Stable small spatial hairs in a power-law k-inflation model

Abstract: In this paper, we extend our investigation of the validity of the cosmic no-hair conjecture within non-canonical anisotropic inflation. As a result, we are able to figure out an exact Bianchi type I solution to a power-law {\it k}-inflation model in the presence of unusual coupling between scalar and electromagnetic fields as $-f^2(\phi)F_{\mu\nu}F^{\mu\nu}/4$. Furthermore, stability analysis based on the dynamical system method indicates that the obtained solution does admit stable and attractive hairs during an inflationary phase and therefore violates the cosmic no-hair conjecture. Finally, we show that the corresponding tensor-to-scalar ratio of this model turns out to be highly consistent with the observational data of the Planck 2018.