# GMR

## Seminar

### Cosmological solutions of the Einstein-Vlasov system

Seminar Room 1, Newton Institute

#### Abstract

I will present some of the global results that have been proved in recent years for the Einstein-Vlasov system in the cosmological case. These results are all obtained under symmetry assumptions and require that spacetime admits an $N$-dimensional symmetry group where $N\geq 2.$ I will mainly focus on the cases $N=2$ and $N=3.$ These situations are rather different since only if $N=2,$ gravitational waves are admitted. The question of global existence is quite well-understood but other important global issues are still open. In the last couple of years studies including a cosmological constant $\Lambda$ or a scalar field have been carried out in cases where $N\geq 3.$ In particular, future geodesic completeness has been proved when $\Lambda>0,$ which is an open problem in the case $\Lambda=0.$