In this talk, I will discuss recent results concerning the global stability to the future of solutions to the relativistic Euler equation on expanding cosmological spacetimes.
The first part of the talk will be a review focusing on what is known about the stability and instability of relativistic fluids on cosmological backgrounds. In the second part of the talk, I will discuss new stability results for relativistic fluids with a linear equation of state p = Kρ on FLRW spacetimes where the equation of state parameter value K satisfies 1/3 < Κ < 1/2 .
This new stability result is of particular interest because it was previously conjectured that instabilities should develop for the parameter values 1/3 < K < 1 .
Time permitting, I will conclude the talk with a discussion of future projects and areas for further research.
