Abstract
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 polarized T-2-symmetric solutions of the vacuum Einstein equations with arbitrary cosmological constant lambda. This stability result generalizes the results proven in Ames E et al. (2022 Stability of AVTD Behavior within the Polarized T-2-symmetric vacuum spacetimes. Ann. Henri Poincare. (doi:10.1007/s00023-021-01142-0)), which focus on the lambda=0 case, and as in that article, the proof relies on an areal time foliation and Fuchsian techniques. Even for lambda=0, the results established here apply to a wider class of perturbations of Kasner solutions within the family of polarized T-2-symmetric vacuum solutions than those considered in Ames E et al. (2022 Stability of AVTD Behavior within the Polarized T-2-symmetric vacuum spacetimes. Ann. Henri Poincare. (doi:10.1007/s00023-021-01142-0)) and Fournodavlos G et al. (2020 Stable 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,T-0] for some T-0 > 0, for certain families of polarized T2-symmetric solutions with cosmological constant. This article is part of the theme issue 'The future of mathematical cosmology, Volume 1'.