We introduce different mass scales corresponding to the Universe, fermion stars, mini boson stars, Planck black holes, the electron, the neutrino, and the cosmon. These mass scales are obtained by combining the maximum mass of fermion stars, boson stars and soliton stars set by general relativity with the Eddington relation connecting the mass me of the electron to the cosmological constant Λ. In this manner, we can express the mass of these objects in terms of the fundamental constants of physics G, c, and Λ. By normalizing the mass Ma of these objects by the Planck mass MP , we find that Ma/MP ∼ χ a/6 , where χ ∼ ρP /ρΛ ∼ 10 120 is the "largest large number" in Nature (the ratio of the Planck density on the cosmological density) and a = 3, 2, 1, 0, −1, −2, −3 for the Universe, fermion stars, mini boson stars, Planck black holes, the electron, the neutrino, and the cosmon respectively. This formula suggests an interesting symmetrical mass scale law connecting cosmophysics (Universe, fermion stars, mini boson stars) to microphysics (electron, neutrino, cosmon). A generalization of this law including the earth mass and another neutrino mass scale is proposed. We also highlight an accurate form of Eddington relation me α(Λ 4 /G 2) 1/6 or Λ G 2 m 6 e /α 6 4 = α −6 (me/MP) 6 l −2 P , where α = e 2 / c 1/137 is the fine structure constant, given in a previous paper [P.H. Chavanis, Phys. Dark Univ. 24, 100271 (2019)] and provide different heuristic derivations of this relation. We suggest that the dark energy particle (cosmon) of mass mΛ = √ Λ/c could be a quantum of mass and entropy and that Λ = (mΛ/MP) 2 l −2 P. Finally, we give hints how to possibly solve the cosmological constant problem, the cosmic coincidence problem, and the large number coincidence problem.