We are investigating the dynamics of a new Poincare gauge theory of gravity model, which has cross coupling between the spin-0(+) and spin-0(-) modes. To this end we here consider a very appropriate situation - homogeneous-isotropic cosmologies - which is relatively simple, and yet all the modes have nontrivial dynamics which reveals physically interesting and possibly observable results. More specifically we consider manifestly isotropic Bianchi class A cosmologies; for this case we find an effective Lagrangian and Hamiltonian for the dynamical system. The Lagrange equations for these models lead to a set of first-order equations that are compatible with those found for the FLRW models and provide a foundation for further investigations. Typical numerical evolution of these equations shows the expected effects of the cross parity coupling.
