K-inflation: the legitimacy of classical treatment

We consider general theory of k-inlation and find out, that it may be in strong coupling regime. We derive accurate conditions of classical description validity using unitarity bounds for this model. Next, we choose simple toy model of k-inflation and obtain the explicit condition, which guarantees that the generation of perturbations is performed in a controllable way, i.e the exit from effective horizon occurs in the weak coupling regime. However, for the same toy model the corresponding experimental bounds on a non-linear parameter $f^{\text{equil}}_{\text{NL}}$ associated with non-Gaussianities of the curvature perturbation provide much stronger constraint than strong coupling absence condition. Nevertheless, for other known models of inflation this may not be the case. Generally, one should always check if classical description is legitimate for chosen models of inflation.