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A conformal approach for the analysis of the non-linear stability of radiation cosmologies. (English) Zbl 1263.83188
Summary: The conformal Einstein equations for a trace-free (radiation) perfect fluid are derived in terms of the Levi-Civita connection of a conformally rescaled metric. These equations are used to provide a non-linear stability result for de Sitter-like trace-free (radiation) perfect fluid Friedman-Lemaître-Robertson-Walker cosmological models. The solutions thus obtained exist globally towards the future and are future geodesically complete.

MSC:
83F05 Cosmology
85A25 Radiative transfer in astronomy and astrophysics
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
83C10 Equations of motion in general relativity and gravitational theory
83C75 Space-time singularities, cosmic censorship, etc.
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