Why Comparable? A Multiverse Explanation of the Dark Matter-Baryon Coincidence

TL;DR

This paper proposes a multiverse-based explanation for the observed similarity in dark matter and baryon densities, showing that probability suppression of overproduction naturally favors comparable densities without relying on anthropic assumptions.

Contribution

It introduces a landscape-based probability model that explains the dark matter-baryon coincidence through overproduction suppression, applicable across various dark matter models.

Findings

Probability suppression favors rac{1}{1+eta} for eta = ho_D / ho_B

This mechanism explains the coincidence without anthropic assumptions

It supports the viability of otherwise implausible dark matter models

Abstract

The densities of dark and baryonic matter are comparable: \zeta = \rho_D / \rho_B ~ O(1). This is surprising because they are controlled by different combinations of low-energy physics parameters. Here we consider the probability distribution over \zeta in the landscape. We argue that the Why Comparable problem can be solved without detailed anthropic assumptions, and independently of the nature of dark matter. Overproduction of dark matter suppresses the probability like 1/(1+\zeta), if the causal patch is used to regulate infinities. This suppression can counteract a prior distribution favoring large \zeta, selecting \zeta ~ O(1). This effect not only explains the Why Comparable coincidence but also renders otherwise implausible models of dark matter viable. For the special case of axion dark matter, Wilczek and independently Freivogel have already noted that a 1/(1+\zeta) suppression prevents overproduction of a GUT-scale QCD axion. If the dark matter is the LSP, the effect can explain the moderate fine-tuning of the weak scale in simple supersymmetric models.