Thèse l'Exploitation du Principe de Grandes Déviations dans les Relevés Cosmologiques H/F - Doctorat.Gouv.Fr

Établissement : Université Paris-Saclay GS Physique École doctorale : Physique en Ile de France Laboratoire de recherche : Institut de PHysique Théorique Direction de la thèse : Francis BERNARDEAU ORCID 0009000730152581 Début de la thèse : 2026-10-01 Date limite de candidature : 2026-04-30T23:59:59 Cette thèse s'inscrit dans le cadre des grands projets d'observation cosmologique, comme la mission Euclid de l'Agence Spatiale Européenne, lancée en 2023. Euclid a pour objectif de cartographier un tiers du ciel avec une précision inégalée afin de mieux comprendre la structure et l'évolution de l'univers.
Le travail de recherche vise à étudier la formation des grandes structures de l'univers - galaxies, filaments, amas - issues de petites fluctuations présentes juste après le Big Bang. Pour cela, la thèse s'appuiera en particulier sur un outil issu de la physique statistique : le principe des grandes déviations (Large Deviation Principle), qui permet de décrire le comportement global de systèmes complexes à partir de leurs fluctuations rares. En combinant modélisation théorique et exploitation de simulations numériques, ce projet cherche à mieux relier les prédictions du modèle cosmologique standard aux observations, et à explorer des questions fondamentales sur la matière noire et l'énergie noire. À terme, il contribuera à améliorer l'analyse et l'interprétation des données des missions d'observation comme Euclid. This thesis is proposed in the context of the exploitation of observational projects in cosmology that aim at mapping vast portions of our observable universe, This is the case in particular for the Euclid mission, an ESA cosmological observation satellite launched in the summer of 2023, which benefits from significant French, and in particular CEA, participation (see https://www.euclid-ec.org), and whose objective is to map one third of the sky with unprecedented sensitivity and angular precision.
The objectives of the thesis is to take advantage of tools that are commonly used in statistical physics, more precisely the Large Deviation Principle, which proved to be useful to identify, and evaluate, key observables is random media. But more generally the proposed work is to study of the statistical properties of the large-scale structure of the universe, as shaped by gravitational interactions over cosmological time. In the standard model of cosmology, the large-scale structure of the universe emerged from primordial metric fluctuations through the gravitational instability mechanism. The standard model provides a compelling description of the properties of the initial metric fluctuations, as scalar only metric perturbations that obey Gaussian statistics and with nearly scale invariant power spectra. The perturbations, initially at 10^-5 level, subsequently evolved to form the large scale structure of the universe as we see them now, encompassing large walls, filaments that can span hundreds of Megaparsecs and self-gravitating clusters aggregating thousands of galaxies. The equations describing the gravitaitonal instabilities are well known; they form the Vlasov-Poisson system widely used in cosmology. In particular it has been used to perform numerous numerical simulations of these phenomena and we are confident that it provides us with the correct picture. However the Vlasov-Poisson system leads in this context to non-equilibrium and nonlinear phenomena that resist standard analytical investigations. The study of this specific system is all the more critical that it may hold the key to fundamental physics problems, such as the nature of dark matter and dark energy.Collisionless self-gravitating systems lead naturally to complex processes of fluctuation transport and growth, driven by a deterministic nonlinear equations. A natural path that has been explored over the last decades has been the Perturbation Theories (PT), in its different incarnations, where the cosmological field solutions are expanded in terms of the amplitude of the initial density perturbations. These investigations have led to a large corpus of results that have been widely used in the community. Some of these results moreover have shown intriguing properties and have been subsequently re-interpreted [1] -- and extended -- in the context of a Large Deviation Principle (LDP). Comparisons of LDP predictions with numerical results show very good agreement, even for modest values of the driving parameter as shown papers given in references [2,3,4].

However, the application of the LDP raises further questions. The LDP makes predictions for certain observables: can the robustness of the results and their validity range be assessed with the help of Next-to-Leading Order (NLO) calculations? Can it be extended to other quantities? For a quantity such as the Scaled Cumulant Generating Function, the computation of NLO contributions seems within reach, either for toy models, limit cases, or for the full system, at least through numerical investigations. Gaining insights into the behavior of NLO solutions might help identify the range of LDP predictions for related observables and develop a full theory for their measurement, including what is known as cosmic variance-the fact that statistical properties are derived from a single sample of finite size. This is the long term objective of the proposed work.

Une formation solide en physique théorique (théorie des champs, méthodes de physique statistiques) est attendue