Dissertation submitted to the Combined Faculties of the Natural Sciences and Mathematics of the Ruperto-Carola University of Heidelberg, Germany for the degree of Doctor of Natural Sciences Put forward by Youness Ayaita born in Paris, France Oral examination: June 19, 2013 Cosmology with strongly coupled quintessence Referees: Prof. Dr. Christof Wetterich Prof. Dr. Matthias Bartelmann Kosmologie mit stark gekoppelter Quintessenz Das Problem der kosmologischen Konstante motiviert alternative Ansätze zur Er- klärung der beobachteten beschleunigten Expansion des Universums. Quintessenz- Modelle beschreiben eine dynamische dunkle Energie mittels eines Skalarfelds, des Kosmons; im Gegensatz zum Szenario einer kosmologischen Konstante ist die erwar- tete gegenwärtige Menge dunkler Energie vergleichbar mit der Energiedichte der Ma- terie. Den einfachsten Modellen fehlt jedoch eine natürliche Erklärung dafür, daß die dunkle Energie gerade in der gegenwärtigen Epoche begonnen hat, die Energiedich- te des Universums zu dominieren. Eine Kopplung zwischen Kosmon und Neutrinos stellt eine mögliche Lösung dieses Koinzidenzproblems dar. Auf der Ebene von Störun- gen in den Energiedichten vermittelt diese Kopplung eine anziehende Kraft zwischen Neutrinos, deren Stärke diejenige der Gravitation übersteigt. Das impliziert drastische Konsequenzen für jedwede quantitative Untersuchung des Modells. Das methodische Standardrepertoire, namentlich lineare Störungstheorie und Newtonsche N-Körper- Simulationen, schlägt fehlt. Selbst die Expansion des Friedmann-Lemaître-Robertson- Walker-Hingergrunds hängt aufgrund eines Rückkopplungseffekts von nichtlinearen Störungen ab. Wir präsentieren eine umfassende Methode, begleitet von einem vertief- ten physikalischen Verständnis, zur quantitativen Beschreibung des Modells und eröff- nen die Möglichkeit, den Parameterraum des Modells systematisch zu untersuchen und einen Vergleich mit Beobachtungen herzustellen. Cosmology with strongly coupled quintessence The cosmological constant problem motivates alternative approaches for explaining the observed accelerated expansion of the Universe. Quintessence models describe a dynamical dark energy component in terms of a scalar field, the cosmon; in contrast to the cosmological constant scenario, the predicted amount of present dark energy is, generically, comparable to that of matter. The simplest models lack, however, a natural explanation why the dark energy has started to dominate the energy budget of the Universe just around the present cosmic epoch. Growing neutrino quintessence, proposing a coupling between the cosmon and the neutrinos, is a potential solution to this coincidence problem. At the level of perturbations in the energy densities, this coupling mediates an attractive force between the neutrinos stronger than gravity. This has drastic consequences for quantitative analyses of the model. The standard technical repertoire of linear perturbation theory and Newtonian N-body simulations fails. Even the evolution of the Friedmann-Lemaître-Robertson-Walker background depends on the nonlinear perturbations by virtue of a backreaction effect. We present a comprehensive method, accompanied with an improved physical understanding, for a quantitatively reliable investigation of the model and open the door to a systematic exploration of its parameter space and a confrontation with observational constraints. V Preface If I were to describe the spirit of this thesis, I would adopt a slogan that served as the title for a 2012 workshop at Ringberg Castle: “The Dark Energy quest: when theory meets simulations.” We are more used to theory meeting observations. However, as will be illustrated throughout this thesis, simulations can play the role of a labora- tory testing and inspiring new theoretical concepts and ideas. The fruitful interplay between numerical approaches, analytical progress, and physical insights characterizes the intellectual journey summarized in this thesis. The research carried out for this thesis took place in exciting times for the science of cosmology. In May 2009, I followed, among scientists and students in the lecture hall of Heidelberg’s Physikalisches Institut, the launch of ESA’s Planck mission that would provide measurements of the anisotropies in the cosmic microwave background radiation — a key observable for cosmology — with unprecedented accuracy. Shortly before the submission of this thesis, I had the pleasure to witness the presentation of the mission’s long-awaited results, which spectacularly confirm our scientific un- derstanding. In October 2011, during a talk at “The Dark Universe Conference” in Heidelberg, we were all surprised and pleased by the announcement that the 2011 No- bel Prize in physics was awarded to Saul Perlmutter, Brian