Power-law Bianchi type I inflation with multiple vector fields

TL;DR

This paper finds and classifies stable power-law inflationary solutions in a Bianchi type I universe with multiple vector fields, demonstrating their attractor behavior through analytical and numerical methods.

Contribution

It introduces new stable power-law solutions in anisotropic inflation models with multiple vector fields and analyzes their stability and attractor properties.

Findings

Four types of power-law solutions classified by vector field configurations

All solutions are stable within certain parameter regions

Numerical simulations confirm the attractor nature of these solutions

Abstract

We seek power-law Bianchi type I solutions for an inflationary universe in a model with one scalar field non-minimally coupled to three vector fields aligned along the three axes. As a result, we find four types of power-law solutions that are classified according to the number of non-vanishing vector fields. Moreover, we find that all these solutions are stable for certain conditions on the parameters (stability regions), which are described both quantitatively and qualitatively. The attractor property of these solutions is also confirmed by numerical calculations.