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