Dynamics of Robertson-Walker spacetimes with diffusion

TL;DR

This paper investigates the evolution of Robertson-Walker spacetimes with diffusive fluids, deriving exact solutions and analyzing their global behavior, revealing scenarios with perpetual accelerated expansion and asymptotic de-Sitter states.

Contribution

It introduces a dynamical systems approach to analyze the cosmological models with diffusion, providing new insights into their qualitative behavior and exact solutions.

Findings

Existence of solutions with asymptotic de-Sitter behavior

Identification of models with eternal accelerated expansion

Global phase space analysis of the dynamical system

Abstract

We study the dynamics of spatially homogeneous and isotropic spacetimes containing a fluid undergoing microscopic velocity diffusion in a cosmological scalar field. After deriving a few exact solutions of the equations, we continue by analyzing the qualitative behavior of general solutions. To this purpose we recast the equations in the form of a two dimensional dynamical system and perform a global analysis of the flow. Among the admissible behaviors, we find solutions that are asymptotically de-Sitter both in the past and future time direction and which undergo accelerated expansion at all times.