A warm‑inflation framework that ties the inflaton field to the scalar curvature of space‑time has been proposed. In the Jordan frame the authors derived altered background equations and, by linearizing the system, identified slow‑roll conditions. The calculation shows that the curvature coupling adds extra damping and reshapes the potential slope, so inflation can proceed even when the potential is steeper than usual.

The team used a stochastic method to study fluctuations. They derived a Langevin equation for the inflaton perturbations and calculated the primordial power spectra for both density (scalar) and gravitational‑wave (tensor) modes.

Results indicate that the combined influence of curvature coupling, the noncanonical kinetic term, and thermal dissipation suppresses the tensor‑to‑scalar ratio compared with standard warm inflation. The scalar spectrum remains nearly scale‑invariant, and under suitable parameter choices the inflaton’s field range stays below the Planck scale, potentially avoiding the large‑field problem.

However, the slow‑roll attractor is only stable when the dissipation coefficient depends on temperature as Γ∝Tⁿ with |n|<4. If the temperature exponent is outside this range, the eigenvalues of the stability matrix fail the necessary condition and the slow‑roll solution loses stability. Also, the radiation energy density stays subdominant, consistent with a potential‑energy–dominated epoch.

The study demonstrates a viable way to extend warm‑inflation models but stresses that the viability hinges on the specific temperature dependence of dissipation and on maintaining the radiation subdominant during inflation.