We investigate the late-time asymptotics of future expanding, polarizedvacuum Einstein spacetimes with T2-symmetry on T3, which, by definition, admittwo spacelike Killing fields. Our main result is the existence of a stableasymptotic regime within this class, that is, we provide here a fulldescription of the late-time asymptotics of the solutions to the Einsteinequations when the initial data set is close to the asymptotic regime. Ourproof is based on several energy functionals with lower order corrections (asis standard for such problems) and the derivation of a simplified model whichwe exhibit here. Roughly speaking, the Einstein equations in the symmetry classunder consideration consists of a system of wave equations coupled toconstraint equations plus a system of ordinary differential equations. Theunknowns involved in the system of ordinary equations are blowing up in thefuture timelike directions. One of our main contributions is the derivation ofnovel effective equations for suitably renormalized unknowns. Interestingly,this renormalization is not performed with respect to a fixed background, butdoes involve the energy of the coupled system of wave equations. In addition,we construct an open set of initial data which are arbitrarily close to theexpected asymptotic behavior. We emphasize that, in comparison, the class ofGowdy spacetimes exhibits a very different dynamical behavior to the one weuncover in the present work for general polarized T2-symmetric spacetimes.Furthermore, all the conclusions of this paper are valid within the frameworkof weakly T2-symmetric spacetimes previously introduced by the authors.
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