Probing new physics in the era of precision cosmology

Over the past decades, advancements in observational cosmology have introduced us in an era of precision cosmology, dramatically enhancing our understanding of the Universe's history as well as bringing new tensions to light. Observations of the Cosmic Microwave Background, large-scale structure, and distant galaxies have provided unprecedented insights into the processes that shaped our Universe. This PhD thesis contributes to this research by exploring how these cosmic observables can be leveraged to constrain new physics beyond the standard $\Lambda$-Cold Dark Matter model.