In this talk, I will discuss the recent work with David Fajman on stability of a subclass of the negatively curved FLRW models, the so-called Milne universe, in the set of the solutions to the Einstein-Vlasov-Maxwell system. The Milne universe is a vacuum non-accelerating expanding cosmological model for which some stability results are known. After reviewing the previous results on the stability of this model, I will describe the ideas of the proof and focus on the subtleties of the Einstein-Vlasov-Maxwell case that arise from the coupling of the two matter fields which again couple to the Einstein equations in the so-called CMCSH gauge. This work provides the first stability result for the Einstein-Vlasov-Maxwell system and it generalizes the results of Andersson-Moncrief, Andersson-Fajman, and Branding-Fajman-Kröncke in 3+1 dimensions.
