We consider the baryon-to-dark matter ratio in models where the dark matter and baryon densities depend on angular fields \theta_{ d} and \theta_{ b} according to \rho_{ d} ~ \theta_{ d}^{ \alpha} and \rho_{ b} ~ \theta_{ b}^{ \beta}, with all values of \theta_{ d} and \theta_{ 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 = \Omega_{ B}/\Omega_{ DM} is purely statistical in nature and is independent of anthropic selection. We compute the probability density function for r as a function of \alpha and \beta and show that the observed value of the baryon-to-dark matter ratio, r \approx 1/5, is natural in this framework.
Categories: hep-ph astro-ph.CO hep-th