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

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 $0.4576_{-0.0831}^{+0.1109}$ at a 2$\sigma$ confidence level.

27 pages, 17 figures

References in corpus (8)

• Dynamics of dark energy
• Aspects of the cosmological "coincidence problem"
• Emergent Cosmology, Inflation and Dark Energy
• Relativistic diffusion
• Cosmological model with decaying vacuum energy law from principles of quantum mechanics
• Dynamics of the diffusive DM-DE interaction--dynamical system approach
• Possible Equilibria of Interacting Dark Energy Models
• Non-linear dark matter collapse under diffusion

Cited by in corpus (11)

• Dynamical systems applied to cosmology: dark energy and modified gravity
• Interacting Diffusive Unified Dark Energy and Dark Matter from Scalar Fields
• Order out of Randomness : Self-Organization Processes in Astrophysics
• Kinetically coupled dark energy
• Observational constraints on the interacting dark energy - dark matter (IDM) cosmological models
• Realising Interactions Between Dark Matter and Dark Energy Using $k$-essence Cosmology
• Time-dependent diffusive interactions between dark matter and dark energy in the context of $k-$essence cosmology
• Diffusive dark matter and dark energy scenario and $k-$essence in the context of Supernova Ia observations
• Thermodynamics of diffusive DM/DE systems
• Kinetic coupled tachyon: A dynamical system analysis
• Modified scaling in $k$-essence model in interacting dark energy - dark matter scenario