  Starting from a quantization relation for primordial black holes, it is shown
that quantum fluctuations can play a fundamental role in determining the
effective scales of self-gravitating astrophysical systems. Furthermore the
Eddington-Weinberg relation between the current scale of the observed universe
to the Planck constant (the standard action unit) is naturally derived.
Finally, such an approach allows to recover the current value of the
cosmological constant.
