The Dynamical Systems Approach to Spatially Homogenous Einstein-Vlasov Cosmology

Explore the dynamical systems approach to spatially homogeneous Einstein-Vlasov cosmology in this 30-minute lecture from the Hausdorff Junior Trimester Program on Kinetic Theory. Delve into theoretical and mathematical cosmology, examining deviations from conventional models that assume spatial homogeneity and isotropy with perfect fluid matter content. Investigate spatially homogeneous Einstein-Vlasov cosmology, where matter is modeled as a collision-free kinetic gas, and learn about the approach initiated by Rendall (1996) that reduces the system to an autonomous dynamical system. Discover the exact past and future asymptotic solutions, including behavior near big-bang or big-crunch singularities and towards an expanding future. Gain insights into Kantowski-Sachs cosmology with Vlasov matter, as presented by Gernot Heißel, and explore topics such as symmetry inheritance, spatial virginity, mansion equations, and physical constraints.

Introduction
Basics
Cosmology
Recap
Fast method
Inheritance of symmetry
Additional symmetry
Spatial virginity
The metric
Warning results
Mansion equations
Physical constraints
Proof
Summary