Title: Stable Big Bang formation for the Einstein equations
Abstract: I will discuss recent work concerning stability of cosmological singularities described by the generalized Kasner solutions. There are heuristics in the mathematical physics literature, going back more than 50 years, suggesting that the Big Bang formation should be stable under perturbations of the Kasner initial data, as long as the Kasner exponents are “sub-critical”. We prove that the Kasner singularity is dynamically stable for all sub-critical Kasner exponents, thereby justifying the heuristics in the full regime where stable monotonic-type curvature blowup is expected. We treat the 3+1-dimensional Einstein-scalar field system and the D+1-dimensional Einstein-vacuum equations for D≥10. This is joint work with Speck and Fournodavlos.