Dark-energy dynamics required to solve the cosmic coincidence

Dynamic dark-energy (DDE) models are often designed to solve the cosmic coincidence (why, just now, is the dark-energy density ρ_de the same order of magnitude as the matter density ρ_m?) by guaranteeing ρ_de∼ρ_m for significant fractions of the age of the Universe. However, such behavior is neither sufficient nor necessary to solve the coincidence problem. Cosmological processes constrain the epochs during which observers can exist. Therefore, what must be shown is that a significant fraction of observers see ρ_de∼ρ_m. Precisely when, and for how long, must a DDE model have ρ_de∼ρ_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 realistic DDE model which can be parametrized as w=w₀+w_a(1-a) over a few e-folds has ρ_de∼ρ_m for a significant fraction of observers in the Universe. This demotivates DDE models specifically designed to solve the coincidence using long or repeated periods of ρ_de∼ρ_m.