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A Model-Independent Approach to Reconstruct the Expansion History of the Universe with Type Ia Supernovae

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A Model-Independent Approach to Reconstruct the Expansion History of the Universe with Type Ia Supernovae A Model-Independent Approach to Reconstruct the Expansion History of the Universe with Type Ia Supernovae Dissertation submitted to the Technical University of Munich by Sandra Ben´ıtezHerrera Max Planck Institute for Astrophysics October 2013 TECHNISHCE UNIVERSITAT¨ MUNCHEN¨ Max-Planck Institute f¨urAstrophysik A Model-Independent Approach to Reconstruct the Expansion History of the Universe with Type Ia Supernovae Sandra Ben´ıtezHerrera Vollst¨andigerAbdruck der von der Fakult¨atf¨urPhysik der Technischen Uni- versitt M¨unchen zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigten Dissertation. Vorsitzende(r): Univ.-Prof. Dr. Lothar Oberauer Pr¨uferder Dissertation: 1. Hon.-Prof. Dr. Wolfgang Hillebrandt 2. Univ.-Prof. Dr. Shawn Bishop Die Dissertation wurde am 23.10.2013 bei der Technischen Universit¨atM¨unchen eingereicht und durch die Fakult¨atf¨urPhysik am 21.11.2013 angenommen. \Our imagination is stretched to the utmost, not, as in fiction, to imagine things which are not really there, but just to comprehend those things which are there." Richard Feynman \It is impossible to be a mathematician without being a poet in soul." Sofia Kovalevskaya 6 Contents 1 Introduction 11 2 From General Relativity to Cosmology 15 2.1 The Robertson-Walker Metric . 15 2.2 Einstein Gravitational Equations . 17 2.3 The Cosmological Constant . 19 2.4 The Expanding Universe . 21 2.5 The Scale Factor and the Redshift . 22 2.6 Distances in the Universe . 23 2.6.1 Standard Candles and Standard Rulers . 26 2.7 Cosmological Probes for Acceleration . 27 2.7.1 Type Ia Supernovae as Cosmological Test . 27 2.7.2 The Cosmic Microwave Background Radiation . 28 2.7.3 Baryonic Acoustic Oscillations . 32 2.8 The Concordance Model: ΛCDM . 34 2.8.1 Dark Matter . 34 2.8.2 Dark Energy . 38 2.8.3 Cosmological Parameters: the Current Picture . 41 2.9 Non-Standard Cosmologies: Modified Gravity . 42 2.9.1 Brane Worlds . 44 2.9.2 f(R) Models . 47 2.10 The Kinematic Approach . 48 3 Supernovae: Candles In The Universe 51 3.1 Supernovae Classification . 51 3.2 Explosion Mechanisms . 53 3.2.1 Thermonuclear Supernovae . 54 3.3 Observational Characteristics . 57 3.3.1 Light Curves and Spectra . 58 3.3.2 Diversity and Correlations: The Phillips Relation . 59 3.4 The Standardization Process of SNe Ia . 63 3.4.1 The SALT Fitter . 64 3.4.2 The MLCS Fitter . 66 3.4.3 Comparison of MLCS and SALT2 Methods . 67 7 8 CONTENTS 3.5 Cosmology with SNe Ia: Basic Principles . 70 3.5.1 The Hubble Diagram . 71 3.5.2 The Expansion History and the Accelerating Universe . 72 3.6 Current SN Ia Samples . 77 3.6.1 Observational Strategy . 77 3.6.2 State-of-the-Art SN Ia surveys . 79 3.6.3 The Union Compilation . 80 3.6.4 Systematic Uncertainties . 83 3.7 Space Versus Ground . 87 3.8 Future Samples and Surveys . 89 4 The Model-Independent Method 93 4.1 Motivation: Why Model Independent? . 93 4.2 Mathematical Formalism . 94 4.2.1 Background . 94 4.2.2 Model-Independent Determination of the Expansion Rate Function . 95 4.2.3 Illustration of the Method: Reconstructing ΛCDM . 98 4.3 Principal Component Analysis . 99 4.3.1 Building the Basis with Principal Component Analysis. 101 4.4 Error Analysis . 104 4.5 Convergence of the Neumann Series . 106 4.6 Combining Different Data Sets and Families of Models . 107 4.7 Improving the Reconstruction . 107 5 Testing the Method with Simulated Data 111 5.1 Different Cosmological Scenarios . 111 5.1.1 ΛCDM Simulations . 111 5.1.2 Non-ΛCDM Simulations . 114 5.2 SNANA: A Tool To Simulate High Quality SN Data. 120 5.2.1 Simulated Data in MLCS and SALT2. 122 6 Extracting the Expansion Rate from Real Data 127 6.1 The Union2.1 Sample Revisited . 127 6.2 Constraining Cosmological Scenarios . 130 6.2.1 Dark Energy Models . 131 6.2.2 Beyond the wCDM Cosmology . 132 6.3 Alternative Cosmological Probes . 136 6.4 Other Interesting Applications . 138 6.4.1 Checking for Systematics in the Supernova Samples . 138 6.4.2 Testing Redshift Ranges for Supernova Campaign Plan- ning . 141 6.5 Ongoing Work . 