General relativity (GR) can be reformulated as a diffeomorphism invariant gauge theory of the Lorentz group, with Lagrangian of the type f(F ∧ F), where F is the curvature two-form of the spin connection. A theory from this class with a generic f is known to propagate eight degrees of freedom: a massless graviton, a massive graviton and a scalar. GR in this formalism avoids extra degrees of freedom because the function f is special and leads to the appearance of six extra primary constraints on the phase space variables. Our main new result is that there are other theories of the type f(F ∧ F) that lead to six extra primary constraints. However, only in the case of GR the dynamics is such that these six primary constraints get supplemented by six secondary constraints, which gives the end result of two propagating degrees of freedom. This is how uniqueness of GR manifests itself in this ‘pure spin connection’ formalism. The other theories we discover are shown to give examples of irregular dynamical systems. At the linear level around (anti-)de Sitter space they have two degrees of freedom, as GR, with the extra ones manifesting themselves only non-linearly.

广义相对论 (GR) 可以重新表述为洛伦兹群的微分同胚不变规范理论，具有f ( F ∧ F )类型的拉格朗日量，其中F是自旋连接的曲率二形式。已知具有泛型f 的此类理论可以传播八个自由度：无质量引力子、有质量引力子和标量。这种形式主义中的 GR 避免了额外的自由度，因为函数f是特殊的，并导致在相空间变量上出现六个额外的主要约束。我们的主要新结果是还有其他类型的理论f ( F ∧ F) 导致六个额外的主要约束。然而，只有在 GR 的情况下，动力学才使得这六个主要约束得到六个次要约束的补充，这给出了两个传播自由度的最终结果。这就是 GR 的独特性在这种“纯自旋连接”形式主义中表现出来的方式。我们发现的其他理论给出了不规则动力系统的例子。在（反）德西特空间周围的线性水平上，它们有两个自由度，作为 GR，额外的自由度仅以非线性方式表现出来。