Future stability of the FLRW fluid solutions in the presence of a positive cosmological constant. (English) Zbl 1346.83023

Oliynyk, Todd A.

Commun. Math. Phys. 346, No. 1, 293-312 (2016).

Summary: We introduce a new method for establishing the future non-linear stability of perturbations of FLRW solutions to the Einstein-Euler equations with a positive cosmological constant and a linear equation of state of the form \(p=K\rho\). The method is based on a conformal transformation of the Einstein-Euler equations that compactifies the time domain and can handle the equation of state parameter values \(0<K\leq 1/3\) in a uniform manner. It also determines the asymptotic behavior of the perturbed solutions in the far future.

MSC:

83C15	Exact solutions to problems in general relativity and gravitational theory
83C55	Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
83F05	Relativistic cosmology
83C25	Approximation procedures, weak fields in general relativity and gravitational theory
83C75	Space-time singularities, cosmic censorship, etc.
37N20	Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
76Y05	Quantum hydrodynamics and relativistic hydrodynamics

Keywords:

future stability; FLRW; fluid solutions; positive cosmological constant; non-linear stability; perturbations; Einstein-Euler equations

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