Departamento de F´ısicaTe´oricae Instituto de F´ısicaTe´orica Universidad Aut´onomade Madrid PROBING THE FOUNDATIONS OF THE STANDARD COSMOLOGICAL MODEL Memoria de Tesis Doctoral presentada por Miguel Zumalac´arreguiP´erez para optar al t´ıtulode Doctor en Ciencias F´ısicas Programa de Doctorado de F´ısicaTe´orica Trabajo supervisado por los Doctores Juan Garc´ıa-BellidoCapdevila, Profesor Titular del Departamento de F´ısicaTe´orica,Universidad Aut´onomade Madrid Pilar Ruiz-Lapuente, Investigadora Cient´ıfica del Instituto de F´ısicaFundamental, Consejo Superior de Investigaciones Cient´ıficas y Tomi S. Koivisto, Investigador Postdoctoral del Instituto de Astrof´ısicaTe´orica,Universidad de Oslo. Octubre de 2012 ii A mis padres. iii iv Contents Statement ix Preface xi Resumen y Conclusiones xv Acknowledgements xix Notation and Acronyms xxi I Foundations1 1 The Standard Cosmological Model3 1.1 Ingredients and Preparation4 1.1.1 General Relativity4 1.1.2 Metric Ansatz: The Copernican Principle5 1.1.3 Inflation: Symmetry and Initial Conditions6 1.1.4 Standard and Dark Matter7 1.1.5 The Cosmological Constant7 1.2 The Need to Go Beyond8 1.2.1 Theoretical Issues8 1.2.2 Observational Reasons 10 1.3 Exotic Tastes and Alternative Recipes 12 1.3.1 Inhomogeneous Models 12 1.3.2 Dynamical Dark Energy 14 1.3.3 Modified Gravity 16 2 Observational Probes of Cosmology 23 2.1 Geometry and Dynamics 24 2.2 Primordial Nucleosynthesis 26 2.3 Cosmic Microwave Background Radiation 26 2.3.1 CMB Distance Priors 28 2.4 Large Scale Structure 29 2.4.1 The Baryon Acoustic Oscillation Scale 31 2.4.2 Other LSS Probes 34 2.5 Type Ia Supernovae 35 v CONTENTS 2.5.1 Local Expansion Rate 37 2.6 Local Gravity Tests 37 II Results 39 3 Large Scale Homogeneity and Non-Copernican Void Models 41 3.1 Lema^ıtre-Tolman-Bondi Models 43 3.1.1 The Adiabatic GBH Model 46 3.2 The Baryon Acoustic Scale in LTB Universes 47 3.2.1 Free-falling Scales in the LTB Metric 48 3.2.2 BAO Scale Evolution Beyond Zero Order 50 3.2.3 The Physical BAO Scale at Early Times and on the Lightcone 51 3.2.4 Comparison with the Observed BAO Scale 52 3.2.5 The Alcock-Paczynski Effect in LTB Models 54 3.3 Analysis and Results 54 3.3.1 Observational Data 55 3.3.2 MCMC Analysis 58 3.3.3 Homogeneous Models 59 3.3.4 Inhomogeneous Models 62 3.3.5 Model Comparison 66 3.4 Discussion 68 4 Phenomenological Modifications: Entropic Gravity 73 4.1 Gravity and Thermodynamics 74 4.2 Modifications from Surface Terms 75 4.2.1 Single Fluid 76 4.2.2 Adding a Cosmological Constant 77 4.3 Modifications from Quantum Corrections to the Entropy-area Law 79 4.4 Dark Energy from a Generalized Entropy-area Law 80 4.5 On the Evolution of Perturbations 84 4.6 Discussion 86 5 Standard Matter and Scalar Fields: Disformal Quintessence 89 5.1 Dark Energy from the Disformal Relation 90 5.1.1 Disformal Dark Energy 91 5.1.2 A Variation of the Model 92 5.2 Disformal Quintessence 93 5.2.1 Background Evolution 93 5.2.2 Cosmological Perturbations 97 5.2.3 Observational Constraints 98 5.3 Discussion 101 6 General Relativity and Scalar Forces: Disformal Coupling 103 6.1 A Test Particle in a Disformal Metric 105 6.2 The Zoo of Disformally Related Theories 106 6.2.1 Disformal Curvature: The Conformal Frame 108 vi CONTENTS 6.2.2 Equations in the Einstein Frame 110 6.3 Background Cosmology 113 6.3.1 An Example Model: Disformally Coupled Dark Matter 113 6.4 Cosmological Perturbations 117 6.4.1 Small Scale Limit 118 6.4.2 Structure Formation for Disformally Coupled Matter 118 6.4.3 Viable Scenarios 123 6.5 The Disformal Screening Mechanism 124 6.5.1 Pressure Instability 125 6.5.2 The Scalar Field in Dense, Non-relativistic Environments 125 6.6 Discussion 128 7 Conclusions and Outlook 131 III Appendices 135 A MCMC Analysis 137 B CMBEasy 139 C Equations for Generalized k-essence 141 D Disformal Relations 143 D.1 Disformal Geodesics 144 D.2 General Disformal Coupling Perturbations 144 D.3 Lagrangian Derivatives for Disformal Quintessence 145 List of Tables 147 List of Figures 149 Bibliography 151 vii CONTENTS viii Statement The results presented in this dissertation (Chapters3-6) are based on original work done in collaboration with other researchers during the course of my PhD, from September 2008 to August 2012. The content of these Chapters is based on the released publications [1{6], as well as another ongoing project which is at a mature stage [3]. These references are listed below for convenience. In particular, Chapter3 is based on Reference [1], Chapter4 on References [5,6], Chapter5 is based on Reference [4] and Chapter6 is based on References [2,3]. The introductory Chapters1 and2 are mainly a review. The exposition there has been very influenced by References [7{10], as well the works cited in the text. Although they represent my own vision about some of the topics in which the results are framed, no claim of originality is made about the introductory Chapters. AppendicesA andB describe some of the tools necessary for the analysis. AppendixD contains some lengthy equations that were not necessary to include in the body of the discussion. Miguel Zumalac´arregui P´erez Madrid, October 2012 1. \Tension in the Void: Cosmic Rulers Strain Inhomogeneous Cosmologies" M. Zumalacarregui, J. Garcia-Bellido and P. Ruiz-Lapuente. JCAP 1210, 009 (2012), [arXiv:1201.2790]. 