Bianchi cosmologies with $p$-form gauge fields

TL;DR

This paper investigates the dynamics of $p$-form gauge fields in Bianchi cosmologies, revealing new self-similar solutions and analyzing their stability and global behavior using dynamical systems methods.

Contribution

It introduces new self-similar cosmological solutions with $p$-form fields in Bianchi types I and V, expanding understanding of anisotropic universe models with gauge fields.

Findings

Discovery of a one-parameter family of self-similar solutions, 'Wonderland'

Identification of stable solutions 'The Rope' and 'The Edge' with rotating spatial fields

Global analysis establishing conditions for solutions to be attractors

Abstract

In this paper the dynamics of free gauge fields in Bianchi type I-VII$_{h}$ space-times is investigated. The general equations for a matter sector consisting of a $p$-form field strength ($p\,\in\,\{1,3\}$), a cosmological constant ($4$-form) and perfect fluid in Bianchi type I-VII$_{h}$ space-times are computed using the orthonormal frame method. The number of independent components of a $p$-form in all Bianchi types I-IX are derived and, by means of the dynamical systems approach, the behaviour of such fields in Bianchi type I and V are studied. Both a local and a global analysis are performed and strong global results regarding the general behaviour are obtained. New self-similar cosmological solutions appear both in Bianchi type I and Bianchi type V, in particular, a one-parameter family of self-similar solutions,"Wonderland ($\lambda$)" appears generally in type V and in type I for $\lambda=0$. Depending on the value of the equation of state parameter other new stable solutions are also found ("The Rope" and "The Edge") containing a purely spatial field strength that rotates relative to the co-moving inertial tetrad. Using monotone functions, global results are given and the conditions under which exact solutions are (global) attractors are found.