Bianchi models with a free massless scalar field: invariant sets and higher symmetries

Abstract

We scrutinize the overall structure of the space of cosmological models of Bianchi type I–VIIh that contain a free massless scalar field, with a spatially homogeneous gradient that generally breaks isotropy, in addition to a standard perfect fluid. Specifically, state space is written as a union of disjoint invariant sets, each corresponding to a particular cosmological model that is classified with respect to the Bianchi type and the matter content. Subsets corresponding to higher-symmetry models, including all locally rotationally symmetric models and FLRW models, and models with a shear-free normal congruence, are also derived and classified. For each model the dimension (d) of the space of initial data is given, after fixing the orientation of the orthonormal frame uniquely relative to matter anisotropies and geometrical anisotropies.