Emerging dark matter from corpuscular dark energy

In the last years, the standard model of cosmology has been corroborated by a wide number of astrophysical observations. Despite its undeniable success, nowadays there is little knowledge about the true nature of dark matter and dark energy. In this thesis we use a different approach to give an intriguing answer to these open problems, in the light of the corpuscular model of gravity. We give a general overview on the reasons behind the need for a corpuscular theory of the gravitational interaction. Then, we show that if the same picture is extended to cosmological spaces, dark energy naturally emerges as a quantum state of the gravitational dynamics, and it is described as a Bose-Einstein condensate of very soft and virtual gravitons without the necessity of introducing an exotic dark fluid. Besides, the cosmic condensate responds locally to the presence of baryonic matter, and the back-reaction manifests itself in the emergence of a dark force that mimics a dark matter behavior. In particular, at galactic scales the MOND formula for the acceleration is recovered. Then, a first attempt of estimating the back-reaction is proposed within the framework of Bootstrapped Newtonian gravity, that allows for an effective field description where Newtonian theory is “bootstrapped" introducing post-Newtonian corrections, providing a useful tool for calculations. Finally, we show that a logarithmic potential arises as a solution of the Bootstrapped field equation, in accordance with MOND prediction.