AIX-MARSEILLE UNIVERSITÉ ECOLE DOCTORALE 352 CENTRE DE PHYSIQUE THEORIQUE / UMR 7332 Thèse présentée pour obtenir le grade universitaire de docteur Discipline: Physique et Sciences de la Matière Spécialité: Astrophysique et Cosmologie Louis PERENON Elements of phenomenology of dark energy Soutenue le 24/10/2017 devant le jury composé de: Alessandra SILVESTRI U. Leiden Rapporteur Álvaro DE LA CRUZ-DOMBRIZ U. Cape Town Rapporteur Pierre TAXIL CPT, U. Aix-Marseille Examinateur Anne Ealet CPPM Examinateur Filippo VERNIZZI CEA Saclay Examinateur Patrick VALAGEAS CEA Saclay Examinateur Christian MARINONI CPT, U. Aix-Marseille Directeur de thèse ABSTRACT A little over a hundred years ago a revolution in modern physics occurred. The description of spacetime provided by General Relativity changed the way physics describes our universe. The Newtonian gravity force is promoted to a gravitational field paving spacetime and links intimately the energy content of the universe with its geometry. Mass curves spacetime which, in turn, dic- tates how bodies move in relation to one another. The foundation provided by General Relativity has allowed cosmologists to establish a well defined cosmological paradigm. Its large scale time evolution is understood to be the direct consequence of the type of energy it contains while the lumpiness of the large-scale structures we observe today, such as galaxies and clusters of galaxies, is the result of gravitational instabilities developing on the evolving frame. The increasing preci- sion of several cosmological probes enabled the possibility of encoding our theoretical and obser- vational knowledge within a standard model of cosmology; the ¤CDM paradigm. This model was able to account for the recent discovery that the expansion of the universe is accelerating; a mile- stone of modern cosmology. In the ¤CDM picture, the universe is constituted today for the major part by Cold Dark Matter along with the Cosmological Constant ¤ that drives cosmic acceleration. However, this standard model is not fully complete and further breakthroughs in modern physics can be expected within this century. These will arise from an accurate description of high energy scales of gravity through a quantum theory of gravity —extremely small lengths— or through a new description of gravity at low energy scales —on cosmological distances. Such breakthroughs are essentially motivated on two grounds: using the Cosmological Constant introduces theoretical issues in a quantum field theory description and tentative observational evidences suggests our large scale description of the universe should be refined. Therefore, we devote the first chapter of this thesis to an overview of today’s cosmological paradigm; starting from its founding principles, up to its shortcomings. Finding alternatives to the standard model is of crucial importance for two reasons. On the one hand, a general theory providing a universal description of all the stages the universe has gone through, and of all physical interactions it contains, still evades our grasp. On the other hand, the second reason is more closely related to the subject of the thesis. A given cosmological model can indeed be tested against many observational probes so as to gauge its viability. However, the soundness and the precision of a viable model can only be assessed once it is compared to an- other model. This is why, the ¤CDM model stands as the most faithful model; describing most of the universe’s evolution according to the observations gathered up to now. This is also why one has to explore alternatives to the standard model. An incredible amount of alternative theories have been put forward and most of them are based on the addition of degrees of freedom to the standard picture given by General Relativity. These additional freedoms can manifest in the form of a new energy component of the universe —the dark energy picture— or through fundamental modifications of the gravitational interaction —the modified gravity landscape. Such a profusion of research material, as much on the observational side as on the theoretical, has substantially increased our understanding of the universe. However, this is also at the expense of our efficiency in doing so, as it is rather cumbersome to study theories one by one and confront each theoretical proposal to observations. Aiming to study or create common formulations, enabling the description of large classes of alternative theories within the same framework, is an efficient path to overcom- ing this obstacle. This is the reason why, in chapter 2, after reviewing some alternative models iii to ¤CDM, we will focus on presenting a promising unifying framework: the effective field theory of dark energy. This approach to modified gravity has established a common formalism virtually describing all alternative theories which add a single extra scalar degree of freedom to Einstein’s equation. A large class of these models fall under Horndeski theories. The increasing amount of theoretical knowledge, and the growing amount of data, is also a cry for phenomenological studies. Future surveys such as