Explaining the dark energy, baryon and dark matter coincidence via domain-dependent random densities

Abstract

The dark energy, dark matter and baryon densities in the Universe are observed to be similar, with a factor of no more than 20 between the largest and smallest densities. We show that this coincidence can be understood via superhorizon domains of randomly varying densities when the baryon density at initial collapse of galaxy-forming perturbations is determined by anthropic selection. The baryon and dark matter densities are assumed to be dependent on random variables θd and θb according to ρdm∝θdα and ρb∝θbβ, while the effectively constant dark energy density is dependent upon a random variable ϕQ according to ρQ∝ϕQn. The ratio of the baryon density to the dark energy density at initial collapse, rQ, and the baryon-to-dark matter ratio, r, are then determined purely statistically, with no dependence on the anthropically-preferred baryon density. We compute the probability distribution for rQ and r and show that the observed values of rQ and r can be naturally understood within this framework. In particular, for the case α = 2, β = 1 and n = 4, which can be physically realized via a combination of axion dark matter, Affleck-Dine baryogenesis and frozen quintessence with a ϕQ4 potential, the range of rQ and r which corresponds to the observed Universe is a quite natural, with a probability which is broadly similar to other ranges of rQ and r.