Title: Anisotropic power-law inflation in a two-scalar-field model with a mixed kinetic term,
Abstract: We examine whether an extended scenario of a two-scalar-field model, in which
a mixed kinetic term of canonical and phantom scalar fields is involved, admits
the Bianchi type I metric, which is homogeneous but anisotropic spacetime, as
its power-law solutions. Then we analyze the stability of the anisotropic
power-law solutions to see whether these solutions respect the cosmic no-hair
conjecture or not during the inflationary phase. In addition, we will also
investigate a special scenario, where the pure kinetic terms of canonical and
phantom fields disappear altogether in field equations, to test again the
validity of cosmic no-hair conjecture. As a result, the cosmic no-hair
conjecture always holds in both these scenarios due to the instability of the
corresponding anisotropic inflationary solutions.