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The recent first detection of gravitational waves (GWs) from binary black hole mergers has spurred a renewed interest in possible deviations from General Relativity (GR), since they could be detected in the GWs emitted by such systems. Of particular interest is the ringdown phase of a binary black hole merger, which can be described by linear perturbations about a background stationary black hole solution. These perturbations mainly correspond to a superposition of 'quasi-normal modes' (QNMs), whose frequencies form a discrete set. One expects that modified gravity models could predict QNMs that differ from their GR counterpart: the detailed analysis of the GW signal represents an invaluable window to test GR and to look for specific signatures of modified gravity. The work done in this thesis takes place in the context of scalar-tensor theories of gravity, and more particularly the Degenerate Higher-Order Scalar-Tensor theories. We start by a review of these theories and their properties, and describe a way to reformulate them in a framework with a clear geometrical interpretation. We then study linear perturbations about several existing nonrotating black hole solutions of such theories, and show why the perturbation equations obtained are very hard to decouple in general. When it is possible, in the case of odd parity perturbations, we describe the propagation of waves and relate it to the stability of the underlying spacetime. When it is not, we circumvent the difficulty by making use of an algorithm proposed recently in the mathematical literature that allows us to decouple the equations both at the black hole horizon and at infinity. This allows us to get the asymptotic behaviour of waves on such spacetimes, yielding valuable information that can allow us to rule some of them out. Finally, we use the asymptotic behaviours obtained to compute QNMs numerically., Comment: PhD thesis (defended 17/06/2022, Universit\'e Paris Cit\'e), 267 pages, 17 figures, 1 appendix, short introduction in French. Based on arXiv:2012.10218, arXiv:2103.14744, arXiv:2103.14750, arXiv:2204.04107, arXiv:2205.07746

This thesis by publication is devoted to the study of aspects of the early universe in the context of primordial black hole (PBH) physics. Firstly, we review the fundamentals of the early universe cosmology and we recap the basics of the PBHs physics. In particular, we propose a refinement in the determination of the PBH formation threshold, a fundamental quantity in PBH physics, in the context of a time-dependent equation-of-state parameter. Afterwards, we briefly present the theory of inflationary perturbations, which is the theoretical framework within which PBHs are studied in this thesis. Then, in the second part of the thesis, we review the core of the research conducted within my PhD, in which aspects of the early universe and the gravitational wave physics are combined with the physics of PBHs. Moreover, aspects of the PBH gravitational collapse process are studied in the presence of anisotropies. Specifically, we study PBHs produced from the preheating instability in the context of single-field inflation. Interestingly, we find that PBHs produced during preheating can potentially dominate the universe's content and drive reheating through their evaporation. Then, we focus on the scalar induced second-order stochastic gravitational wave background (SGWB) induced from Poisson energy density fluctuations of ultralight PBHs. By taking then into account gravitational wave backreaction effects we set model-independent constraints on the initial abundance of ultralight PBHs as a function of their mass. Afterwards, we study in a covariant way the anisotropic spherical gravitational collapse of PBHs during a radiation-dominated era in which one can compute the PBH formation threshold as a function of the anisotropy. Finally, we summarize our research results by discussing future prospects opened up as a result of the research work conducted within this thesis., Comment: PhD thesis: 147 pages, a summary chapter in French at the end

The current description of fundamental interactions is based on two theories with the status of standard models. The electromagnetic and nuclear interactions are described at a quantum level by the Standard Model of particle physics, using tools like gauge theories and spontaneous symmetry breaking by the Higgs mechanism. The gravitational interaction is described on the other hand by general relativity, based on a dynamical description of space-time at a classical level. Although these models are verified to high precision in the solar system experiments, they suffer from several theoretical weaknesses and a lack of predictive power at the Planck scale as well as at cosmological scales; they are thus not viewed anymore as fundamental theories. As its phenomenology involves both these extreme scales, cosmology is then a good laboratory to probe theories going beyond these standard models. The first part of this thesis focus on cosmic strings, topological defects forming during the spontaneous symmetry breaking of grand unified theories in the early universe. I show especially how to study these defects while taking into account the complete structure of the particles physics models leading to their formation, going beyond the standard descriptions in terms of simplified toy-models. The second part is devoted to the construction and the examination of different theories of modified gravity related to the Galileon model, a model which tries in particular to explain the dark energy phenomenology., Comment: Ph.D. Thesis (main body in French, articles in English). 272pp

This article is the detailed version of a paper on dark matter, dark energy, and modified gravity, published in the December 2015-January 2016 special issue of "La Recherche" (in French), Comment: 10 pages, in French, 1 figure