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.
as written by the authors arXiv:2607.23387
Here we discuss the effect of gravitational repulsion on geodesic deviation in the Schwarzschild-de Sitter spacetime. In particular, the geodesic deviation shows different behaviour inside or outside a critical surface, which is the divider between attractive and repulsive regions of gravity. This in turn makes it possible to locate the critical surface and regions of gravitational repulsion and attraction from the behaviour of geodesic deviation.
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.