Anisotropic power-law inflation for the S\'aez-Ballester theory non-minimally coupled to a vector field

TL;DR

This paper investigates anisotropic power-law inflation within the Saez-Ballester theory non-minimally coupled to a vector field, showing the existence of stable solutions and exploring their observational viability in light of Planck 2018 data.

Contribution

It demonstrates that the Saez-Ballester theory admits stable anisotropic inflationary solutions and explores modifications to align with observational constraints.

Findings

Existence of stable anisotropic inflation solutions in Saez-Ballester theory

Equivalence to standard scalar-vector models via field redefinition

Modified models with lower sound speed compatible with Planck data

Abstract

In this paper, we would like to examine whether the S\'aez-Ballester theory admits stable and attractive Bianchi type I inflationary solutions in the presence of a non-minimal coupling between scalar and vector fields such as $f^2(\phi)F_{\mu\nu}F^{\mu\nu}$. As a result, such a solution will be shown to exist within this theory for a suitable setup of fields. Interestingly, the considered S\'aez-Ballester theory can be shown to be equivalent to the standard scalar-vector theory via a suitable field redefinition. This means that the obtained solution can be reduced to that derived in an original anisotropic inflation model proposed by Kanno, Soda, and Watanabe. Consequently, the corresponding tensor-to-scalar ratio of this solution turns out to be higher than the latest observational value of the Planck satellite (Planck 2018) due to the fact that $c_s$, the corresponding speed of sound of scalar perturbations of the S\'aez-Ballester theory, turns out to be one. This result indicates an important hint that the speed of sound, $c_s$, could play an important role in making the corresponding non-canonical anisotropic inflation cosmologically viable in the light of the Planck 2018 data. To be more specific, we will point out that any modifications of the S\'aez-Ballester theory having $c_s \sim 0.1$ will have a great potential to be highly consistent with the Planck 2018 data. For heuristic reasons, a simple modified version of the S\'aez-Ballester theory will be proposed as a specific demonstration. As a result, we will show that this modified model admits an anisotropic power-law inflationary solution as expected.