Two balls dropped from different heights fall to the ground with different accelerations. In space, things are more complicated: even emptiness makes bodies move differently. The authors took a spacetime that includes both the ordinary attraction of matter and a mysterious cosmic repulsion (called dark energy) and watched how the distance between two freely flying particles changes.
It turns out there is a critical surface, an invisible sphere, that divides the world into two zones. Inside it, gravity works in the familiar way: particles come together. Outside, the expansion of space pushes them apart. It's like swimming in a river: near the bank the water is calm, but in the current you get swept along.
The behavior of geodesic deviation (as physicists call the divergence of trajectories) becomes a clear indicator: by whether the separation of particles accelerates or decelerates, you can tell exactly where you are — in the region of attraction or repulsion. This provides a new tool for mapping the large-scale structure of the universe.
Dark energy, which causes repulsion, makes up about 68% of all energy in the universe, yet its nature remains unknown.
In Stanislaw Lem's novel "Fiasco," a planet is described where gravity changes sign, creating bizarre landscapes and dangers for cosmonauts.