Does the diffusion DM-DE interaction model solve cosmological puzzles?

TL;DR

This paper investigates a cosmological model with dark matter-dark energy diffusion effects, showing it can address key issues in the standard Lambda-CDM model by analyzing its dynamics and phase space behavior.

Contribution

The study introduces a diffusion-based interaction model between dark matter and dark energy, analyzed through dynamical systems, demonstrating solutions to the coincidence and fine-tuning problems.

Findings

De Sitter solution is a global attractor in the phase space.

Model fits observational data within specified parameter ranges.

Potential to resolve cosmological puzzles like coincidence and fine-tuning.

Abstract

We study dynamics of cosmological models with diffusion effects modeling dark matter and dark energy interactions. We show the simple model with diffusion between the cosmological constant sector and dark matter, where the canonical scaling law of dark matter $(\rho_{dm,0}a^{-3}(t))$ is modified by an additive $\epsilon(t)=\gamma t a^{-3}(t)$ to the form $\rho_{dm}=\rho_{dm,0}a^{-3}(t)+\epsilon(t)$. We reduced this model to the autonomous dynamical system and investigate it using dynamical system methods. This system possesses a two-dimensional invariant submanifold on which the DM-DE interaction can be analyzed on the phase plane. The state variables are density parameter for matter (dark and visible) and parameter $\delta$ characterizing the rate of growth of energy transfer between the dark sectors. A corresponding dynamical system belongs to a general class of jungle type of cosmologies represented by coupled cosmological models in a Lotka-Volterra framework. We demonstrate that the de Sitter solution is a global attractor for all trajectories in the phase space and there are two repellers: the Einstein-de Sitter universe and the de Sitter universe state dominating by the diffusion effects. We distinguish in the phase space trajectories, which become in good agreement with the data. They should intersect a rectangle with sides of $\Omega_{m,0}\in [0.2724, 0.3624]$, $\delta \in [0.0000, 0.0364]$ at the 95\% CL. Our model could solve some of the puzzles of the $\Lambda$CDM model, such as the coincidence and fine-tuning problems. In the context of the coincidence problem, our model can explain the present ratio of $\rho_{m}$ to $\rho_{de}$, which is equal $0.4576^{+0.1109}_{-0.0831}$ at a 2$\sigma$ confidence level.