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.
as written by the authors arXiv:2606.25015
We study cosmological gravitational particle production (CGPP) of dark matter in two-field inflationary backgrounds with both flat and curved field-space geometries. As a concrete realization of broader multifield mechanisms, we adopt a Starobinsky+quadratic potential and construct benchmark scenarios that interpolate between the flat field-space limit and the sidetracked attractor on a hyperbolic field space, and we compute the production spectrum of a gravitationally coupled spectator scalar for both minimal ($$\xi = 0$$) and conformal ($$\xi = 1/6$$) coupling to the Ricci scalar. We show that negative field-space curvature can strongly enhance the post-inflationary oscillations of the Ricci scalar, leading to an enhancement of up to an order of magnitude in the CGPP number density relative to the flat field-space limit, particularly for minimal coupling. For the sidetracked attractor, this enhanced production competes with a reduced inflationary energy scale, leading to a nontrivial dependence of the relic abundance on model parameters. We derive the relic abundance as a function of spectator mass and reheating temperature, and identify the viable parameter space for each benchmark. The conformal case $$\xi = 1/6$$, whose scalar mode equation is structurally analogous to that of a massive Dirac fermion, is much less constrained by isocurvature and provides a minimal scenario for purely gravitational dark matter production in multifield inflation.
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.