Morphological Studies of the CMB: Non-standard Models and Foregrounds Theresa R. Jaffe Munchen¨ 2006 Morphological Studies of the CMB: Non-standard Models and Foregrounds Theresa R. Jaffe Dissertation an der Fakult¨at fur¨ Physik der Ludwig{Maximilians{Universit¨at Munc¨ hen vorgelegt von Theresa R. Jaffe aus Honolulu, USA Munc¨ hen, den 31. August 2006 Erstgutachter: Prof. Dr. Simon D. M. White Zweitgutachter: PD Dr. Peter Schuc¨ ker Tag der mundlic¨ hen Prufung:¨ 9. Oktober 2006 Contents Zusammenfassung xv Abstract xvii 1 Introduction 1 1.1 The CMB and the Physics of the Early Universe . 2 1.1.1 The Expanding Universe . 2 1.1.2 Primordial Perturbations and Inflation . 3 1.1.3 Physics and the Power Spectrum . 4 1.2 Observations . 13 1.2.1 Measurement to Cosmology . 13 1.2.2 Telescopes . 16 1.2.3 Foregrounds . 17 1.3 Statistical Isotropy and Gaussianity . 24 1.3.1 Queerness of the Quadrupole and the Oddness of the Octopole . 25 1.3.2 Axis of Evil . 26 1.3.3 Cold Spot . 26 1.3.4 Power Asymmetry . 28 1.3.5 Other . 28 1.4 Non-standard Cosmological models . 30 1.4.1 Compact Topologies . 31 1.4.2 Bianchi Models . 32 1.5 Aims . 33 2 Fast and Efficient Template Fitting 35 2.1 Introduction . 35 2.2 Methods . 36 2.2.1 Template Fitting . 36 2.2.2 Total Convolver . 38 2.2.3 \Best" fit model and significance . 39 2.2.4 Visualisation: cross-correlation signal maps . 40 2.3 Data and simulations . 40 2.3.1 Bianchi Models . 41 vi CONTENTS 2.3.2 Data . 42 2.3.3 Gibbs samples . 45 2.3.4 Assumed signal covariance . 45 2.4 Performance, bias, and accuracy . 46 2.4.1 Model selection accuracy . 46 2.4.2 Full-sky fitting accuracy . 47 2.4.3 Cut-sky fitting accuracy . 47 2.4.4 Chance alignments . 48 2.5 Application to the first-year WMAP data . 49 2.5.1 Fits over model space grid . 49 2.5.2 Two best fits . 50 2.5.3 Location and orientation accuracy . 56 2.5.4 DMR fit . 57 2.5.5 Sensitivity to assumed power spectrum . 57 2.6 Implications . 58 2.6.1 Quadrupole amplitude . 59 2.6.2 Low-` alignment and planarity . 59 2.6.3 Large-scale power asymmetry . 60 2.6.4 Wavelet kurtosis . 60 2.7 Discussion and Conclusions . 62 2.8 Addendum . 63 3 Bianchi Type VIIh Models with Dark Energy 65 3.1 Introduction . 65 3.2 Bianchi Models with Λ > 0 . 66 3.2.1 Solution . 66 3.2.2 Properties . 69 3.3 Viability of a Bianchi Type VIIh Model . 71 3.3.1 Matter Density and 'Geometric' Degeneracy . 71 3.3.2 Optical Depth . 73 3.3.3 Supernovae, H0, etc. 75 3.3.4 Other Bianchi Models . 76 3.3.5 Other Dark Energy Models . 77 3.3.6 Small-scale Structure . 77 3.3.7 Early Universe . 78 3.4 Discussion and Conclusions . 79 4 Cross-Correlation in WMAP Foreground Analysis 81 4.1 Galactic Foreground Templates . 81 4.1.1 Dust . 83 4.1.2 Free-Free . 83 4.1.3 Synchrotron . 84 4.2 Method . 86 CONTENTS vii 4.2.1 Simultaneous fitting of multiple templates to multiple bands . 86 4.2.2 Constrained fits . 87 4.2.3 Application . 88 4.3 Simulations and testing . 89 4.3.1 Cross-talk . 89 4.3.2 Monopole and Dipole . 90 4.3.3 Stability . 90 4.3.4 Constrained fits . 90 4.4 Fit Results for WMAP . 91 4.4.1 Smoothing and Sky Cut . 92 4.4.2 DMR comparison . 94 4.4.3 WMAP-team analysis . 96 4.4.4 Finkbeiner analysis . 96 4.5 Spectral variations in synchrotron . 99 4.5.1 Maps . 99 4.5.2 Pseudo-C`s . 99 4.5.3 Simulations . 101 4.6 Conclusions . 103 5 The Spectra of Galactic Components 107 5.1 Introduction . 107 5.2 Templates used in the analysis . 109 5.2.1 WMAP data . 110 5.2.2 The Hα free-free template . 110 5.2.3 The dust template . 112 5.2.4 The synchrotron template . 113 5.3 Field selection . 114 5.4 Cross-correlation analysis . 116 5.4.1 Method . 116 5.4.2 Results of the cross-correlation analysis . 118 5.4.3 Free-free emission . 118 5.4.4 Anomalous dust emission . 119 5.4.5 Synchrotron emission . 119 5.5 Discussion . 122 5.5.1 Free-free emission . 122 5.5.2 Dust emission . 123 5.5.3 Synchrotron emission . 126 5.6 Comparison with WMAP3 . 127 5.7 Conclusions . 128 5.A Aliasing of foregrounds due to CMB subtraction . 130 5.B The reliability of T{T versus C{C fits . 131 5.C Full fit results . 134 viii CONTENTS 6 Phase analysis 137 6.1 Introduction . 137 6.2 Methods . 139 6.2.1 Return mapping statistic . 139 6.2.2 Kuiper's statistic . 141 6.2.3 Statistical mapping . ..