Stabilizing effect of the spacetime expansion on the Euler–Poisson equations in Newtonian cosmology

Abstract

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.