Future Attractors in $2+1$ Dimensional $\mathrm{\Lambda }$ Gravity

Any $2+1$ dimensional Einsteinian spacetime with positive cosmological constant and compact hyperbolic spatial topology evolves in the expanding direction to a de Sitter model with homogeneous hyperbolic spatial geometry. In particular, the latter constitutes the uniform future attractor for this class of spacetimes for arbitrary large initial data. This is an example of large-data homogenization and demonstrates the ability of gravitation to cause late time homogenization in the evolution of cosmological models independently of their initial state.