In the first moments, the universe expanded at an unimaginable rate — a phase called inflation. It is thought that particles of dark matter, the invisible substance that holds galaxies together, could have been born from the vacuum during this time. But what determines exactly how many are produced?
The authors considered a model with two fields. One drove inflation, and the other was responsible for future dark matter. It turned out that if the field space is not flat but curved (with negative curvature, like the surface of a saddle), stronger oscillations arise after inflation. This is like a pendulum: on a flat floor it quickly dies down, but in a pit with steep walls it swings vigorously. Such oscillations boost the production of spectator particles. Up to ten times more particles are produced than in the flat case.
In the end, the scientists built a map: for which particle masses and reheating temperatures of the universe the right amount of dark matter is produced. The curved field space greatly expands the allowed parameter region. Purely gravitational production, without any extra forces, can explain where dark matter came from, even in complex multi-field inflation models.
If inflation had lasted one trillionth of a second longer, our universe would be completely different — possibly without galaxies.
In Carl Sagan's novel "Contact," aliens use wormholes to travel through curved space — much like how curved field space affects particle production.