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Cosmological Newtonian Limits on Large Spacetime Scales

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Abstract

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.

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Acknowledgements

This work was partially supported by the ARC Grant FT120100045 and a Senior Scholarship from the Australia-American Fulbright Commission. Part of this work was completed during visits by the first author to the Erwin Schrdinger International Institute for Mathematics and Physics (ESI), the Max Planck Institute for Gravitational Physics (AEI) and the School of Mathematical Sciences at Xiamen University, and by the second author to the Mathematics Department at Princeton University. They are grateful for the support and hospitality during their visits.

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  1. School of Mathematical Sciences, Monash University, Melbourne, VIC, 3800, Australia

    Chao Liu & Todd A. Oliynyk

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  1. Chao Liu
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  2. Todd A. Oliynyk
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Correspondence to Chao Liu.

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Communicated by P. Chrusciel

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Liu, C., Oliynyk, T.A. Cosmological Newtonian Limits on Large Spacetime Scales. Commun. Math. Phys. 364, 1195–1304 (2018). https://doi.org/10.1007/s00220-018-3214-9

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