Dark-Energy Dynamics Required to Solve the Cosmic Coincidence

TL;DR

This paper investigates the timing and duration of dark energy density being comparable to matter density, showing that current observationally consistent models naturally have this coincidence for many observers, questioning the need for special dynamic models.

Contribution

It demonstrates that existing dynamic dark energy models consistent with observations inherently solve the coincidence problem without requiring ad-hoc tracking or oscillations.

Findings

Most observers see $ ho_{de} \

large fraction of observers experience $ ho_{de} \\sim ho_m$

Long or repeated periods of coincidence are unnecessary for solving the problem

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 $\rho_{de} \sim \rho_m$.