## The nonlinear future stability of the FLRW family of solutions to the irrotational Euler-Einstein system with a positive cosmological constant.(English)Zbl 1294.35164

The authors consider the coupled Euler-Einstein system which models the evolution of a dynamic spacetime containing a perfect fluid with vanishing vorticity. They introduce a positive constant $$\Lambda$$ in this system and they recall the existence of a family of background solutions to this system. The purpose of the paper is to study small perturbations of this family of Friedmann-Lemaítre-Robertson-Walker cosmological solutions. The main results of the paper indeed prove that small perturbations of the initial data may have maximal globally hyperbolic developments that are future causally geodesically complete. For the proof, the authors use a combination of energy estimates and pointwise decay estimates for quasilinear wave equations.

### MSC:

 35Q76 Einstein equations 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems) 35Q31 Euler equations 83F05 Relativistic cosmology
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### References:

 [1] Anderson, M. T.: Existence and stability of even-dimensional asymptotically de Sitter spaces. Ann. Henri Poincaré 6, 801-820 (2005) · Zbl 1100.83004 [2] Bieri, L., Zipser, N. (eds.): Extensions of the Stability Theorem of the Minkowski Space in General Relativity. Amer. Math. Soc., Providence, RI (2009) · Zbl 1172.83001
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