Newtonian Limits of Isolated Cosmological Systems on Long Time Scales

Chao Liu; Todd Oliynyk

doi:10.1007/s00023-018-0686-2

Newtonian Limits of Isolated Cosmological Systems on Long Time Scales

Chao Liu, Todd Oliynyk

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

20 Citations (Scopus)

Abstract

We establish the existence of 1-parameter families of ϵ-dependent solutions to the Einstein–Euler equations with a positive cosmological constant Λ > 0 and a linear equation of state p= ϵ²Kρ, 0 < K≤ 1 / 3 , for the parameter values 0 < ϵ< ϵ₀. These solutions exist globally to the future, converge as ϵ↘ 0 to solutions of the cosmological Poisson–Euler equations of Newtonian gravity, and are inhomogeneous nonlinear perturbations of FLRW fluid solutions.

Original language	English
Pages (from-to)	2157-2243
Number of pages	87
Journal	Annales Henri Poincare
Volume	19
Issue number	7
DOIs	https://doi.org/10.1007/s00023-018-0686-2
Publication status	Published - 1 Jul 2018

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10.1007/s00023-018-0686-2

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abstract = "We establish the existence of 1-parameter families of ϵ-dependent solutions to the Einstein–Euler equations with a positive cosmological constant Λ > 0 and a linear equation of state p= ϵ2Kρ, 0 < K≤ 1 / 3 , for the parameter values 0 < ϵ< ϵ0. These solutions exist globally to the future, converge as ϵ↘ 0 to solutions of the cosmological Poisson–Euler equations of Newtonian gravity, and are inhomogeneous nonlinear perturbations of FLRW fluid solutions.",

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AB - We establish the existence of 1-parameter families of ϵ-dependent solutions to the Einstein–Euler equations with a positive cosmological constant Λ > 0 and a linear equation of state p= ϵ2Kρ, 0 < K≤ 1 / 3 , for the parameter values 0 < ϵ< ϵ0. These solutions exist globally to the future, converge as ϵ↘ 0 to solutions of the cosmological Poisson–Euler equations of Newtonian gravity, and are inhomogeneous nonlinear perturbations of FLRW fluid solutions.

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Newtonian Limits of Isolated Cosmological Systems on Long Time Scales

Abstract

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A mathematical analysis of the influence of small scale inhomogeneities on the evolution of the Universe

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Newtonian Limits of Isolated Cosmological Systems on Long Time Scales

Abstract

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A mathematical analysis of the influence of small scale inhomogeneities on the evolution of the Universe

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