Small-Scale Secondary Anisotropics in the Cosmic Microwave Background by Jonathan Dudley M.Sc. Department of Physics McGill University Montreal, Quebec August 2007 A thesis submitted to McGill University in partial fulfilment of the requirements of the degree of Master of Science in Physics © Jonathan Dudley (2007) Library and Bibliotheque et 1*1 Archives Canada Archives Canada Published Heritage Direction du Branch Patrimoine de I'edition 395 Wellington Street 395, rue Wellington Ottawa ON K1A0N4 Ottawa ON K1A0N4 Canada Canada Your file Votre reference ISBN: 978-0-494-51263-0 Our file Notre reference ISBN: 978-0-494-51263-0 NOTICE: AVIS: The author has granted a non­ L'auteur a accorde une licence non exclusive exclusive license allowing Library permettant a la Bibliotheque et Archives and Archives Canada to reproduce, Canada de reproduire, publier, archiver, publish, archive, preserve, conserve, sauvegarder, conserver, transmettre au public communicate to the public by par telecommunication ou par Plntemet, prefer, telecommunication or on the Internet, distribuer et vendre des theses partout dans loan, distribute and sell theses le monde, a des fins commerciales ou autres, worldwide, for commercial or non­ sur support microforme, papier, electronique commercial purposes, in microform, et/ou autres formats. paper, electronic and/or any other formats. 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Canada ACKNOWLEDGEMENTS First and foremost I wish to acknowledge the the efforts and contributions of my supervisor Gil Holder, whose guidance and discussions have proved invaluable to my graduate experience. I also wish to thank Olivier Dore for valued contributions to this work as well as the use of the Legacy Archive for Microwave Background Data Analysis (LAMBDA). Support for LAMBDA is provided by the NASA Office of Space Science. I would also like to acknowledge all the educators whose dedication and interest in physics helped spark my own. Amongst them there are two that deserve special mention: Mr. Robert Miller and Prof. Roman Koniuk. Their seemingly endless knowledge and genuine passion for teaching are the two principle reasons that I be­ came, and remain, a student of physics. Also deserving of mention are the denizens of ERP-225 who provided the insightful and often esoteric discussion that is so necessary for a productive workspace. Finally I wish to acknowledge the support of family and friends who provided excel­ lent avenues of procrastination while also keeping me apprised of affairs in the "real world". n ABSTRACT One of the main harbingers of the modern age of precision cosmology, the Cosmic Microwave Background (CMB) has proven itself to be a veritable trove of cosmolog- ical information. With the aid of experiments such as the WMAP satellite, precision measurements of the CMB anisotropy spectra are now being made. This work will first explore the physics of the Vishniac effect, a small-scale CMB temperature anisotropy created by the Compton scattering of CMB photons by free electrons caught in a line-of-sight bulk flow. The Vishniac effect arises due to a den­ sity enhancement in the electrons caused by gravitational potentials in both the lin­ ear and nonlinear regimes and contributes significant power to the CMB temperature anisotropy power spectrum on small scales. This effect is strongly dependent upon cosmology and as such this dependence is investigated for all experimentally-allowed values of the fundamental cosmological parameters. This analysis is performed for both the linear Vishniac effect as well as its nonlinear extension. Following this anal­ ysis a fitting function, capable of predicting the power generated by the Vishniac effect over a range of scales for any allowed cosmology, is investigated. This function proves to be an accurate and efficient way of computing the Vishniac effect for any input cosmology. The next small-scale phenomenon to be explored is the small-scale CMB polariza­ tion anisotropies generated by Thomson scattering of the local photon quadrupole iii anisotropy during reionization. The underlying physics behind this effect are stud­ ied along with the observational information it potentially contains. Observational data of the remote quadrupole is capable of improving constraints in the CMB tem­ perature anisotropy spectrum on scales of I ~ 11 as well as offering information concerning the reconstruction of the primordial density perturbations on gigaparsec scales in our local universe. IV ABREGE Etant la principale prediction de la cosmologie moderne, le fond diffus cos- mologique s'est revele