Gravitational vacuum hypothesis and cosmology with variable particle number

A heuristic model of gravitational vacuum as a set of virtual, radiating planckeons, particles with Planck size (L) and mass (h/cL) is discussed. Combined with Dirac's large number hypothesis, this gives the minimum universe scale factor value asub(min) approximately 10-13 cm, the strong interaction length (a = L just when a = asub(min)). Taking this state as an initial one using standard quantum techniques, particle creation by planckeons is considered. Under some reasonable assumptions the present number of particles with nucleon mass close to observations, N approximately 1080 is obtained. A criterion for gravitational stability of particles is formulated and some applications of the corresponding mass formula are considered. In particular, Fermi's weak interaction constant is expressed in terms of a and L and a finite value for the neutrino mass is obtained. (author)