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.

我们分析了在无旋转完美流体存在下的FLRW（Friedmann-Lemaître-Robertson-Walker）时空的全局非线性稳定性。我们假设流体受所谓的（广义）Chaplygin状态方程支配$p=-\frac{{\mathrm{一种}}^{\mathrm{2个}}}{{\rho }^{\alpha }}$ 将压力与质量能密度相关联，其中 $\mathrm{一种}>0$ 和 $\alpha \in （0，\mathrm{1个}]$是常数。我们将波谱仪中的爱因斯坦方程式表达为耦合非线性波动方程式的系统，并在进行了保形变换后，分析了未来解决方案的整体行为。在小扰动下，$（3+\mathrm{1个}）$时空度量，质量能密度和描述几何和流体未知数的速度向量总体上保持接近参考FLRW解。我们的分析还提供了未来扰动解的精确渐近行为。