Anisotropic power-law inflation for models of non-canonical scalar fields non-minimally coupled to a two-form field

TL;DR

This paper demonstrates that non-minimal coupling between non-canonical scalar fields and a two-form field can produce stable anisotropic inflationary solutions, challenging the cosmic no-hair conjecture and aligning with Planck 2018 data.

Contribution

It introduces exact anisotropic power-law inflation solutions in non-canonical scalar field models with two-form coupling, showing these solutions are stable and violate the cosmic no-hair conjecture.

Findings

Stable anisotropic solutions found in k-inflation and DBI models.

Non-minimal coupling generates persistent spatial anisotropies.

Tensor-to-scalar ratio in k-inflation aligns better with Planck 2018 data.

Abstract

In this paper, we investigate the validity of the so-called cosmic no-hair conjecture in the framework of anisotropic inflation models of non-canonical scalar fields non-minimally coupled to a two-form field. In particular, we focus on two typical {\it k}-inflation and Dirac-Born-Infeld inflation models, in which we find a set of exact anisotropic power-law inflationary solutions. Interestingly, these solutions are shown to be stable and attractive during an inflationary phase using the dynamical system analysis. The obtained results indicate that the non-minimal coupling between the scalar and two-form fields acts as a non-trivial source of generating stable spatial anisotropies during the inflationary phase and therefore violates the prediction of the cosmic no-hair conjecture, even when the scalar field is of non-canonical forms. In connection with the Planck 2018 data, tensor-to-scalar ratios of these anisotropic solutions are investigated. As a result, it appears that the tensor-to-scalar ratio of the anisotropic power-law inflationary solution of {\it k}-inflation model turns out to be more highly consistent with the Planck 2018 data than that of Dirac-Born-Infeld model.