Bianchi cosmologies with p-form gauge fields

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.