In general relativity, the geodesics represent the paths that free-falling particles or objects follow in curved spacetime. These paths are the equivalent of the shortest path (straight lines) between two points in Euclidean space. In cosmology, a spacetime is said to be geodesically complete if all its geodesics can be extended indefinitely without encountering any singularities or boundaries. On the contrary, a spacetime that is geodesically past-incomplete features geodesics that reach a boundary or a singularity within a finite amount of proper time into the past.