  We are investigating the dynamics of a new Poincar\'e 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
non-trivial 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.