2. \Screening Modifications of Gravity through Disformally Coupled Fields" T. S. Koivisto, D. F. Mota and M. Zumalacarregui. [arXiv:1205.3167]. 3. \DBI Galileons in the Einstein Frame: Local Gravity and Cosmology," M. Zumalacarregui, T. S. Koivisto and D. F. Mota, [arXiv:1210.8016]. 4. \Disformal Scalar Fields and the Dark Sector of the Universe" M. Zumalacarregui, T. S. Koivisto, D. F. Mota and P. Ruiz-Lapuente. JCAP 1005, 038 (2010), [arXiv:1004.2684]. 5. \Constraining Entropic Cosmology" T. S. Koivisto, D. F. Mota and M. Zumalacarregui. JCAP 1102, 027 (2011), [arXiv:1011.2226]. 6. \Modified Entropic Gravity and Cosmology" M. Zumalacarregui. AIP Conf. Proc. 1458, 539 (2011), [arXiv:1202.1281]. ix Statement x Preface You are pooped and demoralized. Why wouldn't you be? Of course it is exhausting, having to reason all the time in a universe which wasn't meant to be reasonable. Kurt Vonnegut1 stronomy and cosmology are arguably the oldest sciences, and perhaps the second oldest professions in history. After many millenia floating in the darkness of mysticism and speculation, cosmology has finally become an em- pirical and predictive discipline. The effort of thousands of scientists, from Aastronomers to theoretical physicists, has carved a Standard Cosmological Model (SCM) that is able to explain a large and increasing set of phenom- ena. The price to pay is the inclusion of three mysterious elements with no conventional explanation: inflation to account for the large scale homogeneity and initial perturbations of the universe, dark matter to enhance the formation of cosmic structure, and a Cosmological Constant to propel the latter stage of accelerated expansion. The Standard Cosmological Model is undoubtedly beautiful. The elegance of the Gen- eral Relativistic geometric description is supplemented by the symmetry of the large scale metric. Despite its simplicity, this scheme seems able to accurately describe the coarse grained evolution of the universe on the largest scales throughout cosmic history. Yet, many ques- tions regarding the nature of the new elements remain unanswered: What is the mechanism behind cosmic inflation and the properties of the dark matter particle(s)? Is cosmic acceler- ation driven by Einstein's Cosmological Constant? If so, why is its value so small compared to particle physics energy scales but still large enough to be observable? If not, how is its value suppressed and what is the true mechanism for the acceleration? The Standard Cosmological Model has been extremely successful in explaining a broad set of observables with just a handful of parameters. The evidence supporting cosmic ac- celeration has grown since the first decisive data from type Ia Supernovae (SNe) pointing towards the existence, and a number of independent observables agree now on the details of this paradigm. Measurements of the Cosmic Microwave Background (CMB) temperature anisotropies support the spatial flatness of the universe. When combined with the determi- 1Breakfast of Champions (1973) xi Preface nation of the local expansion rate, it follows that a smooth component with negative pressure must dominate the cosmic energy budget. Observations of the Large Scale Structure distri- bution confirm this picture. The formation rate of cosmic structures through gravitational collapse bounds the amount of clustering matter to be well below what is necessary for the universe to be spatially flat. The same physics that produces anisotropies in the CMB im- prints a characteristic Baryon Acoustic (BAO) scale in the LSS distribution, which can be measured by galaxy surveys. It provides a standard ruler that tracks the cosmic expansion, further supporting the paradigm of cosmic acceleration. Cosmology has made the promise of new physics. It not only supports its existence, but also provides means to validate or refute the different scenarios. As in a Gold Rush, myriads of alternatives to the Cosmological Constant have been proposed and studied in recent years. These models necessarily modify some sector of the Standard Cosmological model. It is possible to mimic the observed acceleration without the introduction of new exotic elements, by postulating a metric which is inhomogeneous on large scales.