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

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.