The global nonlinear stability of self-gravitating irrotational Chaplygin fluids in a FRW geometry

Abstract

We analyze the global nonlinear stability of FRW (Friedmann-Robertson-Walker) spacetimes in 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. We express the Einstein equations in wave gauge as a systems of coupled nonlinear wave equations and by performing a suitable conformal transformation, we are able to analyze the global behavior of solutions in future timelike directions. We establish that the (3+1)-spacetime metric and the mass density and velocity vector describing the evolution of the fluid remain globally close to a reference FRW solution, under small initial data perturbations. Our analysis provides also the precise asymptotic behavior of the perturbed solutions in the future directions.