UBC Faculty Research and Publications

WMAP : Measuring how the universe began 2008

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1During today’s  talk, WMAP will survey 1/3 of the sky (again).While we have been talking, WMAP has surveyed 1/3 of the sky. Sun shadow lines WMAP: Measuring how the universe began Mark Halpern, UBC Beginning to constrain Inflation. 2 3 4Graphics from Dicke, Peebles,  Roll and Wilkinson, Ap J  142  1965. The Universe was much hotter and denser in the past. It  has been transparent since the primordial plasma became neutral, ~380,000 years after the start. 5Verification of the big bang:  We see the thermal emission from the primordial plasma everywhere on the sky.  It has the expected spectrum. 6Distortion of the CMB spectrum • Energy release at z>107 double Compton efficient to recreate thermal equilibrium • Energy release at 105<z<107 inverse Compton generates a Bose-Einstein distribution • Energy release at 103<z<105 inverse Compton effective but not toward the equilibrium 7 8Inflation, an incredibly rapid early expansion, solves both the flatness and horizon problems by expanding small causally connected regions beyond their “horizons,” 9Predictions of Inflation: 1. Nearly Scale Invariant spectrum;          COBE 2. Nearly Flat geometry;                           Toco+2Df, Boomerang 3. Superhorizon scale fluctuations;           WMAP-1 4. Gaussian distributed fluctuations;         WMAP-1 5. Spectral index just less than 1; 6. Relic Gravitational radiation. The precision of these tests are now beginning to get interesting. Outline:    Data and simple parameter fits. Comparison to other astronomical data. Extensions of the model to test inflation. 10 Q-Band 41 GHz 30’ FWHM 11 V-Band  61 GHz   19’ FWHM 12 W-Band  94 GHz   12’ FWHM 13 The lowest few terms in the spherical harmonic expansion of the temperature are fit explicitly by maximum likelihood in pixel space. At higher l we use power spectrum estimation like a fourier transform. These images are the decomposition of the ILC map into low l modes and are NOT used in power spectrum estimation. Fluctuation Spectrum: 14 Above l=10 the TE cross- power spectrum is derived from the TT spectrum with no ambiguity; motion giving rise to the acoustic peaks gives rise to a correlated polarized signal. This green model has no free parameters above l~10. Temperature variations Polarization The motion below l~200 is taking place on scales larger than the horizon at the time of the motion. The ripples in the power spectrum--called acoustic peaks--confirm a generic prediction of any big bang model 15 WMAP-3yr (Black) WMAP-1 yr (Grey) Cosmic Variance-(Gum) Notice how little difference there is l by l between 1-year and 3-year data. The sharp “snake bites” at l=180 and 205 are slightly smaller, but still present. The TT power spectrum is now cosmic-variance limited out to l =400. 16 In a flat universe, the angular scale of the first acoustic peak tells us the age of the universe. 17 Baryon density and Dark Matter density are constrained by the heights of the second and third acoustic peaks, respectively. 2nd peak- baryons & DM out of phase 3rd peak--back in phase 18 WMAP data are fit to 6 parameters: Baryon density, Total matter density, Current expansion rate, Optical depth to the CMB, Slope of the fluctuation spectrum, Amplitude of the fluctuation spectrum. In the simplest fits we assume Flat, do not fit for Λ, age or w. Chi-squared is  1.041 for ~4000 DoF 19 Comparison to direct measurements of expansion, H(z) Dark Blue rectangle:  HST Key Project result. Lambda CDM with WMAP parameter values “predicts” direct measurements of expansion rate vs redshift. 20 Location of the first peak In a flat universe the location of the first acoustic peak tells us the age of the universe. In the end, we calculate t from the results of the full 6-D fit. WMAP Age :13.73 +0.13 -0.17 Gyr Richer et al. (2004) Fits to white dwarf cooling curves give an age estimate for the globular cluster they live in: WD Age:  12.1 Gyr Add to this an estimate for globular cluster formation and star ignition. The Universe is older than the stuff in it is. 21 WMAP data alone “predict” the amplitude and shape of the power spectrum probed at much smaller physical scales by 3D surveys of the distribution of galaxies in redshift space. The data here in red and orange are the WMAP 1σ and 2σ predictions. The bars in purple are from the 2 Degree Field redshift survey. (Adjacent bars are correlated.) 22 The baryon-to-photon ratio is the only free parameter in calculating nuclear fusion models of the first few minutes.  The WMAP constraint agrees with direct measurements of primordial abundance (if you ignore lithium). 23 If we do not assume flatness  a variety of fits become acceptable to WMAP alone. 24 Inclusion of any one of a number of other astronomical measurements restricts the allowed region to be very close to flat. Supernavae measure a distance to z~1. Baryon Acoustic oscillations measure a distance to z~0.35. Either of these in combination with the CMB distance to z=1035. Constrains geometry. 25 In addition to the six parameters some others are held at “obvious” values of 1 or 0. For example, flat means Ωb + Ωm + Λ=1 so we do not need to fit for all 3. First, lets see how the six parameter model does against other data. Then let’s see about other parameters, relaxing flatness, exploring non-Λ cosmologies, adding gravitational radiation… 26 Relaxing the model  I: Do not insist on Lambda.  Let the ratio of pressure to density be a free parameter. w = P/ρ w= -1  for a simple cosmological constant. WMAP alone allows a range for w, but the constraints become pretty good when supernovae data are added. 27 Solid: h=0.71  neutrino density=0 Dashed: h=0.60  neutrino density=0.02 2dF Lyman Alpha The comparison of WMAP to 2dF constrains the neutrino mass. Massive neutrinos can hide in the CMB… ... but at low redshift they are no longer relativistic and have a big effect on galaxy clustering. Relaxing the model  II: 28 Lower limit from mass- squared differences in SNO. SNO limit if  lightest ν is single We are moving toward a level of precision where we might usefully fit neutrino mass and w simultaneously.   (We do still need a factor of 10!) 29 Relaxing III: Constraints on Inflation: In monotonic inflationary potentials such as after N e-foldings, we expect the tensor/scalar ratio and spectral index to obey Inflationary expansion simultaneously drives the amplitude of fluctuations, and therefore Gravitational radiation, to zero and also drives towards a scale invariant spectrum, n=1.


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