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 $-f^2(\varphi )F_{\mu \nu }{F}^{\mu \nu }/4$. 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.

15 pages, 2 figures. Substantial revision with discussions on seminal papers of Starobinsky related to the cosmic no-hair conjecture and investigations on the corresponding tensor-to-scalar ratio. Main results and conclusions are not changed. Comments are welcome