Complete asymptotics in the formation of quiescent big bang singularities

Abstract: There are three categories of mathematical results concerning quiescent big bang singularities: the derivation of asymptotics in a symmetry class; the construction of spacetimes given initial data on the singularity; and the proof of big bang formation in the absence of symmetries, including the proof of stable big bang formation. In a recent article, the first author demonstrated the existence of developments corresponding to a geometric notion of initial data on a big bang singularity. Moreover, this article, combined with previous articles by the second author, gives a unified and geometric perspective on large classes of seemingly disparate results in the first two categories. Concerning the third category, Oude Groeniger et al recently formulated a general condition on initial data ensuring big bang formation, including curvature blow up. This result, among other things, generalises previous results on stable big bang formation. However, it does not include a statement saying that the solutions induce initial data on the singularity. Here we tie all three categories of results together by demonstrating that the solutions of Oude Groeniger et al induce data on the singularity. However, the results are more general and can potentially be used to derive similar conclusions in other gauges.