Future stability of the FLRW spacetime for a large class of perfect fluids

28 Oct 2018  ·  Chao Liu, Changhua Wei ·

We establish the future non-linear stability of Friedmann-Lema^{\i}treRobertson-Walker (FLRW) solutions to the Einstein-Euler equations of the universe filled with a large class of Makino-type fluids (the equations of state are allowed to be certain nonlinear or linear types both). Several previous results as specific examples can be covered in the results of this article. We emphasize that the future stability of FLRW metric for polytropic fluids with positive cosmological constant has been a difficult problem and can not be directly generalized from the previous known results. Our result in this article has not only covered this difficult case for the polytropic fluids, but also unified more types of fluids in a same scheme of proofs.

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General Relativity and Quantum Cosmology Analysis of PDEs Primary 35A01, Secondary 35Q31, 35Q76, 83C05, 83F05