Newtonian limits of isolated cosmological systems on long time scales. (English) Zbl 1394.83004
Summary: We establish the existence of 1-parameter families of \(\epsilon\)-dependent solutions to the Einstein-Euler equations with a positive cosmological constant \(\Lambda >0\) and a linear equation of state \(p=\epsilon ^2 K \rho \), \(0<K\leq 1/3\), for the parameter values \(0<\epsilon < \epsilon _0\). These solutions exist globally to the future, converge as \(\epsilon \searrow 0\) to solutions of the cosmological Poisson-Euler equations of Newtonian gravity, and are inhomogeneous nonlinear perturbations of FLRW fluid solutions.
MSC:
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 83F05 | Relativistic cosmology |
| 83C25 | Approximation procedures, weak fields in general relativity and gravitational theory |
| 76Y05 | Quantum hydrodynamics and relativistic hydrodynamics |
| 83C15 | Exact solutions to problems in general relativity and gravitational theory |
| 83C55 | Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) |
Keywords:
Newtonian limits; isolated cosmological systems; Einstein-Euler equations; cosmological Poisson-Euler equations; inhomogeneous nonlinear perturbations; FLRW fluid solutionsSoftware:
GADGETReferences:
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