The new cosmological model founded on the Scale Covariant Theory of   Gravitation and on the Dirac's Large Number Hypothesis. (Part 1)
  The new scale-covariant formulation of the Dirac's Large Number Hypothesis (LNH) is proposed. The basic equations of LNH are formulated in the scale-covariant and "G-invariant" (invariant on the transformation law for G) form. On the basis of the Scale Covariant Theory of Gravitation and Dirac's LNH the cosmological model is constructed that gives as result the closed static Einstein's Universe in the gravitational system of units (g.s.u.) and the closed expanding Universe in the atomic system of units (a.s.u.). The simple dynamical model of atomic clock is proposed that leads to the same connection between the a.s.u. and the g.s.u. as the LNH and allows to specify the parameters of the model. The question about the equivalence of inertial and gravitational masses in the arbitrary system of units is ivestigated. It is deduced that the equivalence of inertial and gravitational masses in the arbitrary system of units takes place only for the unique transformation law for G even if the equivalence of two kinds of mass in the g.s.u. is assumed. It is shown that the model predicts the conservation of the black-body spectrum of the microvave background radiation independently of choice of the transformation law for G. It is argued that the some paradoxes of the standard cosmology can be overcomed in the given model without the supposition about the existence in the past of a phase of inflationary expansion. 
Alexander Rogachev