In this article, we propose a new model of dark matter. According to this new model, dark matter is a substance, that is a new physical element not constituted of classical particles, called dark substance and filling the Universe. Assuming some very simple physical properties to this dark substance, we theoretically justify the flat rotation curve of galaxies and the baryonic Tully-Fisher’s law. Then we give a Physical Interpretation of the CMB Rest Frame (CRF). This new Interpretation of the CRF permits also a new interpretation of the Cosmological time. Moreover it is in agreement with the Standard Cosmological Model (SCM) on many points. For instance it assumes the validity of the Special and General Relativity. Then using these new interpretations of dark matter and of the CRF, we are led to propose a new model of Universe, flat and finite, that is not predicted by the SCM. Despite of this we will see that a first mathematical model of our Physical Interpretation of the CRF, that is based on the equations of the General Relativity as the SCM, leads to an observable Universe with the same theoretical astrophysical predictions as the SCM. We will see that a 2nd mathematical model, much simpler, has nonetheless theoretical astrophysical predictions that are in agreement with astronomical observations. We will then study the theoretical consequences of those 2 models.