Cosmic Microwave Background References: COBE web site WMAP web site Web sites of Wayne Hu, Max Tegmark, Martin White, Ned Wright and Yuki Takahashi R&L Problem 4.13 Show that an observer moving with respect to a blackbody field of temperature T will see blackbody radiation with a temperature that depends on angle according to ( ) 1/ 2 T ʹ = 1 β2 1+ βcosθ ʹ T We showed that where I ʹ ν ʹ = 2h ν ʹ 3 c 2 e hν ʹ ( / kt ' 1) 1 = 2h ν ʹ 3 c 2 e hν / ( kt 1) 1 Planck function 1
The Doppler formula implies So, if we define Then for each direction For β << 1 T T(1-β) > T T(1+β) > T v T So because the Earth is moving with respect to the Cosmic Microwave Background, it appears cooler in the direction towards which we are going, and warmer in the opposite direction 2
Map of T across sky, as measured by WMAP T = 2.725, very accurately Planckian. Uniform to 1 part in 10^5 Subtracting T=2.75K, what you see is a DIPOLE The CMB temperature is 3.353 K hotter in one direction, and 3.353 mk cooler in the opposite direction. Milky Way The CMB defines a cosmic reference frame. The Earth is moving with a peculiar velocity with respect to the Hubble flow of galaxies. 3
The observed dipole indicates that the Solar System is moving at 368+/-2 km/sec relative to the observable Universe in the direction galactic longitude l=263.85 o and latitude b=48.25 o with an uncertainty slightly smaller than 0.1 o Earth s Motions (1) Earth spins on its axis V 0.5 km/sec at equator (2) Earth orbits Sun V 30 km/sec heliocentric velocity (3) Sun orbits Galactic Center, in Milky Way Galaxy V 225 km/sec 4
(4) Milky Way falling towards M31 V 100 km/sec (Andromeda) in the Local Group M31, Andromeda (5) Local Group is falling into the V 220 km/sec Virgo supercluster of galaxies Virgocentric infall center of the Virgo Cluster of Galaxies 5
(6) Virgo Supercluster is falling V 600 km/sec towards the Hydro and Centaurus clusters of galaxies The Great Attractor ~10^16 solar masses at 50 Mpc (7) Claims of larger scale flows??? Probably not Lauer-Postman Brightest cluster E s SN Ia 6
COBE data of CMBR c. 1992 First detection of temperature fluctuations, i.e. CMBR anisotropies Milky Way Subtract dipole temperature fluctuations indicates density fluctuations which later collapse to form galaxies, clusters, etc. 7
4/8/11 Since WMAP: -Balloon experiments at S. Pole - Boomerang - Radio telescopes at S. Pole: - DASI - QUAD - Radio telescopes in Chile Planck Satellite: Launched 2009. All sky picture in mm 8
The History of the Universe from t=0 to t=380,000 years 1. t=0 to the Planck Time. The Planck Time = 10-43 seconds after the Big Bang. This is when the cosmological horizon was smaller than an electron. Before this, we're pretty sure that normal Quantum Mechanics doesn't apply. Horizon: Because the universe is t seconds old, parts of the Universe farther apart than d=ct are not causally connected. Remember, the Universe is infinite; expansion is not like a balloon blowing up, or a raissen bread rising, which has a center of expansion, and where the expansion is in a directions in x,y,z space. 2. The GUT era; Inflation. GUT = grand unified theory When the GUT divided into the strong/electroweak/gravity forces, the Universe INFLATED very very rapidly. In 10-36 sec, a piece of the Universe the size of an atom expanded to the size of the Solar System. INFLATION is a natural explanation of the HORIZON PROBLEM. Why is the CMBR temperature the same in all directions? 9
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The flatness problem Why is space so nearly flat? If Ω were even a tiny bit different than 1, it would by now be WAY different. 11
Inflation of the Universe happened when the Universe had cooled far enough that symmetry breaking of the GUT force could occur -- sometimes described as a phase transition. Only a small part of the Universe which was within our Horizon just prior to inflation remained in our Horizon after inflation. 12
The huge factor by which the Universe expanded also explains why we re nearly flat. Here s a 2D representation of a 3D surface that is nearly flat when expanded. Note that during inflation the radius of curvature of the geometry of the Universe increased effectively faster than the speed of light. But since the expansion was on the geometry of the Universe itself, and not the matter, then there is no violation of special relativity. Our visible Universe, the part of the Big Bang within our horizon, is effectively a `bubble' on the larger Universe. However, those other bubbles are not physically real since they are outside our horizon. We can only relate to them in an imaginary, theoretical sense. They are outside our horizon and we will never be able to communicate with those other bubble universes. 13
Since the Universe was opaque prior to recombination, you might think that it s difficult to observe directly anything that happened before recombination. However, during inflation, the expansion may have generate gravitational waves which would cause ripples in the density of the Universe, which would be reflected in the CMB. The amplitude of the gravity wave generated is proportional to the expansion rate H during inflation, which in turn is proportional to the inflation energy scale squared: GW amplitude H E inf2, where E inf ~<10 16 GeV So detecting the signature of these gravitational waves in the CMBR could test the inflation model and measure E inf. 14
