Consistency of warm k-inflation

We extend the k-inflation which is a type of kinetically driven inflationary model under the standard inflationary scenario to a possible warm inflationary scenario. The dynamical equations of this warm k-inflation model are obtained. We rewrite the slow-roll parameters which are different from the usual potential driven inflationary models and perform a linear stability analysis to give the proper slow-roll conditions in the warm k-inflation. Two cases, a power-law kinetic function and an exponential kinetic function, are studied, when the dissipative coefficient $Γ=Γ_0$ and $Γ=Γ(ϕ)$, respectively. A proper number of e-folds is obtained in both concrete cases of warm k-inflation. We find a constant dissipative coefficient ($Γ=Γ_0$) is not a workable choice for these two cases while the two cases with $Γ=Γ(ϕ)$ are self-consistent warm inflationary models.

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