143 CONTENTS 9 7 Conclusions and Perspectives 147 8 Acknowledgments 153 Bibliography 154 10 CONTENTS 1. Introduction Humankind, given its own nature, has always tried to understand the Universe and its place in it. Since the beginning of history, cosmology has been the science through which women and men have tried to find answers to those fundamental questions by peering into the sky. Problems such as the motion of the planets, the nature of the space between stars, or the formation and evolution of galaxies, have been progressively understood thanks to the efforts of many generations of scientists. For millennia, humans have often observed new stars appearing in the night sky. As early as in 1006, Arabic and Chinese astronomers recorded the observa- tion of a bright newly-born star that shone in the sky for nearly two years and disappeared afterwards. Over the years scientists became aware that some of these events were remarkably more luminous. Moreover, estimated distances to these objects indicated that they had an extragalactic origin. Especially important were the observations of the (super)nova S Andromedae in the An- dromeda galaxy in 1885. It was reckoned, that these bright events were differ- ent from any other object ever observed before. The origin and nature of those stars remained a mystery until the beginning of the 20th century. Considered as beacons in the Universe from which relative distances can be measured, Type Ia supernova explosions play a key role, not only in cosmology, but in other fields of astrophysics. Our understanding of these magnificent objects is fundamental to comprehend the Universe in which we live in. Gravity and its effect on planetary orbits, has equally attracted a great deal of interest over history. From the theoretical, almost spiritual, beliefs of ancient Greek philosophers to the efforts of Galileo Galilei designing experi- ments with inclined planes, understanding the gravitational interactions which govern our planet and our Universe has been a priority for scientists. The first scientist who described gravity in quantitative terms, was Isaac Newton, who formulated the universal inverse-square law and provided extraordinary simple and accurate explanations of a wide range of terrestrial and celestial phenom- ena. Newton's laws were the accepted paradigm for gravity for the following two hundred years. In 1916, Albert Einstein presented his General Relativity, introducing revolutionary concepts that led to a new era in physics and cos- mology. Einstein described the curvature of space-time to be responsible of the effects of gravity but believed that the expansion detected by Edwin Hubble in 1925 would slow down over time, according with the Newtonian ideas. 11 12 1. INTRODUCTION However, the past fifthteen years have brought mounting evidence that the expansion of the Universe is nowadays in an accelerated phase. Amongst the several observational probes that led to such conclusion, and the first to reveal such a striking finding, are Type Ia supernovae. The currently adopted paradigm accounts for the acceleration but it re- quires the presence of an unknown component, dark energy, which is in fact the major constituent of our Universe. Present understanding of this compo- nent is uncomfortably close to nothing, which calls for a significant effort both at an observational and experimental front and on theoretical grounds. Be- cause of the important implications of the acceleration, ambitious experimental efforts are being developed to measure the expansion history and growth of structure in the cosmos with percent-level precision or better. A relatively large number of non-standard theories have been proposed to tackle the nature of dark energy. Indeed, cosmic acceleration is the most profound puzzle in contemporary physics and can lead to new ideas about the interaction between gravity and the quantum vacuum, the existence of extra spatial dimensions or the nature of quantum gravity. A model-independent approach to directly interpret the data is arguably essential, if one would like to avoid introducing prejudices or biases from theo- retical frameworks. The work in this thesis consists in implementing a recently developed methodology to derive the expansion history of the Universe in a model-independent fashion, using currently available Type Ia supernova data. Such reconstructions not only allow to recover the expansion history of the of the Universe, but also provide means to test cosmological models of the nature of dark energy. A number of tests on the improvement that future samples should provide or the effect of the different calibration methods are also presented. These studies shed light on the next necessary steps, from the observational side, to ensure progress. This work is but a first step in the direction of providing tighter constraints on the expansion history of the Universe and some comprehension on the prop- erties of dark energy. Model-independent methodologies are far from trivial, and a better understanding of their power and drawbacks is fundamental. The work presented here extends previous developments in this context. Future work will see to apply these methods to an increasing body of observational data, not only quantitatively, by including results from new observational cam- paigns, but also qualitatively, allowing for the introduction of data such as the Baryonic Acoustic Oscillations detected in the Cosmic Microwave Background. This thesis is organised as follows. The Chapter 2 summarizes the main as- pects of General Relativity and other alternative cosmological models needed to understand the tests and discussions presented here.
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