etre un outil indespensable de la recherche actuelle en cos­ mologie. A l'aide de projets tel que le Satellite WMAP, des mesures precises des anisotropics du rayonnement fossile sont desormais disponibles. Premierement, ce travail explore la physique de l'effet Vishniac. Cette anisotropie de temperature a petite echelle du fond diffus est creee par la diffusion Compton de photons par des electrons libres en mouvement dans la ligne d'observation du flux principal. L'effet Vishniac nait d'une surdensite locale d'electrons due des potentiels gravitationels dans les regimes lineaires et non-lineaires. De plus, l'effet Vishniac contribue significativement aux anisotropics de temperature du fond diffus cosmologique a petite echelle. Cet effet depend fortement de la cosmologie choisie et c'est pourquoi cette dependence est sujette de nombreuses investigations avec toutes les valeurs possibles experimentalement des parametres cosmologiques. L'analyse du regime lineaire de l'effet Vishniac et sa contrepartie non-lineaire ont ete effectue dans le but de produire une fontion d'ajustement de courbe capable de predire la puis­ sance generee par cet effet differentes echelles et ce pour n'importe quelle cosmologie autorisee. Cette fonction d'ajustement est une methode precise et efHcace pour de­ terminer l'effet Vishniac. Le second effet a petite echelle etudie est la polarisation des anisotropics dues la v diffusion Thomson du photon local du quadrupole d'anisotropie au moment de la re-ionisation. Les lois de la physique impliquees par cet effet sont etudiees ainsi que de les informations d'observations potentiellement contenues. Les donnees ob­ servers du quadrupole non local sont capables d'ameliorer les contraintes posees sur les anisotropies de temperature du rayonnement fossile a des echelle de £ ~ 11. De plus, les observations offrent de nombreuses informations sur la reconstruction des perturbations primordiales de densite sur plusieurs gigaparsecs dans notre univers local. VI TABLE OF CONTENTS ACKNOWLEDGEMENTS ii ABSTRACT iii ABREGE v LIST OF TABLES ix LIST OF FIGURES x 1 Introduction 1 1.1 Overview 1 1.2 Physical Cosmology 3 1.3 Preliminaries 6 1.4 Early Times 8 1.5 Inflation and Growth of Perturbations 10 2 Cosmic Microwave Background 16 2.1 Recombination 16 2.2 Fluctuations on the Sky 21 2.3 CMB Anisotropics 24 2.4 Reionization 27 3 Vishniac Effect 31 3.1 CMB Temperature Anisotropy Studies 31 3.2 Reionization and Secondary Anisotropics 33 3.3 Vishniac Effect 35 3.4 Contribution to the CMB spectrum 42 3.5 Modelling the Vishniac Effect 49 3.6 Summary and Future Work 56 vn 4 CMB Remote Quadrupole Studies 58 4.1 Intoduction 58 4.2 CMB Polarization 59 4.3 Polarization from a Quadrupole Anisotropy 61 4.4 Polarization from Reionization 64 4.5 Studying the Remote Quadrupole through Secondary Polarization Anisotropies 67 4.6 Constrained Modes 71 4.7 Summary and Future Work 76 5 Summary 79 References 82 vin LIST OF TABLES Table Page 3-1 Parameters, values and descriptions for the standard ACDM cosmology. All values are taken from [67]. Note that in a flat universe the dark energy density is defined as tt\ = l — flm. 44 3-2 Best fit parameters for the linear Vishniac effect 51 3—3 Best fit parameters for the maximum Vishniac effect 52 IX LIST OF FIGURES Figure Page 3-1 Comparison of the linear Vishniac effect, the approximation of the linear Vishniac effect and the maximum effect from both the linear and nonlinear density power spectra. ... 41 3-2 The spectrum of primary CMB anisotropics is exponentially damped at small scales (large values of £). This allows for secondary anisotropics like the Vishniac effect to dominate on sub-arcminute scales. Primary CMB spectra were produced by the CAMB online implementation of the CMBFAST [65] code for a fiducial model where only zre is allowed to vary and n = 1.0, fif, = 0.04, Q,m = 0.27, ftA = 0.73 and h = 0.72 43 3-3 Histograms of the linear Vishniac effect power for £=1000 (solid red), 5000 (long-dashed green) and 10000 (short- dashed blue). Results from 9187 allowed cosmologies binned in 0.02/Ltk2 intervals 46 3-4 Histograms of the maximum Vishniac effect power for £=1000 (solid red), 5000 (long-dashed green) and 10000 (short-dashed blue). Results from 9187 allowed cosmolo­ gies binned in 0.02/xk2 intervals 47 3-5 Plot of rms power for ten values of £ for the linear (left) and maximum (right) Vishniac effects. The shaded region represents the 68% confidence contour while the dotted lines represent the spectra for three randomly-chosen cosmologies 48 x 6 Linear (left) and Maximum (right) Vishniac Effect Fitting Residuals.