Wave Equations on Silent Big Bang Backgrounds

The subject of these notes is the asymptotic behaviour of solutions to linear systems of wave equations in the vicinity of big bang singularities. In particular, we are interested in the case of crushing singularities (cf. Definition 2.1) with silent and anisotropic asymptotics. Beyond studying wave equations, we here develop a geometric framework for understanding such singularities, and in a companion article (H. Ringström, <italic>On the geometry of silent and anisotropic big bang singularities</italic> , Preprint, 2025), we combine this framework with Einstein’s equations in order to deduce additional information.