According to the present paradigm of cosmology which is in agreement with all existing observational data, the history of the whole observable part of our Universe consists of 4 main epochs: 1) primordial vacuum-like (de Sitter, or inflationary) stage; 2) radiation-dominated stage; 3) matter-dominated stage, and now we are living in the process of transition to the second vacuum-like stage which is remarkably qualitatively similar to the first one. The quantitative phenomenological description of this history is based on known principles of classical and quantum physics. However, it requires the introduction of 4 new fundamental constants, in addition to whose known from laboratory experiments, and two kinds of matter seen through their gravitational interaction only: non-relativistic dark matter and vacuum-like dark energy (primordial and present ones). I describe these 4 constants and physical theories standing beyond each of them and discuss which new constants may be expected soon from cosmological observations and how the theory may help us to keep the number of these constants at the same level (if not diminish it by some unification). The remarkable analogy between the primordial dark energy which drove inflation long ago and the present one suggests that the latter is not stable and eternal, too.