We sketch the Poincare gauge theory of gravity (PG) and introduce the most general gravitational Lagrangian quadratic in torsion and curvature. In particular, we include all terms that are parity odd. They mirror the parity even terms and allow new couplings to antimatter. With Hamiltonian methods it was investigated which Lagrangian provide a consistent theory in the sense of decent mode propagation and having a well-defined initial value problem. Generalizing [1], we propose a new Lagrangian [2]. This may be the most general consistent one. We study Friedman-Lemaitre-Robertson- Walker type cosmological solutions of the corresponding field equations. For the Chen et al. subcase of our model, we find numerically periodic oscillations between accelerating and decelerating phases of the cosmos.

[1] K.F. Shie, J.M. Nester, H.J. Yo, Torsion cosmology and the accelerating Universe, Phys. Rev. D 78, 023522 (2008). [2] BHN, arXiv:1009.5112.