Back to the history of the Early Universe: 3. t=10-38 sec to 10-10 second after the big bang: THE ELECTROWEAK era 4. 10-10 second to 0.001 second: The Particle Era The Universe was filled with electrons, neutrinos and quarks. 3 quarks = proton, anti-proton, neutron, antineutron but the universe was too hot for the quarks to be bound together as protons or neutrons. When the Universe finally cooled for the quarks to form protons, neutrons, etc. the protons and anti-protons rapidly annihilated, forming photons. The protons slightly outnumbered anti-protons, so we were left with protons and photons. Photons outnumber protons by a billion to one. There are approximately 400 photons / cm 3 currently in the CMBR. 5. 0.001 second to 3 minutes: The era of Nucleosynthesis The Universe cooled to temperature = 10 9 K, similar to the core of the Sun. As in the core of the Sun, fusion of hydrogen into helium created a Universe with about 25% helium (by mass), plus very small amounts of deuterium (proton + neutron) and lithium. The exact ratios of He/hydrogen, deuterium/hydrogen etc depend on the density of baryons (protons & neutrons) and the temperature of the Universe at during this era. These in turn depend on cosmological parameters such as the expansion rate of the Universe. 15
Helium-4 is measured in by looking at emission lines in spectra of H II regions in dwarf galaxies. Li/H is measured by spectroscopy of old star stellar atmospheres. D/H is measured by looking at quasar absorption lines from distant galaxies. (6) t=300,000 years: Recombination. Electrons and protons recombined, the opacity of the universe to Thomson scattering went to zero, and the photons were then free to stream to us. 16
CMBR Anisotropies Shortly after the CMB was discovered by Penzias & Wilson, Sachs & Wolfe (1967 ApJ, 147, 73) and others realized that there should be angular variations in temperature, as a result of density inhomogeneities in the Universe at the time of recombination. The denser regions cause the CMB photons to be gravitationally redshifted compared to photons arising in less dense regions. Another effect is that regions that were overdense recombined first because the recombination rate depends on n 2. The amplitude of the T fluctuations is roughly 1/3 of the density fluctuations. These slightly overdense regions at the time of CMB production later became gravitationally unstable and collapsed to form galaxies, clusters of galaxies and all other structures we see in the Universe today. From the observed CMBR angular anisotropies in temperature, it is straight-forward to derive what density fluctuations created them. WMAP temperature fluctuations 17
The fluctuations in temperature are at a level of 10-5 T, and so were difficult to measure first detection was in 1992. The angular distribution of the temperature fluctuations are modeled in terms of spherical harmonics, which are the convenient functions for describing a scalar field projected on a sphere: This is like describing a light curve in terms of the power series, i.e. the coefficients of the sine s and cosines of different frequencies which, when summed, reproduce the observed light curve. If the underlying density fluctuations are described by a gaussian random process, as inflation predicts, then all the information is contained in the angular power spectrum, The angled brackets indicate the average over all observers in the Universe; the absence of a preferred direction in the Universe implies that the coefficients are independent of m. 18
Usually people don t plot C l but since you can write So is a measure of the power in the temperature fluctuations per logarithmic interval in l space 19
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The exact mixture of material in the early Universe (baryonic, neutrinos, cold dark matter), cosmological parameters (H0, vacuum energy) and initial perturbation spectrum control the position and amplitude of these peaks and troughs. 21
The dependence of the peaks on parameters are understandable in terms of physical processes, but are beyond the scope of this discussion. The position of the first peak is sensitive to the total energy density and can be used to determine the geometry of the Universe:. It moves to smaller angles as l decreases because the distance to the last-scattering surface increases (the expansion slows less in a low-density universe) and geodesics (i.e. the path of light rays) diverge in negatively curve spaced (fixed distance on the last-scattering surface subtends a smaller angle). Individual l s 22
Cumulative C l Temperature differences between points on the sky separated by angle θ are related to the multipoles with spherical-harmonic indices around For example, the density fluctuations of wavelength around 2Mpc, which seed galaxies, subtend an angle θ of around an arcminute; those of 20Mpc that seed clusters of galaxies subtend about 10 arcminutes; and those of around 200Mpc that seed the largest structures seen today subtend about 1 degree. (All of these distances were a thousand times smaller at the time of last scattering, when the linear size of the universe was a thousand times smaller... But it is conventional to quote ``comoving separations'' as they would be now.) 23
