Hamiltonian formulation of Bianchi cosmological models in quadratic theories of gravity

We use Boulware's Hamiltonian formalism of quadratic gravity theories in order to analyse the classical behaviour of Bianchi cosmological models for a Lagrangian density in four spacetime dimensions. For this purpose we define a canonical transformation which leads to a clear distinction between two main variants of the general quadratic theory, i.e. for or conformal Lagrangian densities. In this paper we restrict the study to the first variant. For the Bianchi-type I and IX models, we give the explicit forms of the super-Hamiltonian constraint, of the ADM Hamiltonian density and of the corresponding canonical equations. In the case of a pure quadratic theory , we solve them analytically for the Bianchi I model. For the Bianchi-type IX model, we reduce the first-order equations of the Hamiltonian system to three coupled second-order equations for the true physical degrees of freedom. This discussion is extended to isotropic FLRW models.