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Phase transition between shock formation and stability in cosmological fluids

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arxiv 2405.03431 v1 pith:6V65TXK3 submitted 2024-05-06 gr-qc math-phmath.MP

David Fajman , Maciej Maliborski , Maximilian Ofner , Todd Oliynyk , Zoe Wyatt This is my paper · ORCID
classification gr-qcmath-phmath.MP
keywords stablealphafluidregionstabilitytransitionunstablecosmological
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abstract

We demonstrate a novel phase transition from stable to unstable fluid behaviour for fluid-filled cosmological spacetimes undergoing decelerated expansion. This transition occurs when the fluid speed of sound $c_S$ exceeds a critical value relative to the expansion rate $a(t) = t^\alpha$ of spacetime. We present an explicit relationship between $\alpha$ and $c_S$ , which subdivides the $(\alpha,c_S)$-parameter space into two regions. Using rigorous techniques, we establish stability of quiet fluid solutions in the first stable region. Numerical experiments reveal that the complement of the stable region consists of unstable solutions, implying sharpness of our stability result. We provide a definitive analytical bound and high-precision numerical evidence for the exact location of the critical line separating the stable from the unstable region.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Nonlinear stability of Einstein-de Sitter universes

    gr-qc 2026-07 accept novelty 8.0 of 10

    Near-flat initial data for Einstein-Euler with polytropic equation of state n>3 on T^{3} produce future-global solutions that homogenise and asymptote to Einstein-de Sitter.

  2. Boundedness and decay of waves on spatially flat decelerated FLRW spacetimes

    gr-qc 2025-05 conditional novelty 6.0 of 10

    A twisted vector-field method yields energy boundedness, local energy decay, r^p-weighted estimates, and energy and pointwise decay for waves on all spatially flat decelerated FLRW backgrounds with scale factor t^q, 0<q<1.

  3. Instability of Slowly Expanding FLRW Spacetimes

    gr-qc 2025-02 conditional novelty 6.0 of 10

    Numerical simulations of Gowdy-symmetric perturbations of decelerated FLRW Einstein-Euler solutions indicate finite-time shock formation for every linear equation of state p=K rho with 0<=K<=1.

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