Dark-Energy Dynamics Required to Solve the Cosmic Coincidence

Abstract

Dynamic dark energy (DDE) models are often designed to solve the cosmic coincidence (why, just now, is the dark energy density $\rho_{de}$, the same order of magnitude as the matter density $\rho_m$?) by guaranteeing $\rho_{de} \sim \rho_m$ for significant fractions of the age of the universe. This typically entails ad-hoc tracking or oscillatory behaviour in the model. However, such behaviour is neither sufficient nor necessary to solve the coincidence problem. What must be shown is that a significant fraction of observers see $\rho_{de} \sim \rho_m$. Precisely when, and for how long, must a DDE model have $\rho_{de} \sim \rho_{m}$ in order to solve the coincidence? We explore the coincidence problem in dynamic dark energy models using the temporal distribution of terrestrial-planet-bound observers. We find that any dark energy model fitting current observational constraints on $\rho_{de}$ and the equation of state parameters $w_0$ and $w_a$, does have $\rho_{de} \sim \rho_m$ for a large fraction of observers in the universe. This demotivates DDE models specifically designed to solve the coincidence using long or repeated periods of $\rho_{de} \sim \rho_m$.