Self-similar Bianchi models: I. Class A models

We present a study of Bianchi class A tilted cosmological models admitting a proper homothetic vector field together with the restrictions, both at the geometrical and dynamical level, imposed by the existence of the simply transitive similarity group. The general solution of the symmetry equations and the form of the homothetic vector field are given in terms of a set of arbitrary integration constants. We apply the geometrical results for tilted perfect fluids sources and give the general Bianchi II self-similar solution and the form of the similarity vector field. In addition we show that self-similar perfect fluid Bianchi VII${}_0$ models and irrotational Bianchi VI${}_0$ models do not exist.