Initial data on big bang singularities in symmetric settings

In a recent article, we propose a general geometric notion of initial data on big bang singularities. This notion is of interest in its own right. However, it also serves the purpose of giving a unified perspective on many of the results in the literature. In the present article, we give a partial justification of this statement by rephrasing the results concerning Bianchi class A orthogonal stiff fluid solutions and solutions in the $\mathbb{T}^3$-Gowdy symmetric vacuum setting in terms of our general geometric notion of initial data on the big bang singularity.