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Nonlinear stability of self-gravitating irrotational Chaplygin fluids in a FLRW geometry. (English) Zbl 1464.83026

Summary: 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 \(p=-\frac{A^2}{\rho^\alpha}\) relating the pressure to the mass-energy density, in which \(A>0\) and \(\alpha\in (0, 1]\) 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 \((3+1)\)-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.

MSC:

83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
83F05 Relativistic cosmology
35Q31 Euler equations
35Q76 Einstein equations
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
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