Future instability of FLRW fluid solutions for linear equations of state p=Kρ 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-Lemaître-Robertson-Walker (FLRW) fluid solutions to the Einstein-Euler equations with a positive cosmological constant Λ>0 and a linear equation of state p=Kρ 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 Poincaré 5, 1041 (2004)1424-063710.1007/s00023-004-0189-1; 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)AVRMAW0003-952710.1007/s00205-013-0655-3]. 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.