# Anisotropic power-law inflation in a two-scalar-field model with a mixed kinetic term

## TL;DR

This paper investigates anisotropic inflation driven by two scalar fields with mixed kinetic terms, finding that the cosmic no-hair conjecture remains valid due to the instability of anisotropic solutions.

## Contribution

It introduces a two-scalar-field inflation model with mixed kinetic terms and analyzes the stability of anisotropic solutions in this context.

## Key findings

- Anisotropic power-law solutions are unstable during inflation.
- The cosmic no-hair conjecture holds in the model.
- Stability analysis includes a special case with pure kinetic terms.

## 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.