Future stability of the FLRW spacetime for a large class of perfect fluids

Abstract

We establish the future non-linear stability of Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) solutions to the Einstein-Euler equations of the universe filled with a large class of perfect fluids (the equations of state are allowed to be certain nonlinear or linear types both). Several previous results as specific examples can be covered in the results of this article. We emphasize that the future stability of FLRW metric for polytropic fluids with positive cosmological constant has been a difficult problem and can not be directly generalized from the previous known results. Our result in this article has not only covered this difficult case for the polytropic fluids, but also unified more types of fluids in a same scheme of proofs.