Kaluza-Klein inspired a model of the inflation with the inversed power law potential in Bianchi type-I universe

TL;DR

This paper investigates a Kaluza-Klein inspired inflationary model with an inverse power-law potential in Bianchi type-I spacetime, showing the universe evolves from anisotropic to isotropic during inflation.

Contribution

It introduces a dynamical system analysis of Kaluza-Klein inspired inflation with inverse power-law potential in anisotropic Bianchi type-I universe, highlighting isotropization.

Findings

Existence of a non-hyperbolic fixed point requiring center manifold analysis.

Identification of an isotropic attractor point leading to accelerated expansion.

Support for the isotropization of the universe during inflation.

Abstract

This work considers the dynamics of the gauge vector and inflaton (dilaton) fields inspired by Kaluza-Klein theory in an inflationary universe with Bianchi type-I spacetime. The inverse power-law potential of the inflaton field is used to study dynamical system analysis. As a result, all fixed points in the autonomous system are non-hyperbolic fixed points, and one cannot determine their stability. Therefore, a center manifold theory is required to analyze the stability of the dynamical system properly. Interestingly, we found an isotropic attractor point which means that the universe undergoes accelerated expansion (inflation) from an anisotropic phase to an isotropic phase of the universe. According to the dynamical system analysis of the anisotropic Bianchi type-I universe with the inspired Kaluza-Klein model, our results supported the isotropization of the observed universe.