Nonlinear stability of homogeneous models in Newtonian cosmology

TL;DR

This paper proves the nonlinear stability of homogeneous solutions in a cosmological Vlasov-Poisson model, shedding light on the evolution of large-scale structures like galaxies from early universe homogeneity.

Contribution

It establishes the nonlinear stability of homogeneous solutions under small perturbations in a Newtonian cosmological setting.

Findings

Homogeneous solutions are nonlinearly stable against small spatial perturbations.

The stability result relates to the evolution of large-scale cosmic structures.

Provides a mathematical foundation for understanding structure formation in cosmology.

Abstract

We consider the Vlasov-Poisson system in a cosmological setting and prove nonlinear stability of homogeneous solutions against small, spatially periodic perturbations in the sup-norm of the spatial mass density. This result is connected with the question of how large scale structures such as galaxies have evolved out of the homogeneous state of the early universe.