Two gravitational routes narrow a warm-inflation dark matter model

How could dark matter have formed if it interacts with ordinary matter only through gravity? In an arXiv preprint posted on November 6, 2026, Phongsakorn Sereewat investigates that question within warm inflation: a proposed early-universe history in which rapid expansion occurs alongside a sustained bath of hot particles.

The study does not identify a dark matter particle or establish that warm inflation happened. Instead, it calculates which combinations of particle mass and gravitational coupling would produce too much dark matter in a particular model.

A hot bath during inflation

In the conventional cold-inflation picture described in the paper, the field driving expansion—the inflaton—later oscillates and transfers energy into particles during reheating. Warm inflation instead allows the inflaton to lose energy continuously into radiation while inflation is still underway. In the model studied here, radiation takes over smoothly, without a separate oscillatory reheating stage.

Sereewat adopts an inflaton potential proportional to the fourth power of the field, with an energy-dissipation coefficient proportional to temperature. The background parameters are selected to satisfy the cosmic microwave background constraints used in the paper.

The hypothetical dark matter is a massive vector field. Unlike a scalar field, a massive vector has transverse modes and a longitudinal mode, corresponding to different orientations of its polarization relative to its motion. Their responses to cosmic expansion differ, making that distinction important for particle production.

Two contributions that must be added

The first production route is gravitational freeze-in. Particles in the hot bath scatter into dark matter through graviton exchange. The interactions are sufficiently weak that dark matter never reaches thermal equilibrium with the bath, but a population gradually accumulates.

The second route does not require collisions. The changing geometry of the expanding universe can excite the dark matter field from its vacuum state. The paper calls this cosmological gravitational particle production.

Sereewat calculates thermal scattering rates and numerically evolves the vector field's modes through inflation into radiation domination. Both processes operate on the same background, so their final contributions must be added before comparing the prediction with the observed dark matter abundance.

In the examples examined, expansion-driven production dominates at sufficiently low masses. Thermal freeze-in takes over at higher masses. Counting only one mechanism can therefore leave apparently acceptable masses that the other mechanism rules out through overproduction.

A small coupling can change the answer

The model also includes an additional coupling between the vector field and spacetime curvature, described by a dimensionless parameter, ξ. Setting ξ to zero gives the minimal-coupling case.

For light particles, this additional interaction can strongly enhance thermal production through the longitudinal mode. For heavy particles, it can instead interfere destructively with the ordinary graviton-exchange contribution, reducing production near particular coupling values.

The expansion-driven results also require a careful comparison. At the same particle mass measured relative to the expansion rate at inflation's end, the warm-inflation example produces roughly 20–1,000 times more light particles than the cold-inflation example. That is not a universal enhancement in physical units: the paper's cold model has a larger absolute expansion rate, which changes the comparison.

What survives both mechanisms?

For the stronger-dissipation benchmark with ξ equal to zero, the combined calculation permits masses below approximately 2.4 × 10⁻⁵ GeV, a narrow interval from about 7.2 × 10⁹ to 1.5 × 10¹⁰ GeV, and masses above approximately 4.3 × 10¹⁴ GeV. These are regions that avoid overproduction; they do not all yield the entire observed dark matter abundance.

The intermediate window disappears in another benchmark. Nonzero curvature coupling further restricts the lighter possibilities: theoretical consistency conditions demand extremely small couplings on the light branch, while enhanced freeze-in closes the intermediate window. The heavy branch is the only region that remains viable across the studied coupling range |ξ| ≲ 1.

These boundaries are conditional, not general exclusions of vector dark matter. The analysis uses one warm-inflation model, approximates thermal particle distributions with Maxwell–Boltzmann statistics and neglects thermal masses. Its cold-inflation comparison also omits production by the oscillating inflaton condensate. The central result is narrower but consequential: within this setup, the thermal bath and the expanding geometry cannot be treated as alternative sources. Their combined production determines which dark matter scenarios survive.