The commonly-known Chern–Simons extension of Einstein gravitational theory is written in terms of a square-curvature term added to the linear-curvature Hilbert Lagrangian. In a recent paper, we constructed two Chern–Simons extensions according to whether they consisted of a square-curvature term added to the square-curvature Stelle Lagrangian or of one linear-curvature term added to the linear-curvature Hilbert Lagrangian (Fabbri in Gen Relativ Gravit 52:96, 2020). The former extension gives rise to the topological extension of the re-normalizable gravity, the latter extension gives rise to the topological extension of the least-order gravity. This last theory will be written here in its torsional completion. Then a consequence for cosmology and particle physics will be addressed.

爱因斯坦引力理论的著名的Chern-Simons扩展是用平方曲率项加到线性曲率Hilbert Lagrangian上来写的。在最近的一篇论文中，我们构造了两个Chern-Simons扩展，根据它们是由添加到平方曲率Stelle Lagrangian的平方曲率项还是包含添加到线性曲率Hilbert Lagrangian（Fabbri in Gen Relativ Gravit 52:96，2020）。前者扩展引起可重归一化重力的拓扑扩展，后者扩展引起最小阶重力的拓扑扩展。这最后一个理论将在其扭转完成时写在这里。然后将解决宇宙学和粒子物理学的后果。