What caused the density fluctuations? There are basically two models: (1) Before inflation, there were quantum fluctuations on subatomic scales which were stretched to astrophysical size during inflation. These fluctuations became density perturbations when the vacuum energy that drove inflation decayed into radiation and matter. (2) The competing theory says that the density perturbations were seeded by topological defects. Depending upon how the symmetry is broken during inflation these defects might be point-like (global monopoles), one-dimensional (cosmic strings), or three-dimensional (spacetime textures). It turns out that topological defects create density perturbations which develop significantly later than the quantum fluctuation model, and so there is a signature in the CMB. The current anisotropy data appear to be consistent with inflation and inconsistent with the topological defect scenario 24
Hot /cold Spots in the CMB Observed Predicted, For different Geometries Of the Universe Flat theory CMB temperature fluctuations reality 25
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One thing to keep in mind: All these maps require that you clean out the foreground emission, i.e. the emission from the solar system, Milky Way and foreground galaxies. How this is done is a long story, but essentially they make maps at several frequencies, and subtract out models for the foreground emission sources. Zodiacal Light: thermal emission from dust in the solar system Milky Way: thermal emission from dust in the Milky Way 27
COBE DIRBE map The foreground is particularly bad for measurements of CMBR polarization. WMAP measurement of polarization: white lines indicate direction of linear polarization; most of this is caused by B-fields in the Milky Way. 28
Polarization of the CMBR itself is very interesting. If the Universe were perfectly homogeneous and isotropic, Thompson scattering would of course produce linear polarization as we discussed in class, but the directions of polarization from all the photons would cancel out so no net polarization would be seen. However, if there are quadrupole anisotropies in the density of the Universe, then the Thompson scattering will have preferred direction for each size scale, resulting in a net polarization. The % polarization is really small so the fluctuation map of fluctuations in polarization will have amplitudes several orders of magnitude smaller than the temperature fluctuations. But WMAP, and DASI have recently claimed detection of the spectrum of polarization fluctuations for the CMB. Thomson Scattering 29
Thomson scattering in Isotropic Radiation Field Thomson Scattering in Radiation Field with quadropole anisotropy 30
When an electromagentic wave is incident on a free electron, the scattered wave is polarized perpendicular to the incidence direction. If the incident radiation were isotropic or had only a dipole variation, the scattered radiation would have no net polarization. However, if the incident radiation from perpendicular directions (separated by 90 ) had different intensities, a net linear polarization would result. Such anisotropy is called "quadrupole" because the poles of anisotropy are 360 /4 = 90 apart hotter colder Wayne Hu What would cause quadrupole anisotropies? 3 possibilities: Scalar perturbation: Energy density fluctuations Vector perturbation: Vorticity in the plasma cause Doppler shifts resulting in the quadrupole lobes in the figure. However, vorticity would be damped by inflation and is expected to be negligible. Tensor perturbation: Gravity waves stretch and squeeze space in orthogonal directions (as shown by the test 'circles' in the figure). This also stretches the wavelength of radiation, therefore creating quadrupole variation in incoming radiation temperature. Gravity waves from inflation would produce tensor perturbation. 31
The NASA press release had this representation of the WMAP data on polarization: The polarization pattern in the sky can be decomposed into 2 components: Curl-free component, called "E-mode" (electric-field like) Grad-free component, called "B-mode" (magnetic-field like) The E-mode may be due to both the scalar and tensor perturbations, but the B-mode is due to only vector or tensor perturbations. E-mode: <= Scalar / Tensor perturbations, corr. w/ T perturbations B-mode: <= Vector / Tensor perturbation, not corr. w/ T perturbations E-mode B-mode 32
E-mode polarization fluctuations have been detected by a number of experiments, most notably DASI. B-mode polarization fluctuations Based on the WMAP data, we have a limit on B-mode polarization -- all we know is that the energy scale of inflation must have been < 3x10 16 GeV. When we detect the gravity wave signal in the CMBR polarization maps, we will be able to measure the energy scale of inflation: so it will be an observation of the Universe 10-35 seconds after the Big Bang. 33