In this paper basic cosmological consequences of zatrikean pregeometry are studied. It is shown that many universal quantities can be calculated with simple applications of this theory. An equation directly linking the angular velocity of the universeω, the Hubble constantH and the mean densityρ of the universe is derived. The relation between the massM and the radiusR of the universe is examined. This relation leads to various cosmological scenarios, including variations in physical constants and/or violation of the mass conservation and/or variable geometrical properties.