The validity of the cosmic no-hair theorem for polytropic perfect fluids has been established by (Brauer et al 1994 Class. Quantum Grav. 11 2283) within the context of Newtonian cosmology, specifically under conditions of exponential expansion. This paper extends the investigation to assess the nonlinear stability of homogeneous Newtonian cosmological models under general accelerated expansion for perfect fluids. With appropriate assumptions regarding the expansion rate and decay properties of the homogeneous solution, our results demonstrate that the Euler–Poisson system admits a globally classical solution for initial data that are small perturbations to the homogeneous solution. Additionally, we establish that the solution asymptotically approaches the homogeneous solution as time tends to infinity. The theoretical framework is then applied to various types of perfect fluids, including isothermal gases, Chaplygin gases, and polytropic gases.

中文翻译：

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牛顿宇宙学中时空膨胀对欧拉-泊松方程的稳定作用


多方完美流体的宇宙无发定理的有效性是由 （Brauer et al 1994 Class. Quantum Grav. 11， 2283） 在牛顿宇宙学的背景下建立的，特别是在指数膨胀的条件下。本文扩展了研究范围，以评估均匀牛顿宇宙学模型在完美流体的一般加速膨胀下的非线性稳定性。通过对齐次解的膨胀率和衰减特性进行适当的假设，我们的结果表明，Euler-Poisson 系统对齐次解的微小扰动的初始数据接受了全局经典解。此外，我们确定，随着时间趋于无穷大，解逐渐接近齐次解。然后将理论框架应用于各种类型的完美流体，包括等温气体、Chaplygin 气体和多方气体。