Author’s summary: “We consider the Vlasov-Poisson system in a cosmological setting as studied in [G. Rein and A. D. Rendall, ibid. 126, 183-201 (1994; Zbl 0808.35109)] and prove nonlinear stability of homogeneous solutions against small, spatially periodic perturbations in the \(L^\infty\)-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”.