Stability of asymptotic behaviour within polarized T2-symmetric vacuum solutions with cosmological constant

We prove the nonlinear stability of the asymptotic behaviour of perturbations of subfamilies of Kasner solutions in the contracting time direction within the class of polarizedT2-symmetric solutions of the vacuum Einstein equations with arbitrary cosmological constantΛ. This stability result generalizes the results proven in Ames Eet al.(2022 Stability of AVTD Behavior within the PolarizedT2-symmetric vacuum spacetimes.Ann. Henri Poincaré. (doi:10.1007/s00023-021-01142-0)), which focus on theΛ=0case, and as in that article, the proof relies on an areal time foliation and Fuchsian techniques. Even forΛ=0, the results established here apply to a wider class of perturbations of Kasner solutions within the family of polarizedT2-symmetric vacuum solutions than those considered in Ames Eet al.(2022 Stability of AVTD Behavior within the PolarizedT2-symmetric vacuum spacetimes.Ann. Henri Poincaré. (doi:10.1007/s00023-021-01142-0)) and Fournodavlos Get al.(2020Stable Big Bang formation for Einstein’s equations: the complete sub-critical regime. Preprint. (http://arxiv.org/abs/2012.05888)). Our results establish that the areal time coordinate takes all values in(0,T0]for someT0>0, for certain families of polarizedT2-symmetric solutions with cosmological constant.This article is part of the theme issue ‘The future of mathematical cosmology, Volume 1’.