Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 1 / 37E / d

This is the Past incompleteness of the expanding flat slicing of de Sitter spacetime. The coordinate patch covers only half of global de Sitter spacetime, and the surface $t=-\infty$ is its past boundary. The finite proper-time endpoint is a coordinate-patch boundary, not a curvature singularity: the timelike geodesic continues smoothly after passing to global de Sitter coordinates.