Anisotropic Constant-roll \(k\)-inflation Model

In this paper, we would like to figure out whether a {\it k}-inflation model admits the Bianchi type I metric as its inflationary solution under a constant-roll condition in the presence of the supergravity motivated coupling between scalar and vector fields, \(f^2(\phi)F_{\mu\nu}F^{\mu\nu}\). As a result, some novel anisotropic inflationary solutions are shown to appear along with a power-law one in this scenario. Furthermore, these solutions are numerically confirmed to be attractive, in contrast to the prediction of the Hawking's cosmic no-hair conjecture.