A theory of gravity alternative to general relativity is trace-free Einstein gravity, which has the remarkable property that the cosmological constant emerges as an integration constant. In this paper, we report two fully diffeomorphism-invariant actions for trace-free Einstein gravity. They describe the theory as two BF theories supplemented with some constraints. The first action comprises two copies of the constrained BF theory for the Husain–Kuchař model plus an interaction term involving the fields that impose the constraints on the B fields. The second action employs two copies of the chiral Plebanski action for general relativity plus an additional constraint. Both actions use complex variables, and naturally include one of the reality conditions imposed in the Plebanski formulation of general relativity. The new actions have the advantage of not involving any nondynamical fields or unimodular condition, and their only gravitational sector is trace-free Einstein gravity.

中文翻译：

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无痕爱因斯坦引力作为两个相互作用的约束 BF 理论


广义相对论的替代方案是无痕爱因斯坦引力，它具有宇宙学常数作为积分常数出现的显着特性。在本文中，我们报告了无痕爱因斯坦引力的两个完全微分同态不变作用。他们将该理论描述为两个 BF 理论，并辅以一些约束。第一个操作包括 Husain-Kuchař 模型的约束 BF 理论的两个副本，以及一个涉及对 B 场施加约束的场的交互项。第二个动作使用广义相对论的手性 Plebanski 动作的两个副本和一个附加约束。这两个动作都使用复变量，自然而然地包括广义相对论的 Plebanski 公式中施加的现实条件之一。新动作的优点是不涉及任何非动力学场或单模条件，它们唯一的引力扇区是无痕的爱因斯坦引力。