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arXiv · 1712.08752

Bianchi cosmologies with $p$-form gauge fields

Ben David Normann·Sigbjørn Hervik·Angelo Ricciardone·Mikjel Thorsrud
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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 ($λ$)" appears generally in type V and in type I for $λ=0$. 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.

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Ben David Normann, Sigbjørn Hervik, Angelo Ricciardone, Mikjel Thorsrud. 2018-04-09. Bianchi cosmologies with $p$-form gauge fields. https://doi.org/10.1088/1361-6382%2Faab3a7

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