Past instability of FLRW solutions of the Einstein-Euler-scalar field equations for linear equations of state p=Kρ with 0≤K<1/3

Abstract

Using numerical methods, we examine, under a Gowdy symmetry assumption, the dynamics of nonlinearly perturbed Friedmann-Lemaître-Robertson-Walker (FLRW) fluid solutions of the Einstein-Euler-scalar field equations in the contracting direction for linear equations of state p=Kρ and sound speeds 0≤K<1/3. This article builds upon the numerical work from Beyer et al. [Phys. Rev. D 107, 104030 (2023)PRVDAQ2470-001010.1103/PhysRevD.107.104030] in which perturbations of FLRW solutions to the Einstein-Euler equations with positive cosmological constant in the expanding time direction were studied. The numerical results presented here confirm that the instabilities observed in previous work [Phys. Rev. D 107, 104030 (2023)PRVDAQ2470-001010.1103/PhysRevD.107.104030, Lett. Math. Phys. 113, 102 (2023).LMPHDY0377-901710.1007/s11005-023-01722-7] for 1/3 <1/3. Our numerical solutions show that the fractional density gradient of the nonlinear perturbations develop steep gradients near a finite number of spatial points and become unbounded toward the big bang. This behavior, and in particular the characteristic profile of the fractional density gradient near the big bang, is strikingly similar to what was observed in the expanding direction near timelike infinity by Beyer et al. [Phys. Rev. D 107, 104030 (2023)PRVDAQ2470-001010.1103/PhysRevD.107.104030].