Cosmogony and the magnitude of the dimensionless gravitational coupling constant

Abstract

SIMPLE arguments involving gravitational fragmentation indicate that for the Universe to contain galaxies and stable nuclear-burning stars, the dimensionless gravitational coupling constant α_g(= Gm_p²/ħc) must lie within several orders of magnitude of its actual value (5×10⁻³⁹). The characteristic mass of a galaxy is shown to be α⁵ α_g⁻² nucleons. If galaxies and galaxy clusters form by gravitational instability and fragmentation of inhomogeneities in the early Universe, the large-scale structure of the Universe imposes a lower bound, and the instability requirement an upper bound (equal to α_g^−1/4), on the entropy per particle.