Future instability of FLRW fluid solutions for linear equations of state p =K? with 1/3 < K < 1

Using numerical methods, we examine the dynamics of nonlinear perturbations in the expanding time direction, under a Gowdy symmetry assumption, of Friedmann-Lemaitre-Robertson-Walker (FLRW) fluid solutions to the Einstein-Euler equations with a positive cosmological constant ? > 0 and a linear equation of state p = K? for the parameter values 1/3 < K < 1. This paper builds upon the numerical work in [arXiv:2209.06982] in which the simpler case of a fluid on a fixed FLRW background spacetime was studied. The numerical results presented here confirm that the instabilities observed in [arXiv:2209.06982] are also present when coupling to gravity is included as was previously conjectured in [A. D. Rendall, Asymptotics of solutions of the Einstein equations with positive cosmological constant, Ann. Henri Poincare'5, 1041 (2004); J. Speck, The stabilizing effect of spacetime expansion on relativistic fluids with sharp results for the radiation equation of state, Arch. Ration. Mech. Anal. 210, 535 (2013)]. In particular, for the full parameter range 1/3 < K < 1, we find that the fractional density gradient of the nonlinear perturbations develop steep gradients near a finite number of spatial points and becomes unbounded there at future timelike infinity.

Automated summary

Using numerical methods, this paper examines the dynamics of nonlinear perturbations in the expanding time direction of FLRW fluid solutions to the Einstein-Euler equations. The results confirm previous conjectures about the instabilities and the development of steep gradients in the fractional density gradient of the nonlinear perturbations. The study highlights the importance of considering the coupling to gravity in understanding the behavior of the perturbations.