Our knowledge of our universe is deeply related to our understanding of physics at the sub- atomic scale. Indeed, at its early stage, our universe was so hot and so dense that the only relevant interactions were those between fundamental particles. Therefore, to improve our comprehension of the phenomena that take place over very large scales, we should improve our understanding of the physics at extremely small ones. The so-called Standard Model of particle physics (SM) provides us with a description of these fundamental particles and their interactions. Despite its enormous success, this model fails to explain several experimental evidences. In this thesis, we focus on the following three questions that are not answered by the SM. What is the so-called dark matter that is present in every galaxy? Why is our present universe made of matter with almost no trace of anti-matter? Finally, why can a neutrino of one family transform into a neutrino of another family? In this thesis, we show that the simple addition of three new neutrinos to the Standard Model allows us to answer the three questions above. The model that realizes this scenario is known as Neutrino Minimal Standard Model (νMSM). In this work, we give a comprehensive summary of all known constraints in the νMSM. We present the first complete quantitative study of the parameter space of the model where no physics beyond the νMSM is needed to simultaneously explain the three phenomena cited above. Moreover, these new particles can be looked for using current day experimental techniques and our results provide a guideline for future experimental searches.