Beyond Einstein’s theory of gravitation : some aspects of loop quantum cosmology, black holes and the dark universe

In this thesis we explore the phenomenology of some extensions to General Relativity and quantum gravity theories.The motivation for this research lies in the incompleteness of the current theoretical models that describe the behaviour of matter on cosmological scales.The standard model of particle physics and general relativity, combined together along with experimental probes in particle colliders and astrophysics, lead to a model for our universe, which is today dominated by dark matter. Moreover, according to the best model, the universe is currently undergoing an accelerated expansion and had started its existence with a space-time singularity: the big bang.The challenge for theoretical physics is therefore to obtain a model without singularity and with less invisible matter (or none). To this respect, the last two decades have been particularly fruitful: there is a large number of competing modified gravity and dark energy theories as well as quantum gravity proposals at our disposal.The purpose of the work presented here is to set up a phenomenological framework that enables a clear comparison and possible exclusions of these new theories by confronting them to current and future observational data.The first part of the thesis is dedicated to modified gravity and dark energy models. The second part deals with loop quantum cosmology, and the last part is a presentation of a new probe for dark energy: the thermal Sunyaev Zeldovich power spectrum.