Anisotropic power-law inflation for the Sáez-Ballester theory non-minimally coupled to a vector field

Abstract

In this paper, we would like to examine whether the Sáez-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 $f^2(\varphi )F_{\mu \nu }{F}^{\mu \nu }$. As a result, such a solution will be shown to exist within this theory for a suitable setup of fields. Interestingly, the considered Sáez-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 Sáez-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 Sáez-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 Sáez-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.

37 pages, 5 figures. Accepted for publication in the European Physical Journal C (EPJC). Comments are welcome

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• Gravitational Foundations and Exact Solutions in $n$-Dimensional Fractional Cosmology
• Power-law Bianchi type I inflation with multiple vector fields