Baryon-to-Dark Matter Ratio from Random Angular Fields

TL;DR

This paper models the baryon-to-dark matter ratio using random angular fields and demonstrates that the observed ratio is a natural statistical outcome within this framework, independent of anthropic selection.

Contribution

It introduces a statistical model linking baryon and dark matter densities to angular fields, explaining the observed ratio without anthropic bias.

Findings

The probability density function for the ratio is independent of anthropic selection.

The observed ratio r ≈ 1/5 is statistically natural in the model.

The model relates the ratio to parameters lpha and eta.

Abstract

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.