We analyze the global nonlinear stability of FLRW (Friedmann-Lemaître-Robertson-Walker) spacetimes in the presence of an irrotational perfect fluid. We assume that the fluid is governed by the so-called (generalized) Chaplygin equation of state relating the pressure to the mass-energy density, in which and are constants. We express the Einstein equations in wave gauge as a system of coupled nonlinear wave equations and, after performing a conformal transformation, we analyze the global behavior of solutions toward the future. Under small perturbations, the -spacetime metric, the mass-energy density, and the velocity vector describing the geometry and fluid unknowns remain globally close to a reference FLRW solution. Our analysis provides also the precise asymptotic behavior of the perturbed solutions toward the future.
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Philippe G. LeFloch, Changhua Wei, Nonlinear stability of self-gravitating irrotational Chaplygin fluids in a FLRW geometry. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 3, pp. 787–814DOI 10.1016/J.ANIHPC.2020.09.005