Formation of large-scale structure in various cosmological scenarios

The study of physical cosmology has reached an exciting era. For the first time in human history, a quantitative model for the formation and the evolution of the Universe exists, which explains a wide range of phenomena and has been tested with incredible accuracy during the last century. Moreover, weare approaching a time when a bounty of high quality cosmological data will be available,allowing us to use cosmology as a tool to test fundamental physics.In particular, as the large-scale structures of the Universe are governed by gravity, cosmology can help us to asses the correctness of Albert Einstein’s general relativity. This idea fueledmost of the work described in this manuscript,in which we study alternative theories to the standard cosmological model and large-scale structure tests for general relativity.In particular, we focus on two scalar-tensor theories of gravity, the K-mouflage models described in Chapter 2 and the ultra-localmodels of gravity presented in Chapter 3. The K-mouflage theories are k-essence models with a non-standard kinetic term that were already studied at the linear and background levels. In this manuscript, we extend this description showing how the scalar field, which is responsible for the late time acceleration of the Universe, has a non-negligible impact on cluster dynamics, arguing that future surveysmay have the power of constraining K-mouflage models via X-ray observations. Next,we study the ultra-local models of gravity,where a scalar field with a negligible kinetic term is added to the Einstein-Hilbert action,investigating how the latter modifiescosmological structure formation and howthese models can be related to super-chameleonmodels.In Chapter 4, we present a cosmic shear data analysis in the context of f (R) and Dilaton models, and we show how current data canaccommodate most of the theories considered,once baryonic and neutrino physicsdegeneracies are taken into account. Finally, in Chapter 5 we present an analysis of consistency relations for large-scale structures,which are non-perturbative relations among correlations of cosmic fields. They are alsovalid in the non-linear regime, where very few analytical results are known, and only rely on the Equivalence Principle and primordial Gaussian initial conditions. This makes them a powerful tool to test general relativity and inflationary models using the cosmologic allarge-scale structures.We provide here the first non-vanishing equaltime consistency relations, which we use to obtain consistency relations involving observational quantities.In this Thesis manuscript, we highlight the major results of the full analysis done in the articles that are appended to the main text,where the reader can quench any thirst for technical details.