Anisotropic hyperbolic inflation for a model of two scalar and two vector fields

TL;DR

This paper introduces a hyperbolic inflation model with two scalar and two vector fields, demonstrating stable anisotropic solutions that challenge the cosmic no-hair conjecture.

Contribution

It extends existing models to hyperbolic field space, providing exact solutions and stability analysis showing violation of the cosmic no-hair conjecture.

Findings

Derived exact Bianchi type I solutions.

Proved stability and attractor nature of anisotropic solutions.

Showed violation of the cosmic no-hair conjecture.

Abstract

In this paper, we extend a recent proposed model of two scalar and two vector fields to a hyperbolic inflation scenario, in which the field space of two scalar fields is a hyperbolic space instead of a flat space. In this model, one of the scalar fields is assumed to be a radial field, while the other is set as an angular field. Furthermore, both scalar fields will be coupled to two different vector fields, respectively. As a result, we are able to obtain a set of exact Bianchi type I solutions to this model. Stability analysis is also performed to show that this set of anisotropic solutions is indeed stable and attractive during the inflationary phase. This result indicates that the cosmic no-hair conjecture is extensively violated in this anisotropic hyperbolic inflation model.