance sound can travel in the amount of time before recombination From: W.Hu and M.White, The cosmic Symphony, 2004

61 ANGULAR SCALE (ROUGH) At recombination z =1100, hence a(t rec ) 1/1100 The comoving horizon (or conformal time) was largely determined by matter dominated epoch The comoving horizon now is equal to the physical horizon now Hence we see the comoving horizon at recombination to subtend an angle (angular size of the moon is 0.5 ) corresponding to multipole l 210

62 HORIZON PROBLEM There must not have any causal contact beyond Horizon But the Universe is very nearly isotropic and homogeneous! Why then are the large number of causally disconnected regions we see on the microwave sky all at the same temperature? WAY OUT = INFLATION Univese should have expanded faster than speed of light

63 Angular peaks Consider the CMB at recombination Since sound horizon is huge - on order 100 Mpc (comoving) or 100,000 light years (physical), an observer right around recombination will see an essenentially isotropic CMB As time progresses, radiation from more distant regions reach us You first see a quadrupole, then an octopole, etc Spatial temperature variations are viewed as angular variations of an increasingly fine angular scale

64 Modes caught at extrema of their oscillations become the peaks in the CMB power spectrum. They form a harmonic series based on the sound horizon distance, that is about a degree on the sky today.

65 PEAK MULTIPOLES a spatial inhomogeneity in the CMB temperature of wavelength λ at redshift z appears as an angular anisotropy of scale In a flat matter dominated universe and since z * = 1100 comoving angular diameter distance from the observer to redshift z Now with So, acoustic peaks are located at

66 but HENCE Since we are measuring ratios of distances the absolute distance scale drops out; the Hubble constant sneaks back because the Universe is not fully matter-dominated at recombination

67 First peak First peak precisely measured. Shape and position in beautiful agreement with standard cosmological models The position of that first peak, and indeed all of the peaks, depend sensitively on the spatial curvature of the universe Flat Open As the curvature decreases the peaks move to smaller angles (higher multipole l) while preserving their shape

68 In a spatially curved universe, the angular diameter distance no longer equals the coordinate distance making the peak locations sensitive to the spatial curvature of the Universe Consider a curved universe with radius of curvature R CLOSED FLAT OPEN objects in a closed universe open universe appear closer further than they are!.as if seen through a lens! HENCE l a < 160 l a = 160 l a > 160

69 The position of that first peak, and indeed all of the peaks, mildly depends on dark energy Consider some amount of dark energy making the universe flat despite a sub-critical density of matter. There is a small shift* to larger angular scales (lower multipoles) *This is because the cosmological constant produces a small change in the distance light can travel since recombination (related to its well known effect on the age of the universe).

70 Observationally The position of the first peak indicates that the universe is close to spatially FLAT, i.e. its energy density close to critical A flat universe has W m +W L =1 and lies on the red line Many observations indicate that the matter energy density is sub-critical, so that dark energy is required to make these statements consistent (required amount of dark energy also consistent with that needed to explain distant supernovae)

71 Second peak Is evidence of sound waves. First detection in 2001 by the DASI, Boomerang and Maxima Baryons load down the photon-baryon oscillations The odd peaks are associated with how much the plasma compresses: they are enhanced by an increase in the amount of baryons in the universe. The even peaks are associated with how much the plasma rarefies): they are not changed. With the addition of baryons odd peaks are enhanced over even ones. In particular: the first acoustic peak becomes much larger than the second. The more baryons, the more the second peak is relatively suppressed.

72 If the baryons contribute a negligible amount of mass to the plasma, the CMB temperature oscillates symmetrically around zero. With more baryons in the system, compressions inside potential wells are increased over rarefactions: the oscillation is now asymmetric

73 If the baryons contribute a negligible amount of mass to the plasma, the CMB temperature oscillates symmetrically around zero. With more baryons in the system, compressions inside potential wells are increased over rarefactions: the oscillation is now asymmetric The power spectrum doesn't care about the sign. First and third peaks are enhanced over the second peak.

74 This is indeed reflected in the power spectrum of the anisotropies. Odd peaks are enhanced in amplitude over even ones as we increase the baryon density of the universe Other related effects due to the baryons: 1. adding baryons to the plasma decrease the frequency of the oscillations pushing the position of the peaks to slightly higher multipoles l. 2. baryons affect the way the sound waves damp and hence how the power spectrum falls off at high multipole moment lorsmall angular scales. The many ways that baryons show up imply that the power spectrum has many independent checks on the baryon density of the universe The baryon density is measured to exquisite precision by CMB.

75 Observationally Second peak is observed to be substantially lower than first peak indicating that the baryon density is around W b h 2 =0.02 (in agreement with nucleosynthesis) Evidence that there are missing baryons in the universe, i.e. that most the baryons are not in stars (hence dark baryons).

76 Higher peaks Series of higher acoustic peaks is sensitive to the energy density ratio of dark matter to radiation in the universe. If the energy density of the radiation dominates the matter density, we can no longer consider the photon-baryon fluid to be oscillating in a fixed gravitational potential well: pressure support in the radiation causes the gravitational potential to decay, at exactly the right time to drive the amplitude of the oscillations up The higher peaks began their oscillation in the radiation dominated universe and have an enhanced amplitude

77 This driving effect does happen once the density of the universe is dominated by the dark matter. We expect a distinction between large l oscillation started when universe was radiation dominated small l oscillation started when the universe was already matter dominated We expect a peak amplitude enhancement going from low to high multipoles. Where this transition occurs tells us the energy density ratio of matter to radiation in the universe. Raising the dark matter density: 1- reduces the overall amplitude of the peaks, in particular small l ones 2- enhances the baryon loading effect So, a high third peak is an indication of dark matter

78 Observationally a third peak that is boosted to a height comparable to or exceeding the second, is an indication that dark matter dominated the matter density in the plasma before recombination.

79 Diffusion damping The amplitude of the acoustic peaks drops off rapidly at the highest multipoles or smallest angular scales. CMB photons random walk through the baryons during recombination For fluctuations with a short wavelength, hot and cold photons mix and average out The acoustic peaks are exponentially damped on scales smaller than the distance photons random walk during recombination the damping tail provides a beautiful consistency test for the standard model of cosmology

80 The physical scale of the damping depends on: - the baryon density through the mean free path - the matter density through the time available for the photons to random walk. Raising the baryon density shifts the damping tail to higher multipoles Raising the matter density shifts the damping tail to lower multipoles Consistency checks from the damping tail will verify or falsify our assumptions about recombination and initial conditions

81 Galactic coordinates The galactic coordinates use the Sun as vertex. Galactic longitude l (0-360) Is measured with baseline the direction to the center of the galaxy from the Sun in the galactic plane, while the galactic latitude b (0-180) is measured between the object and the galactic plane with origin at the Sun Artist's depiction of the Milky Way galaxy, showing the galactic longitude relative to the sun