Cosmological Newtonian limits on large spacetime scales. (English) Zbl 1402.83116
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 on the manifold \(M = (0, 1] \times \mathbb{R}^{3}\), are future complete, and converge as \(\epsilon \searrow 0\) to solutions of the cosmological Poisson-Euler equations. They represent inhomogeneous, nonlinear perturbations of a FLRW fluid solution where the inhomogeneities are driven by localized matter fluctuations that evolve to good approximation according to Newtonian gravity.
MSC:
| 83F05 | Relativistic cosmology |
| 53Z05 | Applications of differential geometry to physics |
| 83C25 | Approximation procedures, weak fields in general relativity and gravitational theory |
| 83C55 | Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) |
Keywords:
cosmological Newtonian limits; positive cosmological constant; linear equation of state; nonlinear perturbationsReferences:
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