The article is divided in 2 parts. In the 1^st part (PART I) we propose that a substance, called ether-substance, fills and constitutes all what is called “vacuum” in the Universe. We assume that it has a mass and consequently it could be the nature of dark matter. Modelling it as an ideal gas, we obtain the flat rotation curve of spiral galaxies. Using a very simple model of thermal transfer between baryonic particles and ether-substance, we obtain the baryonic Tully-Fisher’s law. So we introduce a new concept of ether, different from the pre-relativistic concept of ether, and we called “Cosmology based on ether” (CBE) Cosmology based on this new concept. In this CBE, topology of the Universe is much simpler and more attractive than topologies proposed by the Standard Cosmological model (SCM) (whose some fundamental aspects are kept in CBE). We propose 2 models in CBE. The first one does not need dark energy nor cosmological constant, and does not need the complex mathematics of General Relativity, contrary to SCM (and to the 2^nd model of CBE). Nonetheless, we obtain in the 1^st model of CBE a very simple Hubble’s constant, in 1/t, t age of the Universe, and many cosmological observations that were previously explained only by the SCM. Moreover we interpret in both models of CBE the Referential in which fossil radiation is isotropic. CBE is, as SCM, compatible with Special and General Relativity, despite that it is based on a new concept of ether. In the 2^nd part, (Part II), we will study some problems raised by the Part I (motion of galaxies in the space, concentration of ether-substance around stars…).

Topology of the Universe, Tully-Fisher’s law, dark matter, fossil radiation, ether