Astrophysical Naturalness - Soker, Noam (Frontiers in Astronomy and Space Sciences, 2022)
I suggest that stars introduce mass and density scales that lead to `naturalness' in the Universe. Namely, two ratios of order unity. (1) The combination of the stellar mass scale, $M_*(c,\hbar,G, m_p, m_e, e, …)$, with the Planck mass, $M_{\rm Pl}$, and the Chandrasekhar mass leads to a ratio of order unity that reads $N_{{\rm Pl *}} \equiv {M_{\rm Pl}}/({M_*} m^2_p )^{1/3} \simeq 0.15 - 3$, where $m_p$ is the proton mass. (2) A system with a dynamical time equals to the nuclear life times of stars, $τ_{\rm nuc *}$, has a density of $ρ_{\rm D *}(c,\hbar,G, m_p, m_e, e, …) \equiv ( G ~ τ^2_{\rm nuc *} ) ^{-1}$. The ratio of this density to the density of the dark energy, $ρ_{Λ}$, is $N_{λ *} = {ρ_{Λ}}/{ρ_{\rm D *}} ≈ 10^{-7} - 10^{5}$. Although the range is large, it is critically much smaller than the 123 orders of magnitude usually referred to when $ρ_{Λ}$ is compered to the Planck density. In the pure fundamental particles domain there is no naturalness; either naturalness does not exist or there is a need for a new physics or new particles. The `Astrophysical Naturalness' offers a third possibility: stars introduce the combinations of, or relations among, known fundamental quantities that lead to naturalness.