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 \b[a coordinate-patch boundary, not a curvature singularity]: the timelike geodesic continues smoothly after passing to global de Sitter coordinates.

Solution

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

 Solution (source code)