Baryon-to-Dark Matter Ratio from Random Angular Fields

Abstract

We consider the baryon-to-dark matter ratio in models where the dark matter and baryon densities depend on angular fields θ_{d} and θ_{b} according to ρ_{d} ~ θ_{d}^α and ρ_{b} ~ θ_{b}^β, with all values of θ_{d} and θ_{b} being equally probable in a given randomly-selected domain. Under the assumption that anthropic selection depends primarily on the baryon density in galaxies at spherical collapse, we show that the probability density function for the baryon-to-dark matter ratio r = Ω_{B}/Ω_{DM} is purely statistical in nature and is independent of anthropic selection. We compute the probability density function for r as a function of αand βand show that the observed value of the baryon-to-dark matter ratio, r \approx 1/5, is natural in this framework.