Dynamics of Robertson-Walker spacetimes with diffusion

Understand

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.