Future stability of the FLRW fluid solutions in the presence of a positive cosmological constant

Todd A. Oliynyk

doi:10.1007/s00220-015-2551-1

Future stability of the FLRW fluid solutions in the presence of a positive cosmological constant

Todd A. Oliynyk

School of Mathematics

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

63 Citations (Scopus)

Abstract

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 = Kρ. 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 ≤ 1/3 in a uniform manner. It also determines the asymptotic behavior of the perturbed solutions in the far future.

Original language	English
Pages (from-to)	293-312
Number of pages	20
Journal	Communications in Mathematical Physics
Volume	346
Issue number	1
DOIs	https://doi.org/10.1007/s00220-015-2551-1
Publication status	Published - 1 Aug 2016

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10.1007/s00220-015-2551-1

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abstract = "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 = Kρ. 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 ≤ 1/3 in a uniform manner. It also determines the asymptotic behavior of the perturbed solutions in the far future.",

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AB - 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 = Kρ. 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 ≤ 1/3 in a uniform manner. It also determines the asymptotic behavior of the perturbed solutions in the far future.

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Future stability of the FLRW fluid solutions in the presence of a positive cosmological constant

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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Future stability of the FLRW fluid solutions in the presence of a positive cosmological constant

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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