Instability of slowly expanding FLRW spacetimes

Abstract We numerically study, under a Gowdy symmetry assumption, nonlinear perturbations of the decelerated FLRW fluid solutions to the Einstein–Euler system toward the future for linear equations of state <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>=</mml:mo> <mml:mi>K</mml:mi> <mml:mi>ρ</mml:mi> </mml:mrow> </mml:math> with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mtext>⩽</mml:mtext> <mml:mi>K</mml:mi> <mml:mtext>⩽</mml:mtext> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> . This article builds on the work of Fajman et al (2024 arXiv:2405.03431) in which perturbations of the homogeneous fluid solution on a fixed, decelerating FLRW background were studied. Our numerical results show that for all values of K , perturbations of the FLRW solution develop shocks in finite time. This behaviour contrasts known results for spacetimes with accelerated expansion in which shock formation is suppressed.