The characteristic sizes of astrophysical structures, up to the whole
observed Universe, can be recovered, in principle, assuming that gravity is the
overall interaction assembling systems starting from microscopic scales, whose
order of magnitude is ruled by the Planck length and the related Compton
wavelength. This result agrees with the absence of screening mechanisms for the
gravitational interaction and could be connected to the presence of Yukawa
corrections in the Newtonian potential which introduce typical interaction
lengths. This result directly comes out from quantization of primordial black
holes and then characteristic interaction lengths directly emerge from quantum
field theory.Comment: 11 page
