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  • Letter
  • Open Access

Nonlinear stability of the matter-dominated universe

David Fajman1,* and Elliot Marshall2

  • *Contact author: david.fajman@univie.ac.at

Phys. Rev. D 114, L081501 – Published 5 October, 2026

DOI: https://doi.org/10.1103/t92p-mhpw

Abstract

We numerically study nonlinear perturbations of the Einstein-de Sitter spacetime as a solution to the Gowdy-symmetric Einstein-Euler system for a polytropic equation of state. The results suggest that the Einstein-de Sitter spacetime is stable for sufficiently small but otherwise generic perturbations. This is in stark contrast to the well-known instability of this spacetime when the matter model is dust. Moreover, this indicates a previously unknown stable regime of the Einstein-Euler equations with direct implications for cosmology.

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References (25)

  1. B. Ryden, Introduction to Cosmology, 2nd ed. (Cambridge University Press, Cambridge, England, 2016).
  2. A. Einstein and W. de Sitter, Proc. Natl. Acad. Sci. U.S.A. 18, 213 (1932).
  3. S. Weinberg, Cosmology (Oxford University Press, New York, 2008).
  4. E. Marshall, Classical Quantum Gravity 42, 105005 (2025).
  5. H. Friedrich, Commun. Math. Phys. 107, 587 (1986).
  6. H. Ringström, On the Topology and Future Stability of the Universe, Oxford Mathematical Monographs (Oxford University Press, New York, 2013).
  7. I. Rodnianski and J. Speck, J. Eur. Math. Soc. 15, 2369 (2013).
  8. J. Speck, Sel. Math. 18, 633 (2012).
  9. T. Oliynyk, Commun. Math. Phys. 346, 293 (2016).
  10. C. Lübbe and J. V. Kroon, Ann. Phys. (Amsterdam) 328, 1 (2013).
  11. L. Andersson and V. Moncrief, J. Diff. Geom. 89, 1 (2011).
  12. D. Fajman, M. Ofner, and Z. Wyatt, Arch. Ration. Mech. Anal. 248, 83 (2024).
  13. D. Fajman, M. Ofner, T. Oliynyk, and Z. Wyatt, Int. Math. Res. Not. 2024, 4328 (2023).
  14. M. Taylor, J. Math. Phys. (N.Y.) 65, 022503 (2024).
  15. L. Bernhardt, arXiv:2508.15303.
  16. G. Efstathiou and S. Gratton, Mon. Not. R. Astron. Soc. 496, L91 (2020).
  17. R. Gowdy, Ann. Phys. (N.Y.) 83, 203 (1974).
  18. P. LeFloch and A. Rendall, Arch. Ration. Mech. Anal. 201, 841 (2011).
  19. P. Chruściel, Ann. Phys. (N.Y.) 202, 100 (1990).
  20. See Supplemental Material at http://link.aps.org/supplemental/10.1103/t92p-mhpw for the recovery of the primitive variables and convergence tests.
  21. D. Fajman, M. Maliborski, M. Ofner, T. Oliynyk, and Z. Wyatt, Classical Quantum Gravity 42, 14LT01 (2025).
  22. L. Bernhardt, D. Fajman, and Z. Wyatt, arXiv:2607.09326.
  23. M. P. Leubner, Astrophys. J. 632, L1 (2005).
  24. J. P. Ostriker, P. Bode, and A. Babul, Astrophys. J. 634, 964 (2005).
  25. D. Fajman, M. Ofner, T. Oliynyk, and Z. Wyatt, arXiv:2501.12798.

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