EUCLID, SKA, WFIRST and DESI, to name but a few, will provide ever more precise constraints on deviations from the standard model. In light of this, understanding the phenomenology behind alternative theories, extracting and test- ing observables which would characterise measurable deviations from standard gravity are thus a crucial step cosmological studies must go through today. Therefore, we consider the effective field theory of dark energy and attempt to provide answers to the following three guiding questions: What is the cosmological portrait of gravity that emerges in Horndeski theories ? Are there any universal behaviours and, if yes, where do they stand with respect to the standard model ? Can we identify observables that will, in the future, enable us to discriminate between theories ? To do so, in chapter 3, we show how one can parametrise the effective field theory of dark energy framework in order to extract predictions on a set of large-scale structure observables and how the effective field theory of dark energy framework can embed early modifications of gravity in Horndeski theories. Following this, we adopt a Monte Carlo procedure to explore Horndeski models, paying a signifi- cant attention to the viability of the models we obtain. This procedure enables us to identify some definite and less definite observational features Horndeski theories yield. This corresponds, for the major part, to what was explained in [1]. In the second half of chapter 3, we use the Monte Carlo approach to further synthesise the previous conclusions, and more, into an observable diagnostic. The goal of this diagnostic is to assess how Horndeski theories could be strongly disfavoured in an observable space given where future measurements will point. This corresponds to the results developed in [2]. The effective field theory of dark energy framework having allowed the exploration of the phe- nomenology of a large number of dark energy and modified gravity models we provide a review of the results it has produced in chapter 4. The goal of this final is twofold. It allows us to give a presentation of the landscape this framework can be applied to. In particular, we show the novel predictions it has brought up, the constraints that were derived with observations, but also how in- formation on modified gravity can be extracted in an astrophysical context. We also discuss further theoretical an numerical developments without forgetting the caveats the effective field theory of dark energy presents. This chapter also has the purpose of discussing the results presented in chapter 3 with respect to other studies, and suggest paths needing to be explored in the future. iv RÉSUMÉENFRANÇAIS Un peu plus d’une centaine d’années en arrière, une révolution de la physique moderne s’est pro- duite. La description de l’espace-temps fournie par la Relativité Générale a changé la façon dont la physique décrit notre univers. La force gravitationnelle newtonienne est remplacée par un champ gravitationnel, pavant l’espace-espace, qui relie le contenu énergétique de l’univers à sa géométrie de façon intrinsèque. L’espace-temps, courbé par les objets massifs, dicte comment les corps se meu- vent les uns par rapport aux autres. La Relativité Générale a permis aux cosmologistes d’établir un paradigme cosmologique bien défini. L’évolution homogène, spatiale et temporelle, de l’univers à grande échelle est la conséquence directe du type d’énergie qu’il contient et la croissances des grandes structures que nous observons aujourd’hui, comme les galaxies et amas de galax- ies, est le résultat d’instabilités gravitationnelles qui se développent dans l’univers en expansion. La précision croissante de plusieurs sondes cosmologiques a permis d’englober les connaissances théoriques et observationnelles dans un modèle standard de la cosmologie: le paradigme ¤CDM. Ce modèle fournit notamment un cadre simple pour expliquer la découverte récente que notre univers est entré il y à peu de temps dans une phase d’expansion accéléré: un jalon de la cosmolo- gie moderne. S. Perlmutter, B.P. Schmidt et A.G. Riess ont reçu le prix Nobel en 2011 pour cette découverte effectuée en 1998. Dans le paradigme ¤CDM, l’univers est constitué aujourd’hui en ma- jorité de matière noire froide (CDM) et d’énergie noire, décrite par la constante cosmologique, qui produit l’accélération cosmique. Cependant, ce modèle standard n’est pas entièrement complet et d’autres avancées dans la physique moderne peuvent être attendues au cours de ce siècle. Celles- ci pourront notamment découler d’une description précise de la gravité aux régimes d’énergie très élevée — échelles de distance extrêmement petites — grâce à une théorie quantique de la gravité ou à travers une nouvelle description de la gravité à faible énergie — sur les distances cos- mologiques. Celles-ci sont essentiellement motivées par deux raisons: l’utilisation de la constante cosmologique introduit des problèmes théoriques dans une description de la théorie des champs quantiques et certaines tension naissantes suggèrent que notre description à grande échelle de l’univers doit être affinée.