Cosmological coincidence problem in interacting dark energy models

TL;DR

The paper addresses the cosmological coincidence problem in an interacting dark-energy framework by introducing a coupling $Q = \lambda_m H \rho_m + \lambda_d H \rho_d$ between phantom dark energy and dark matter. By focusing on the transition near $\omega = -1$, it derives general conditions for crossing using near-transition expansions and shows that crossing can occur with $\dot{H}$ changing sign at $t=0$, under an even order $\alpha$ and $h_1>0$. The authors then demonstrate, for two phantom potentials—the quadratic and the exponential—the simultaneous realization of $\omega = -1$ crossing and a finite, order-one ratio $r_0 = \rho_m/\rho_d$ at the transition, achieving $r_0 \approx 3/7$ with suitable parameter choices. These results suggest a concrete mechanism by which the observed near-equality of dark matter and dark energy densities can be reconciled with a dynamical, crossing dark-energy sector, subject to the usual caveat of phantom-field quantum instabilities.

Abstract

An interacting dark energy model with interaction term $Q= λ_m Hρ_m+λ_dHρ_d$ is considered. By studying the model near the transition time, in which the system crosses the w=-1 phantom-divide-line, the conditions needed to overcome the coincidence problem is investigated. The phantom model, as a candidate for dark energy, is considered and for two specific examples, the quadratic and exponential phantom potentials, it is shown that it is possible the system crosses the w=-1 line, meanwhile the coincidence problem is alleviated, the two facts that have root in observations.