A quantitative criteria for the coincidence problem

TL;DR

This paper introduces a quantitative criterion to evaluate the severity of the cosmic coincidence problem and applies it to various dark energy models, finding the interacting Chaplygin gas model most effectively addresses the issue.

Contribution

It proposes a new quantitative measure for the coincidence problem and compares different models, highlighting the effectiveness of the interacting Chaplygin gas model.

Findings

The coincidence index C for the interacting Chaplygin gas model is significantly lower.

The criterion effectively distinguishes models based on their ability to solve the coincidence problem.

Interacting Chaplygin gas model outperforms others by six orders of magnitude in the coincidence index.

Abstract

The cosmic coincidence problem is a serious challenge to dark energy model. We suggest a quantitative criteria for judging the severity of the coincidence problem. Applying this criteria to three different interacting models, including the interacting quintessence, interacting phantom, and interacting Chaplygin gas models, we find that the interacting Chaplygin gas model has a better chance to solve the coincidence problem. Quantitatively, we find that the coincidence index C for the interacting Chaplygin gas model is smaller than that for the interacting quintessence and phantom models by six orders of magnitude.