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

Primordial black holes, astrophysical systems and the Eddington-Weinberg relation