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The conformal Einstein equations for a tracefree (radiation) perfect fluidare derived in terms of the Levi-Civita connection of a conformally rescaledmetric. These equations are used to provide a non-linear stability result forde Sitter-like tracefree (radiation) perfect fluidFriedman-Lema\^{\i}tre-Robertson-Walker cosmological models. The solutions thusobtained exist globally towards the future and are future geodesicallycomplete.

A conformal approach for the analysis of the non-linear stability of pure radiation cosmologies