Strong dissipation does not necessarily make thermal fluctuations the main signal in a warm-inflation model, according to a new arXiv preprint. In its calculations, strong dissipation in the frame where the model is defined coexisted with quantum-dominated scalar perturbations even when the temperature-to-Hubble ratio was above 1.
The study examines what happens when warm inflation is specified in a non-minimally coupled scalar-tensor model and then related to the Einstein frame. The setup uses a quartic potential and either constant or quadratic field-dependent dissipation; the dissipation coefficient and stochastic noise are obtained in the defining frame and translated to the Einstein frame.
One model, two regime labels
At the center of the analysis is a dissipation ratio: Q in the defining frame and Q̃ in the Einstein frame. The paper reports the approximate conversion Q̃ ≃ Q/(K̄F̄). When K̄F̄ is greater than 1, the two frames can assign different strong- and weak-dissipation labels to the same setup.
When the Einstein-frame temperature-to-Hubble ratio T̂/Ĥ is above 1, the reported criterion is quantum dominance for Q̃ roughly 0.5 or lower, with thermal perturbations dominating otherwise.
That makes it possible for strong defining-frame dissipation to coexist with a quantum-dominated spectrum. The defining-frame label alone does not determine which source dominates the scalar perturbations in this model.
What survived the model’s screening
The scans used three reference tests: a scalar spectral index n_s, which describes the tilt of the scalar spectrum, between 0.957 and 0.985; a tensor-to-scalar ratio r below 0.04; and a scalar amplitude P_s of about 2.1 × 10−9.
With constant dissipation, a no-exit band appeared at σ0 > 4. Other regions were excluded by the tensor-ratio limit and by the T > H condition. The points that remained were weakly dissipative in the Einstein frame, with Q̃ < 1.
Among the selected constant-dissipation benchmarks, cases A–C had Q⋆ < 1 and n_s between 0.960 and 0.970, while D–F had Q⋆ > 1. All six had quantum-dominated spectra, g_eff between 10 and 200, and P_s ≃ 2.1 × 10−9.
Field-dependent dissipation broadens the picture
Allowing dissipation to vary quadratically with the field produced a different pattern. In the d = −2 scan, slow-roll inflation ended even at arbitrarily large dissipation; no scan region was excluded by r, although a wedge remained outside the accepted n_s range.
The benchmark cases showed the range of possibilities. C and E were strongly dissipative in the Einstein frame, with Q̃⋆ = 1.17 and 1.26 and T/H about 90, and their spectra were thermally dominated. B, D and F were strongly dissipative in the defining frame but had Q̃⋆ between 0.08 and 0.09 and quantum-dominated spectra.
One example also shows how the regime can change during a single inflationary trajectory. In benchmark C, Q fell from 516 at the pivot to 104 at the end, while Q̃ fell from 1.17 to 0.43; over the same evolution, T/H rose from 93 to 903 and the radiation-to-potential ratio from about 7 × 10−5 to 0.16. Q̃ therefore crossed from strong to weak dissipation.
The calculation still has open tests
The analytic scalar-spectrum calculation was restricted to temperature-independent dissipation, represented by c = 0, and neglected metric perturbations. The authors also identify higher-order slow-roll perturbations, temperature-dependent dissipation and full numerical perturbation calculations as open work.
The work is an arXiv preprint, version 1, dated 20 August 2026. Its results come from the specified model and parameter scans, while the authors identify tests of local thermal-equilibrium correspondence across the frames as another unresolved question.
Paper data and sources
Original title: Non-Minimally Coupled Warm Inflation in the Defining Frame
Authors: Adrián Casado-Turrión, Paulo B. Ferraz, Mindaugas Karčiauskas, José Jaime Terente Díaz
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text