Interacting Cosmological Fluids and the Coincidence Problem

TL;DR

This paper studies a universe with two interacting fluids, showing that their density ratio tends to a constant or oscillates, which offers a solution to the coincidence problem by explaining why dark matter and dark energy densities are comparable today.

Contribution

It introduces a model of interacting fluids with a specific interaction term, providing exact solutions and demonstrating how it addresses the coincidence problem in cosmology.

Findings

The density ratio approaches a constant for matter fluids.

Periodic solutions occur when w < -1, leading to oscillating density ratios.

The ratio of dark matter to dark energy remains bounded and can be O(1) infinitely often.

Abstract

We examine the evolution of a universe comprising two interacting fluids, which interact via a term proportional to the product of their densities. In the case of two matter fluids it is shown that the ratio of the densities tends to a constant after an initial cooling-off period. We then obtain a complete solution for the cosmological constant (w = -1) scenario. Finally, we investigate the general case in which the dark energy equation of state is p = w*rho, where w is a constant, and show that periodic solutions can occur if w < -1. We further demonstrate that the ratio of the dark matter to dark energy densities is confined to a bounded interval, and that this ratio can be O(1) at infinitely many times in the history of the universe, thus solving the coincidence problem.