P. Schmidt, and Adam G. Riess for their 1998 discovery of the accelerated expansion of the Universe. One of the potential explanations for this observation, dynamical dark energy, is the starting point for this thesis. Apart from this, our understanding of many cosmological and astrophysical observations relies on the assumption of dark matter, which does not interact with light. During the last years, cosmologists hoped for possible hints for its detection at CERN’s Large Hadron Collider (LHC). Although LHC data confirmed, as became public in July 2012, the existence of a new particle, presumably the Standard Model Higgs boson, hints for dark matter have not yet been found. In addition to the remarkable efforts in observational cosmology undertaken in recent years, many new projects are planned today. For example, the Euclid space telescope, with the largest astronomical collaboration so far, is expected to provide, during the next decade, pre- cision information about the large-scale structure in the Universe thereby scrutinizing the idea of a hypothetical dynamical dark energy component. Fortunately, working on this thesis has not been a solitary effort. I am indebted to many people who have accompanied and supported me in different ways. First of all, I am grateful to Christof Wetterich for giving me the opportunity to work in his group and for his constant support and encouragements. With his admirable optimism and unconventional ideas, he has a large share of the success of this thesis. My grateful thanks are also extended to Matthias Bartelmann who agreed to be the second ref- eree. I immensely enjoyed the innumerable fruitful discussions with my collaborators, namely Maik Weber, Björn Malte Schäfer, Marco Baldi, and Ewald Puchwein. David Fonseca Mota kindly provided his numerical implementation of linear perturbation theory for the growing neutrino quintessence model, which I wish to acknowledge. Special thanks should also be given to Rocky Kolb, who motivated the investigation VII whether the neutrino detections from SN1987A constrain growing neutrino quintes- sence. I am also thankful for discussions with Luca Amendola, Nico Wintergerst, Valeria Pettorino, Joschka Beyer, Lily Schrempp, Wessel Valkenburg, Ignacy Sawicki, Valerio Marra, Nelson Nunes, Andy Taylor, Nicolai Christiansen, and Igor Böttcher. Like every member of the institute, I very much appreciate the excellent administra- tive work of Eduard Thommes and the reliable technical support by Elmar Bittner. Finally, I wish to express my gratitude to the Deutsche Forschungsgemeinschaft and the Transregional Collaborative Research Centre “The Dark Universe” both for the financial support and for providing an excellent research environment. The results presented in this thesis base largely on three published works: Ayaita et al. (2012b): “Structure formation and backreaction in growing neutrino quintes- sence”; Ayaita et al. (2013): “Neutrino lump fluid in growing neutrino quintessence”; Ayaita et al. (2012a): “Investigating clustering dark energy with 3d weak cosmic shear”. There is, consequently, an overlap between this thesis and the papers as regards the derivations and the figures showing quantitative results. For each corresponding fig- ure individually, I refer to the publication from which it is taken. Similarly, I indicate whenever a section follows the presentation of one of the papers. Since these are collab- orative works, credit is shared among the authors. My contributions focus mainly on the overall cosmological evolution of growing neutrino quintessence (in particular on the backreaction effect on the expansion dynamics), the modeling and the dynamics of the cosmon perturbation, the physics and the cosmological evolution of the cosmon- neutrino lump fluid, the analytical understanding of the pressure cancellation within lumps and of the role of the total angular momentum in stabilizing the lumps, and nu- merical techniques allowing for an efficient calculation of the 3d weak lensing Fisher matrix. So far unpublished results of this thesis include the overcoming of the techni- cal difficulties in evolving the simulations beyond the cosmological redshift z = 1, the discussion of the subsequent cosmological evolution, the investigation of the varying coupling model at the nonlinear level, and an analysis of the idea whether the model can be constrained by the detection of high-energy neutrinos emitted, e. g., by super- novae. VIII Contents 1 Introduction 1 1.1 TheacceleratingUniverse ............................. 1 1.2 Quintessence....................................... 6 1.3 Outline .......................................... 9 2 Cosmology 11 2.1 Homogeneousapproximation . ... ... ... ... ... .... ... ... 11 2.1.1 Dynamicsofexpansion..........................