The cosmic no-hair theorem and the non-linear stability of homogeneous Newtonian cosmological models

Abstract

The validity of the cosmic no-hair theorem is investigated in the context of\nNewtonian cosmology with a perfect fluid matter model and a positive\ncosmological constant. It is shown that if the initial data for an expanding\ncosmological model of this type is subjected to a small perturbation then the\ncorresponding solution exists globally in the future and the perturbation\ndecays in a way which can be described precisely. It is emphasized that no\nlinearization of the equations or special symmetry assumptions are needed. The\nresult can also be interpreted as a proof of the nonlinear stability of the\nhomogeneous models. In order to prove the theorem we write the general solution\nas the sum of a homogeneous background and a perturbation. As a by-product of\nthe analysis it is found that there is an invariant sense in which an\ninhomogeneous model can be regarded as a perturbation of a unique homogeneous\nmodel. A method is given for associating uniquely to each Newtonian\ncosmological model with compact spatial sections a spatially homogeneous model\nwhich incorporates its large-scale dynamics. This procedure appears very\nnatural in the Newton-Cartan theory which we take as the starting point for\nNewtonian cosmology.\n