Compactified and reduced dynamics for locally rotationally symmetric Bianchi type IX perfect fluid models

The field equations for the locally rotationally symmetric Bianchi type IX perfect fluid models are reduced to a regularised first-order system of differential equations for three new bounded gravitational variables. The entire dynamics is described in a single coordinate patch covering the evolution all the way from the initial big bang singularity to the final big crunch singularity. This is made possible by exploitation of the algebraic properties of the Hamiltonian describing these models and use of the scale invariance symmetry. By investigating the compactified reduced phase space with qualitative and numerical techniques the authors are able to follow all solutions from the initial singularity to the final singularity, thus obtaining a complete picture of the solution space.